IRRIGATION   CANALS 


AND   OTHER 

Irrigation   Works, 

INCLUDING 

The  Flow  of  Water  in  Irrigation  Canals 

AND 

OPEN  AND  CLOSED  CHANNELS  GENEKALLY, 

WITH 

TABLES 

Simplifying  and  Facilitating  the  Application  of    the  Formulae  of 
KUTTEE,  D'AKCY  AND  BAZIN, 

BY 


p.  j.  FLYNisr,  o.  E. 


Member  of  the  American  Society  of  Civil  Engineers;   Member  of  the  Technical  Society  of  the 
Pacific  Ooast;  Late  Executive  Engineer,  Public  Works  Department,  Punjab,  India. 

AUTHOR  OF 

"  Hydraulic  Tables  based  on  Kutter's  Formula."  .  „  » 

"Flow  of  Water  in  Open  Channels,"  etc.,       •  *      •  !' 


[ALL   RIGHTS   RESERVED *J* 


SAN  FRANCISCO,  CALIFORNIA. 

1892. 


• 


Entered  according  to  Act  of  Congress  in  the  year  1891, 

BY  P.  J.  FLYNN, 
In  the  office  of  the  Librarian  of  Congress,  at  Washington,  D.  C. 


&  Ox, 


PRINTERS  AND 


PREFACE. 


It  is  fully  admitted  that  a  work  on  Irrigation  Canals 
is  much  needed  in  this  country.  Since  this  work  has 
been  in  the  printer's  hands,  I  have  received  letters 
from  prominent  engineers,  from  all  parts  of  the  United 
States,  who  are  anxiously  awaiting  its  issue. 

The  work  is  divided  into  two  parts.  The  first  part 
treats  of  Irrigation  Canals  and  Other  Irrigation  Works, 
and  the  second  part  of  the  Floiv  of  Water  in  Open  and 
Closed  Channels,  generally. 

I  have  aimed  at  making  the  work  useful,  not  only  to 
the  engineer  engaged  in.  active  practice,  but  also  to  the 
engineering  student.  With  this  object  in  view  I  have 
arranged  the  articles,  as  well  as  I  could  judge,  in  the 
order  in  which  they  should  follow  each  other.  It  is  the 
first  time,  so  far  as  I  am  aware,  that  a  work  on  Irriga- 
tion Canals  has  been  arranged  on  this  plan. 

In  preparing  the  work  on  Irrigation  Canals,  the  best 
authorities  have  been  consulted  and  due  acknowledg- 
ment is  given  to  them  throughout  the  work. 

Over  ninety  per  cent,  of  the  matter  in  the  Flow  of 
Water  is  original.  Some  of  it,  however,  has  appeared 
before  in  my  other  publications. 

In  order  to  simplify  and  facilitate  the  application  of 
the  modern  and  accurate  formulae  of  Kutter,  D'Arcy  and 


363777 


IV  PREFACE. 

Ba-zin,  1  first  reduced  them  to  the  Chezy  form  of  for- 
mula:— 

v  =  c  X  \/r  X  V* 
Q  =  a  )<  c  X  \/r  X  \/s 

Then,  for  open  channels  I  have  constructed  three 
tables: — 

1.  Tables   giving  the   values   of  «,   r,  \/r  and  a\/r 
for  a  large  range  of  channels  and  for  several  side  slopes. 

2.  Tables  giving  the   values  of  c  and  q/r  for  differ- 
ent grades  and  different  values  of  ?i. 

3.  Table  of  slopes  giving  also  the  value  of  \/s. 
Also,  for  circular  and  egg-shaped  pipes,  sewers  and 

conduits,  I  have  constructed  two  tables: — 

1.  Tables   giving   the  values  of  a,  r,  c\/r  an^   ac\/r 
for  several  values  of  n. 

2.  Table  of  slopes  giving  also  the  value  of  \/s.  This 
is  the  same  as  Table  3  above. 

By  making  \/s  a  separate  factor,  the  work  of  compu- 
tation is  very  much  simplified. 

By  the  use  of  the  above  Tables,  any  problem  relating 
to  Open  or  Closed  Channels,  likely  to  arise  in  practice, 
can  be  rapidly  solved.  A  great  saving  of  time  and  labor 
can  be  gained  by  the  use  of  the  tables. 

There  are  thirty-seven  examples  relating  to  Open  and 
Closed  Channels,  which  will  be  of  especial  use  to  the 
student. 

Tables  30,  31  and  32  give  the  velocity  and  discharge 
of  a  large  range  of  open  channels,  and  Tables  68  and  69 
give  the  velocity  and  discharge  of  circular  and  egg- 
shaped  pipes,  sewers  and  conduits  with  n  =  .013. 


PREFACE. 


At  pages  8,  195,  etc.,  is  given  the  most  complete  col- 
lection of  formulae,  old  and  modern,  sixty-nine  in  num- 
ber, that  has  ever  before  been  published,  in  a  single 
work,  in  the  English  language. 

The  Floiv  of  Water  will  be  useful,  not  only  to  the  Irri- 
gation Engineer,  but  also  to  the  Engineer  engaged  on 
Water  Supply,  Sewerage,  Drainage  of  Land  and  Im- 
provement of  Rivers,  etc. 

The  Tables  of  Contents  of  Volumes  1  and  2,  and  the 
Index  of  Volume  1,  are  very  full,  and  will  enable  the 
reader  to  find  any  subject,  referred  to  in  the  books, 
without  loss  of  time. 

I  have  to  acknowledge  the  many  obligations  I  am 
under  to  Mr.  George  Spaulding,  of  George  Spaulding 
&  Co.,  printers,  San  Francisco,  who  has  superintended 
the  printing  of  the  book,  and  also  the  plates  for  the 
illustrations.  Asa  specimen  of  splendid  typography,.! 
refer  the  reader  to  the  whole  book,  and  particularly  to 
the  formulae  and  tables. 

P.  J.  FLYNN. 

Los  Angeles,  California,  January  9th,  1892. 


TABLE  OF  CONTENTS. 


Page 

ARTICLE  1.     Canals  divided  into  two  classes 1 

Canals  solely  for  Irrigation 1 

Canals  for  Irrigation  and  Navigation  combined 1 

ARTICLE  2.     Systems  of  Irrigation 2 

Perennial  Canals — Inundation  Canals — Tanks  or  Reservoirs — 

Wells — Pumping 2 

ARTICLE  3.     American  and  Indian  Canals  compared 2 

ARTICLE  4.     Diverting  the  Water  from  the  River  to  the  land ,  . . . .  5 

ARTICLE  5.     Quantity  of  Water  required  for  Irrigation 11 

Duty  of  Water — Sone  Canals  and  Ganges  Canal,  India 11 

Water  required  for  navigation 12 

ARTICLE  6.     Depth  to  Bed-width  of  Canal,  and  Dimensions  of  Canals.  12 

Cross-sections  of  Canals,  by  A.  D.  Foote,  M.  Am.  Soc.  C.  E 13 

Dimensions  and  grades  of  Canals  given  by  T.  Login,  M.  I.  C.  E.  14 

ARTICLE  7.     Side  Slopes 17 

Silting  up  of  side  slopes. . . . 18 

ARTICLE  8.     Grade  or  Slope  of  Bed  of  Canal 20 

Adjustment  of  grade  and  sectional  area  to  diminished  discharge.  22 

ARTICLE  9.     Dimensions  of  Banks 26 

Cross-sections   of   Nira  Canal,   India,   and   of   Henares   Canal,  • 

Spain 27 

Sub-grade 28 

Cross-section  of  canal,  Central  District,  California 28 

ARTICLE  10.     A  List  of  Irrigation  Canals,  giving  Dimensions,  Grades, 

etc 29 

ARTICLE  11.     The  Surface  Slope  of  Rivers  through  the  Plains 32 

ARTICLE  12.     Safe  Mean  Velocities 32 

Slope  of  bed 32 

Velocity  required  to  prevent  deposition  of  silt  or  the  growth  of 

aquatic  plants 33 

Maximum  mean  velocity 34 

High  mean  velocities 35 

Velocity  on  Navigation  Canals 35 

Slope  of  Canals — Slope  too  great  on  Ganges  Canal 36 

Velocities  in  Ganges  Canal,  by  Major  J.  Crofton,  R.  E 37 

Velocities  in  the  Western  Jumna  and  Baree  Daub  Canals,  by 

Colonel  Dyas,  R.  E 39 

Humphreys  and  Abbot,  on  Velocities  in  the  Mississippi 40 

ARTICLE  13.     Mean,  Surface  and  Bottom  Velocities 41 

Bazin — Rankiue— Prony — Dubuat 41 

Revy 42 


Vlll  TABLE    OF    CONTENTS. 

Page 

ARTICLE  14.     Mean  Velocities  from  Maximum  Surface  Velocities 42 

Ganging  Channels 42 

ARTICLE  15.     Destructive  Velocities 43 

Destruction  of  the  Deyrah  Dhoon  Water  Courses 45 

Velocities  destructive  to  brickwork 46 

ARTICLE  16.     Velocity  Increases  with  Increase  in  Depth 47 

ARTICLE  17.     Abrading  and  Transporting  Power  of  Water 48 

Observations  on  the  Ganges  Canal  and  Biver  Ravee,  India,  and 

on  the  Loire,  in  France 49 

Sweaton,  experience — Blackwell's  experiments 50 

Baldwin    Latham's    experience — Sir  John    Leslie's  formula — 

Chailly's  formula 51 

Experience  with  bowlder  flooring  on  Indian  Canals 51 

ARTICLE  18.     On  Keeping  Irrigation  Canals  Clear  of  Silt 52 

ARTICLE  19.     Fertilizing  Silt 56 

Deposits  from  the  Nile 56 

Four  kinds  of  water  for  irrigation 58 

Kistna,  Midnapure,  Durance,  Punjab  Rivers ' 59 

Kivers   Po,    Dora,    Baltea,    Durance,    in    Madras — Reservoirs, 

Colorado 60 

Idaho,  Utah 61 

Well  Water,  Punjab 62 

ARTICLE  20.     Silt  Carried  by  Rivers 62 

Silt  ca-ried  by  the  Nile,  Godavery,  Mahanuddy,  Kistna,  Indus, 

Durance,  Vistula,  Garonne,  Rhine  and  Po 63 

Nile,  Ganges,  Mississippi,  Danube 64 

ARTICLE  21.     Improvement  of  Land  by  Silting  up,   Warping  or  Colma- 

tage 65 

Colmatage  on  the  Moselle,  in  France 66 

ARTICLE  22.     Equalizing  Cuttings  and  Embankments 63 

ARTICLE  23.     Canal  on  Sidelong  Ground 73 

ARTICLE  24.     Shrinkage  of  Earthwork 75 

ARTICLE  25.      Works  of  Irrigation  Canals 77 

ARTICLE  26.      Wells  and  Blocks 77 

Well  of  Sone  Weir— Block  of  Solani  Aqueduct— Method  of  Sink- 
ing   1 77 

ARTICLE  27.     Headworks  of  Irrigation  Canals 79 

Requirements  for  good  Headworks 80 

Deposition  of  Silt  in  Canals 81 

ARTICLE  28.     Diversion  Weirs 81 

Weirs — Dams — Anicuts — Barrages 81 

Canals  sometimes  taken  from  rivers  without  weirs 82 

Kern  River  Dam — Myapore  Dam — Barrage  of  the  Nile 83 

Difference  between  a  river  Weir  and  Dam 83 

Regulator— Temporary  dam  on  crest  of  weir — Oblique  weirs ...  85 


TABLE    OF    CONTENTS.  lx 

Page 
ARTICLE  28 — Diversion.  Weirs.     (Continued.) 

Proper  location  of  dam  or  weir 86 

Okhla  Weir — Godavery  Anicut — Turlock  Weir — Henares  Weir — 
Cavour  Canal  Weir — Streeviguntum,  Anicut — Narora  Weir — 

Phoenix,  Arizona,  Brush  and  Bowlder  Danis 7. .  87 

Kern  River  Dam — Galloway  Canal 88 

Weir  at  Head  of  Bear  Eiver  Canal,  Utah— Weir  at  Head  of  North 

Poudre  Canal,  Colorado 90 

Headworks  of  Upper  Ganges  Canal 93 

Dam  and  Regulator  of  Upper  Ganges  Canal  at  Myapore 94 

The  Sone,  the  Okhla  and  the  Lower  Ganges  Weirs 98 

Barrage  of  the  Nile 97 

Okhla  Weir,  River  Juruna 102 

Headworks  of  Sone  Canals 103 

Weir  at  head  of  Sone  Canals — Movable  dam  on  crest  of  Weir.  . .  104 

Okhla  Weir,  Agra  Canal 103 

Streeviguntum  Anicut — Tambrapoorney  River,  Madras 109 

Naroro  Weir,  Lower  Ganges  Canal,  India. 110 

Dowlaishwaram  Branch  of  the  Godavery  Anicut 115 

Turlock  Weir,  Tuolumne  River,  California 117 

Bhim  Tal  Dam — Betwa    Weir — Vrynwy   Dam — Geelong  Dam — 

Lozoya  Dam 119 

Henares  Weir 119-  120 

Proposed  Weir,  Cavour  Canal,  Italy 121 

Headworks  of  Cavour  Canal,  Italy 122 

A.RTICLE  29.     Scouring  Sluices,  Under  Sluices 124 

ARTICLE  30.     Regulators 126 

Regulating  Gates,  Del  Norte  Canal 127 

Idaho  Canal  Regulator  Head 128 

ARTICLE  31.     Sluices — Gates — Movable   Dams  or  Shutters 128 

Sluice  Gates,  Indian  Canal 129 

Regulating  Bridge,  Regulating  Apparatus  for  Canals 131 

Sluice  Gate,  Henares  Canal 133 

Shutters  of  the  Mahanuddy  Weir 136 

Formula  for  finding  the  tension  011  the  chains  of  Shutters 137 

Movable  Dams  on  the  Sone  Weir 138 

Tumbler  Regulating  Gear  for  Distributaries  of  Midnapore  Canal  139 

Lifting  Sluice  Gate   144 

ARTICLE  32.     The  Loss  of  Water  by  Percolation  under  a  Weir 147 

Godavery  Anicut  or  Weir 147 

ARTICLE  33.     Bridges— Culverts 149 

Formula  for  finding  area  of  Culvert 150 

ARTICLE  34.     Aqueducts — Flumes 150 

Aqueduct  over  the  Dora  Baltea  River — Flume  011  UiT.compahgre 

Canal. .                                                                                                  .  152 


X  TABLE    OF    CONTENTS. 

Page 
ARTICLE  34 — Aqueducts — Flumes.     (Continued.) 

Big  Drop,  Grand  River  Ditch,  Colorado — Flume  on  Flatte   Ca- 
nal, Colorado , 153 

Aqueduct  of  Platte  Canal,  crossing  Plum  Creek  at  Acequia 155 

High  Flume  over  Malad  River,  Bear  River  Canal,  Utah 156 

Iron  Flume  over  Malad  River,  Bear  River  Canal,  Utah 157 

Solani  Aqueduct,  Ganges  Canal,  India    158 

Iron  Aqueduct  over  the  Majanar  Torrent  on  the  Henares  Canal  163 

ARTICLE  35.     Level  Crossings 164 

Level  Crossing  at  Dhunowree,  Ganges  Canal 166 

ARTICLE  36.     Superpassages 169 

Ranipore  Superpassage,  Ganges  Canal 171 

Seesooan  Superpassage  on  the  Sutlej  or  Sirhind  Canal 172 

ARTICLE  37.     Inverted  Syphons 175 

Inverted  Syphon  under  Stony  Creek,  Central  Irrigation  Canal, 

California 175 

Inverted  Syphon  carrying   the   Buriya    torrent  under  the  Agra 

Canal,  India 177 

Inverted  Syphon  canning  the  Hurron  Creek  (nullah)  under  the 

Sutlej  Canal 177 

Inverted  Syphon  carrying  the  Cavour   Canal   under   the   Sesia 

torrent 179 

Wrought  iron  inverted  Syphons  on  the  Verdon  Canal,  France. .   179 

Syphons  on  Lozoya  Canal,  Jucar  Canal,  Mijares  Canal 182 

ARTICLE  38.     Retrogression  of  Levels 183 

General  Cautley  and  the  Ganges  Canal 185 

Committee  to   report    on  Ganges   Canal — T.   Login's   work  on 

Ganges  Canal 186 

Erosion  at  Toghulpoor  Sand  Hill,  Ganges  Canal 188 

Erosion  and  Silting  up  on  Eastern  Jumna  Canal,  India 189 

ARTICLE  39.     Falls— Drops— Checks 189 

Ogee  Falls 192 

Asufnuggur  Falls,  Ganges  Canal 193 

Vertical  Falls  with  Water  Cushions 195 

Timber  Fall,  Canterbury  Plains,  New  Zealand 197 

Timber  Fall,  Turlock  Canal,  California - 197 

Formula  for  depth  of  Water  Cushion  below  fall 198 

Raising  Crest    of  Fall 199 

Vertical  Fall  with   Gratings 202 

Vertical  Fall  with  Grating  on  Baree  Doab  Canal 203 

Computing  the  Spacing  of  Bars 206 

Grating  of  Fall,  with  Horizontal  Bars 210 

Sliding  Gate  Falls  on  the  Sukkur  Canal,  India 211 

Fall  on  Calloway  Canal,  with  Plank  Panels  or  Flash  Boards 214 

Box  floor  for  Falls.  .  .   214 


TABLE    OF    CONTENTS.  XI 

Page 

ARTICLE  40.     Rapids 215 

Kapid  on  the  Baree  Doab  Canal,  India 215 

ARTICLE  41.     Inlets 219 

ARTICLE  42.     Heads  of  Branch  Canals -^.  .^. . .  221 

Needle  Dam  on  the  Sidhnai  Canal,  India 222 

Kotluh  Branch  Head  at  Surranah,  Sutlej  Canal 225 

ARTICLE  43.     Escapes — Relief  Gates —  Waste.  Gates 226 

Location  of  Escape  Channel , 227 

Escapes  on  the  Sone,  Ganges,  Agra,    Naviglio   Grande,  Muzza 
and  Martesana  Canals 228 

ARTICLE  44.     Depositing  Basins — Silt  Traps — Sand  Boxes 229 

Trap  on  Canal  in  Idaho,  by  A.  D.  Foote,  M.  Am.   Soc.  C.  E 229 

Depositing  Basin  on  the  Marseilles  Canal,  France 230 

Depositing  Keservoir  on  the  Wutchumna  Canal,  California 231 

ARTICLE  45.     Tunnels 232 

Tunnels  on  the  Merced,  High  Level  and  Henares  Canals 232 

Tunnels  on  the  Marseilles   and   Verdou   Canals — San   Antonio 
Tunnel 234 

ARTICLE  46.     Retaining    Walls 238 

ARTICLE  47.     Combined  Irrigation  and  Navigation  Canals 240 

Required  Velocities  on  Canals 241 

Beruegardo  and  Sutlej  Canals — Madras  Canals 242 

ARTICLE  48.    Survey 243 

Arrangement  of  Distributaries 245 

ARTICLE  49.     Distributaries — Laterals — Rajbuhas '252 

Fall  and  Inverted  Syphon .252 

Distribution  System 253 

Cross-sections  of  Distributaries 256 

Details  of  Distributaries 257 

Cross-sections  of  Distributaries 261 

ARTICLE  50.     Submerged  Dams 261 

ARTICLE,  51 .     Construction— Canal  Dredger 263 

ARTICLE  52.      Water  Power  on  Irrigation  Canals 268 

Cigliano,  Eotto  and  Ivrea  Canals 268 

Water  Power  on  Crappone  and  Marseilles  Canals,  France  , 269 

Water  Power  on  Verdon  and  Henares  Canals 270 

ARTICLE  53.     Cost  of  Pumping  and  Water 270 

Pumping  in  Egypt * 270 

ARTICLE  54.     Maintenance  and  Operation  of  Irrigation  Canals 273 

The  Sources  of  Destruction  of  Canals 276 

ARTICLE  55.     Methods  of  Irrigation 279 

Flooding — Checks 279 

Flooding  in  India 285 

Furrow  Irrigation 286 

ARTICLE  56.     Duty  of  Water  for  Irrigation 289 

Efficiency  of  a  Canal  for  Irrigation 290 


xil  TABLE    OF    CONTENTS. 

Pa-e 

ARTICLE  57.     Pipe  Irrigation 292 

Economy  of  Water  by  the  use  of  Pipes 294 

Pipe  Irrigation  System,  Ontario,  California 296 

ARTICLE  58 '.     Number  and  Depth  of  Waterings 298 

Marcite  Irrigation — Irrigation  Southern  California  and  Henares 

Canal 298 

Esla  Canal— Valencia,  Spain — South  of  Prance 299 

Marseilles  and  Bari  Doab  Canals — Madras — Colorado— Prof  essor 

G.  Davidson 300 

C.  L.  Stevenson,  Utah— General  Scott  Moncrieff,  India 301 

ARTICLE  59.     Horary  Rotation 302 

ARTICLE  60.    Forestry  and  Irrigation 304 

ARTICLE  61.     Rainfall 308 

Statistics  of  Irrigation 314 

ARTICLE  62.    Evaporation 316 

Evaporation  at  Kingsbridge,  Tulare  County,  California — Col- 
orado    316 

Evaporation  in  Italy,  Spain  and  India 317 

Evaporation  in  Hyderabad,  Nagpur,  the  Deccan  and  Northern 

India 318 

Evaporation  in  Egypt  and  the  South  of  France 320 

ARTICLE  63.    Percolation  or  A  bsorption 321 

Percolation  in  Calorado — New  Zealand — Marterana  Canal,  Italy .  323 
Percolation  in  Lombardy — Marseilles  Canal — Canal  from  the 

Khone— Agra  Canal— Achti  Tank 324 

Percolation  in  Palkhed  Canal — Ojhar  Tambet  Canal,  Ganges 

Canal 325 

Percolation  in  Ganges  Canal — Egypt— London 326 

ARTICLE  64.    Drainage 327 

Waterlogged  land  in  India  and  Egypt 328 

Waterlogged  land  in  Colorada 329 

Alkali  (reh),  Subsoil  Drainage 330 

Area  Irrigated  in  India 331 

ARTICLE  65.     Defective   Irrigation — Alkali — The  affect  of  Irrigation 

on  Health 332 

Defective  Irrigation  in  California ' 332 

Defective  Irrigation  in  India 335 

Defective  Irrigation  in  Europe 336 

ARTICLE  66.     Cost  of  Irrigation  per  acre,  in  different  countries 336 

ARTICLE  67.     Annual  earning  of  a  cubic  foot  of  water  per  second. . . .   338 
ARTICLE  68.     Cost  of  Canals  per  acre  Irrigated  and  per  cubic  foot  per 

second 339 

Cost  of  the  Ganges  Canal  and  the  Orisa  Canals 339 

Cost  of  Henares  Canal,  Spain,  and  Mussel  Slough  Canal,  Cali- 
fornia. .  340 


TABLE    OF    CONTENTS.  Xlll 

Page 

ARTICLE  69.     Measurement  of  Water — Modules — Meters 341 

Essentials  of  a  good  Module 341 

Mr.  A.  D.  Foote's  Water-meter 341 

Module  adopted  on  the  Henares  and  Esla  Canals,  Spain 344 

ARTICLE  70.     Report  on  the  Proposed  Works  of  the   Tulare  Irrigation 

District 347 

Borings  and  Trial  Pits 348 

Side  Slopes 349 

Tunnels 356 

Headworks 358 

Eeservoir 360 

Reservoir  Supply  combined  with  Canal  from  Kaweah  Eiver ....  362 

Duty  of  Water 364 

Reservoir  Supply  combined  with  Canal  from  Kaweah  River ....  366 

Loss  from  Evaporation  and  Seepage 368 

Earthen  Dams 374 

Shrinkage  of  Earthworks 376 

Canal  on  steep  side  hill  ground 378 

Cross-sections  of  Channels  on  side  hill  ground 381 

Rock  cutting  on  side  hill  ground  with  wall  on  lower  side 382 

Rainfall 583 

Prevention  of  Waste  of  Water 385 

Measurement  of  Water. . .                                                                     .  385 


LIST   OF  TABLES. 


Number 

Table.  Page 

1.  Giving  Dimensions  and  Grades  of  Canals 15 

2.  Giving  Velocities  of  Channels  by  Kutter's  formula  with  n  =  .025  17 

3.  Giving  the  Inner  Side  Slopes  of  Canals  in  Earth  and  Sandy 

Loam 20 

4.  Giving  the  Natural  Slopes  of  Materials  with  the  Horizontal  Line  20 

5.  Giving  full  details  of.  Channels  computed  by  Kutter's  formula 

with  n  =  .025 23 

6.  Giving  a  list  of  Irrigation  Canals 30 

7.  Giving  the  Surface  Slopes  of  Rivers  through  the  Plains 32 

8.  Giving  value  of  c , 43 

9.  Giving  Safe  Bottom  and  Mean  Velocities  of  Channels 44 

10.  Giving  Dimensions,  Grades  and  Velocities  of  Masonry  Chan- 

nels    45 

11.  Giving  Dimensions,  Grades  and  Velocities  of  Channels 47 

12.  Giving  the  Transporting  Power  of  Water 49 

13.  Giving  Length,  Discharge,   etc.,    of  Eivers 64 

14.  Giving  Values  of  the  Co-efficient  k 74 

15.  Giving  Shrinkage  of  Different  Materials 76 

16.  Giving   Velocities   and    Discharge    of  Channels    with    different 

values  of  n 1 74 

17.  Giving  Velocity  in  Feet  per  second,  and  Discharge  in  Cubic 

Feet  per  second,  of  Channels  with  Different  Bed  Widths, 
but  all  other  things  being  equal,  based  011  Baziii's  formula 

for  Earthen  Channels 258 

18.  Giving  the  Duty  of  Water  in  Different  Countries . . . .  293 

19.  Statistics  of  Irrigation 314 

20.  Giving  Temperature  and  Rainfall  in  the  south  of  France 330 

21.  Giving  Cost  of  Irrigation  per  acre  in  Different  Countries 337 

22.  Showing  the  Annual  Earning  of  a  Cubic  Foot  of  Water  per  sec- 

ond in  Different  Countries 339 

23.  Giving  the  Cost  of  Canals  per  acre  Irrigated,  and  also  the  Cost 

per  Cubic  Foot  per  second  of  Discharge 340 


LIST  OF  ILLUSTRATIONS. 


Number  of 

Figure.                                                      DESCRIPTION.  Page 

1 .  Plan  — Diverting  Water  from  a  River 8 

2.  Section  —  Diverting  Water  from  a  Eiver 8 

3.  Section  —  Diverting  Water  from  a  River 8 

4.  Cross-Sections  of  Canal,  by  A.  D.  Foote,  M.  Am.  Soc.  C.  E.  . .  13 

5.  Cross-Sections  of  Canal,  by  A.  D.  Foote,  M.  Am.  Soc.  C.  E.  . .  13 

6.  Cross-Sections  of  Canal,  by  A.  D.  Foote,  M.  Am.  Soc.  C.  E.  . .  13 

7.  Cross-Sections  of  Canal,  showing  silting  tip 19 

8.  Cross-Section  of  Nira  Canal,  India 27 

9.  Cross-Section  of  Henares  Canal,  Spain,  in  deep  cutting 27 

10.  Cross-Section  of  Henares  Canal,  Spain,  in  cut  and  fill 27 

11.  Cross-Section  of  Canal,  Central  District,  California 28 

12.  Plan  showing  arrangement  of   Channels  for  Silting  up  land, 

also  known  as  Warping  and  Colmatage 67 

13.  Cross-Section   explaining   the   Equalization   of   Cuttings   and 

Embankments 69 

14.  Cross-Section    explaining   the   Equalization   of   Cuttings   and 

Embankments 70 

15.  Cross-Section    explaining    the   Equalization   of   Cuttings   and 

Embankments 73 

16.  Plan  of  Well  Foundation 78 

17 .  Section  of  Well  Foundation 78 

18.  Plan  of  Block  Foundation 78 

19.  Section  of  Block  Foundation 78 

20.  Cross-Section  of  timber  Weir  at  head  of  Galloway  Canal,  Kern 

River,  California 88 

21.  Cross-Section  of  Weir  at  head  of  Bear  River  Canal,  Utah 90 

22.  Sectional   Elevation    of  Crib  Dam   at  head    of   North   Poudre 

Canal,  Colorado 91 

23.  Sectional  Plan  of  Crib  Darn  at  head  of  North  Poudre  Canal, 

Colorado 91 

24.  Cross-Section  through  center  of  Cribs  of  North  Poudre  Canal, 

Colorado 92 

25.  Cross-Section  at  ends  of  Cribs  of  North  Poudre  Canal,  Colorado  92 

26.  Plan  of  Head- Works  of  Upper  Ganges  Canal,  India 93 

27.  Elevation  of  Regulating  Bridge  at  head  of  Upper  Ganges  Canal, 

India 94 

28.  Plan  of  Regulating  Bridge  and  Dam  at  head  of  Upper  Ganges 

Canal,  India 


X^7i  LIST    OF    ILLUSTRATIONS. 

Number  of 

Figure                                                         DESCRIPTION.  Page 

29.  Cross-Section  through  Floor  of  Dam  and  Elevation  of  Flank 

of  Upper  Ganges  Canal,  India 94 

30.  Cross-Section  through  Center  of  Dani  and  Elevation  of  Pier  of 

Upper  Ganges  Canal,  India 94 

31.  Plan  of  part  of  the  Nile  Delta,  showing  location  of  Barrages 

and  Canals 97 

32.  Longitudinal  Section  of  the  Rosetta  Branch  Barrage  on  the  Nile  100 

33.  Plan  of  the  Eosetta  Branch  Barrage  on  the  Nile 100 

34.  Cross-Section  of  the  Rosetta  Branch  Barrage  on  the  Nile 100 

35.  View  of  the  Nile  Barrage 102 

36.  Plan  of  Headworks  of  the  Sone  Canals,  India 103 

37.  Cross-Section  of  Weir  of  the  Soue  Canals,  India 104 

38.  Movable  Dam  on  Crest  of  Weir  of  the  Sone  Canals,  India 104 

39.  Cross-Section  of  Okhla  Weir  or  Anicut  at  head  of  Agra  Canal.  10G 

40.  Plan  of  Okhla  Weir  or  Aiiicut  at  head  of  Agra  Canal 107 

41.  Cross-Section  of  Streeviguiitum  Weir  or  Anicut,  Madras 109 

42.  Diagram  showing  the  Afflux  during  flood  at  Narora  Weir 110 

43.  Cross-Section    of    Narora    Weir    or  Anicut  at  head  of   Lower 

Ganges  Canal,  Ganges  River,  India Ill 

44.  Cross-Section  of  Godavery  Weir  or  Anicut 116 

45.  Cross-Section  of  Turlock  Weir 117 

46.  Cross-Section  of  Henares  Weir 119 

47.  View  of  Stone  Block  Facing,  Henares  Weir 119 

48.  Bird's-eye  view  of  Site  of  Headworks,  Cavour  Canal 122 

49.  Cross-Section  of  proposed  Weir  at  Headworks  of  Cavour  Canal  123 

50.  Plan  of  proposed  Weir  at  Headworks  of  Cavour  Canal 123 

51.  Cross-Section  of  top  of  proposed  Weir  at  Headworks  of  Cavour 

Canal 123 

52.  Longitudinal-Section  of  top  of  proposed  Weir  at  Headworks  of 

Cavour  Canal 123 

53.  Elevations  of  Iron  Spikes 123 

54.  View  of  Myapore  Regulating  Bridge,  Ganges  Canal 126 

55.  Elevation  of  Regulating  Gates  of  Del  Norte  Canal 127 

56.  Cross-Section  of  Regulating  Gates  of  Del  Norte  Canal 127 

57.  Longitudinal-Section  of  Idaho  Canal  Regulator  Head 128 

58.  End  Elevation  of  Idaho  Canal  Regulator  Head 128 

59.  Elevation  of  Sluice  Gate,  Cavour  Canal 129 

60.  Cross-Section  of  Sluice  Gate,  Cavour  Canal 129 

61.  Cross-Section  of  Drop-Gates  on  the  Jumna  Canal,  India 129 

62.  Cross-Section  of  Drop-Gates  on  the  Ganges  Canal 129 

63.  Elevation  of  Regulating  Bridge,  with  Lift-Gate  and  Sleepers. .  131 

64.  Plan  of  Regulating  Bridge,  with  Lift-Gate  and  Sleepers 131 

65.  Elevation  of  Windlass  for  working  Sleepers 131 

66.  Plan  of  Sleeper 131 

67.  Cross-Section  of  Drop-Gate  for  River  Diuns 131 


LIST    OF    ILLUSTRATIONS  XV11 

Number  of 

Figure                                                    DESCRIPTION.  Page 

68.  Plan  of  Drop-Gate  for  River  Dams 131 

69.  Cross-Section  of  Sluice  of  Henares  Canal 133 

70.  Cross-Section  of  Gear  for  Working  Sluice  of  Henares  Canal*-.-.-  133 

71.  Plan  of  Gear  for  Working  Sluice  of  Henares  Canal 133 

72.  Cross-Section  of  Shutters  of  Mahaiiuddy  Weir 136 

73.  Cross-Section  of  Tumbler  regulating  gear  for  Distributaries  of 

the  Midiiapore  Canal 139 

74.  View  of  Fouracre's  Sluices  at  the  Weir  on  the  River  Sone 140 

75.  View  of  Fouracre's  Sluices  at  the  Weir  on  the  River  Sone. . . .  140 

76.  View  of  Fouracre's  Sluices  at  the  Weir  on.  the  River  Sone. . . .  141 

77.  Section  of  Hydraulic  Brake-Head  for  Shutters  of  Sone  Weir. .  141 

78.  Section  of  Hydraulic  Brake-Head  for  Shutters  of  Sone  Weir. .  141 

79.  Cross-Section  of  Movable  Dam,  Sone  Weir 142 

80.  Plan  of  Lifting  Sluice  Gate 144 

81.  Down-Stream  Elevation  of  Lifting  Sluice  Gate,  showing  Foot- 

Bridge  and  Lifting  Gear 145 

82.  Cross-Section,  showing  Lifting  Sluice,  shut 146 

83.  Cross-Section,  showing  Lifting  Sluice,  open 146 

84.  Plan  showing  End  of  Girder  Pressing  Against  Free  Rollers. . .  146 

85.  Elevation  of  Flume  on  Uncompahgre  Canal,  Colorado 152 

86.  Cross-Section  of  Flume  on  Uncompahgre  Canal,  Colorado. . . .  152 

87.  Plan  of  Penstock  and  Boom,  Grand  River  Canal,  Colorado 153 

88.  Longitudinal   Section  of   Penstock  and   Boom  Flume,  Grand 

River  Canal,  Colorado 153 

89.  View  of  Platte  River,  with  Platte  Canal,  Colorado 154 

90.  View  of  Aqueduct  of  Platte  Canal  (  High  Line ),  crossing  Plum 

Creek  at  Acequia 155 

91.  View   of   High   Flume   over  Malad  River,  West  Branch  Bear 

River  Canal,  Utah 156 

92.  View  of  Iron  Flume  over  Malad  River,  Coriiine  Branch  Bear 

River  Canal,  Utah 157 

93.  View  of  Solani  Aqueduct,  Ganges  Canal,  India 158 

94.  Cross-Section  of  Solani  Aqueduct  Embankment 161 

95.  Elevation  of  Half  of  Solani  Aqueduct 162 

96.  Section  of  Two  Arches  and  Abutment  of  Solani  Aqueduct 162 

97.  Sectional  Plan  of  Solani  Aqueduct,  showing  Wells  and  Blocks 

of  Foundations 162 

98.  Plan  of  Half  of  Wrought-Iron  Aqueduct  over  the  Arroyo  Ma- 

jauar,  Henares  Canal 164 

99.  Elevation  of  Wrought-Iron  Aqueduct  over  the  Arroyo  Majanar, 

Henares  Canal 164 

100.  Cross-Section  of  Wrought-Iron  Aqueduct  over  the  Arroyo  Ma- 

janar, Henares  Canal ' 164 

101.  Details  of  Wrought-Iron  Aqueduct  over  the  Arroyo  Majanar, 

Henares  Canal. .  164 


XV111  LIST    OF    ILLUSTRATIONS. 

Niivnber  of 

Figure  DESCRIPTION.  Page 

102.  Details  of  Wrought-Iron  Aqueduct  over  the  Arroyo  Majanar, 

Heuares  Canal 164 

103.  Section  of  End  of  Iron  Aqueduct  and  Pier,  showing  arrange- 

ment to  prevent  leakage 164 

104.  Plan  of  Level  Crossing 165 

105.  View  of  the  Dhunowree  Level  Crossing,  Ganges  Canal 166 

106.  Plan  of  Eutmoo  Level  Crossing  at  Dhunowree,  Gauges  Canal  167 

107.  Plan  of  Escape  Dani  at  Dhunowree  Level  Crossing,  Ganges 

Canal 168 

108.  Longitudinal-Section    of    Escape   Dam   at   Dhunowree  Level 

Crossing,  Ganges  Canal 168 

109.  Cross-Section  of  Escape  Dam  at  Dhunowree  Level  Crossing, 

Ganges  Canal 168 

110.  View  of  Raiiipore  Superpassage,  Ganges  Canal 171 

111.  Plan  of  Seesooan  Superpassage,  Sutlej  Canal  Project 173 

112.  Half  Elevation  and  Half   Section  Superpassage,  Sutlej  Canal 

Project 1 

113.  Section  of  Wing  Wall  Superpassage,  Sutlej  Canal  Project 1 

114.  Half  Cross  -  Section   of   Seesooan  Superpassage,  Sutlej  Canal 

Project 173 

115.  Longitudinal  Section  of  Conduit  under  Stony  Creek,  Central 

Irrigation  District  Canal,  California 178 

116.  Plan  of  Section  of  Conduit  under  Stony  Creek,  Central  Irriga- 

tion District  Canal,  California 178 

117.  Section  of  Conduit  under  Stony  Creek,  Central  Irrigation  Dis- 

trict Canal,  California 178 

118.  Cross-Section  of  Conduit  under  Stony  Creek,  Central  Irriga- 

tion District  Canal,  California 178 

119.  Enlarged  Cross-Section  of  one  Span  of  Conduit  under  Stony 

Creek,  Central  Irrigation  District  Canal,  California 178 

120.  Plan   of   End   of   Syphon   for  Drainage   Crossing  at    Hurron 

Nullah  Sirhind  Canal 180 

121.  Section   Plan   of   Syphon   for   Drainage   Crossing   at   Hurron 

Nullah  Sirhind  Canal 180 

122.  Longitudinal    Section   of   Syphon    for   Drainage   Crossing  at 

Hurron  Nullah  Sirhind  Canal 180 

123.  Cross-Section   of   Syphon   for  Drainage   Crossing  at   Hurron 

Nullah  Sirhind  Canal 180 

124.  Diagram  to  Illustrate  Retrogression  of  Levels  in  Canals 183 

125.  Diagram  to  Illustrate  Retrogression  of  Levels  in  Canals 183 

126.  Plan  Showing  the  Effects  of  Erosion  at   Toghulpoor,  on  the 

Ganges  Canal 188 

127.  Section  Showing  the  Effects  of  Silting  up  at  Toghulpoor,  on 

the  Ganges  Canal 188 


LIST    OF    ILLUSTRATIONS.  XIX 

Number  of 

Figure                                                         DESCRIPTION.  Page 

128.  Cross-Section  to  Illustrate  the  Effects  of  Erosion  on  the  East- 

ern Jumna  Canal,  India 189 

129.  Cross-Section  to  Illustrate  the  Effects   of  Silting  ujr  on-4he 

Eastern  Jumna  Canal,  India 189 

130.  Longitudinal  Section  of  Canal  in  Embankment 190 

131.  Longitudinal  Section  of  Canal,  showing  Falls 190 

132.  Section  of  Ogee  Fall  with  Kaised  Crest 192 

133.  Plan  of  Asufnuggur  Falls,  Ganges  Canal 193 

134.  View  of  Asufnuggur  Falls,  Ganges  Canal 194 

135.  Section  of  Vertical  Fall ; 195 

136.  Section  of  Vertical   Fall,  with  Water  Cushion,  on  the  Baree 

Doab  Canal 196 

137.  Cross-Section  of   Fall  Constructed  of   Timber  and  Bowlders, 

Canterbury,  New  Zealand    196 

138.  Longitudinal    Section    of    Fall    Constructed    of   Timber  and 

Bowlders,  Canterbury,  New  Zealand 196 

139.  Plan  of  Fall  Constructed  of  Timber  and  Bowlders,  Canterbury, 

New  Zealand 196 

140.  Cross-Section   of   Timber  Fall   with  Water   Cushion,  Turlock 

Canal,  California 197 

141.  Section  of  Vertical  Fall  with  Water  Cushion 198 

142.  Elevation,  Looking  Up-Stream,  of  Vertical  Fall  with  Grating.  203 

143.  Plan  of  Vertical  Fall  with  Grating 203 

144.  Section  of  Vertical  Fall  with  Grating 2d3 

145.  Plan  of  one  Bar  of  Grating 204 

140.     Section  of  Grating 204 

147.  Section  of  Shoe  holding  Grating  Bar 204 

148.  End  Elevation  of  Grating  Bars 204 

149.  Plan  of  Bars  of  Grating 209 

150.  Plan  of  Bars  of  Grating 209 

151.  Section  of  Horizontal  Bars  of  Grating 210 

152.  Plan  of  Fall  with  Sliding  Gate 211 

153.  Section  of  Fall  with  Sliding  Gate 211 

154.  Elevation  of  Fall  with  Sliding  Gate 211 

155.  Section  of  Timber  Fall  with  Plank  Panel  or  Flash  Boards 214 

156.  Plan  of  Rapid  on  Baree  Doab  Canal 216 

157.  Transverse  Section  at  Crest  and  Tail  of  Eapid 216 

158.  Section  of  Eapid 216 

159.  Section  of  Bowlder  Pavement. ........' 217 

160.  Plan  of  Inlet  on  a  Level 219 

161.  Elevation  of  Inlet  on  a  Level 219 

162.  Section  of  Inlet  on  a  Level 219 

163.  Section  of  Arch  and  Pier  of  Inlet 219 

164.  Section  of  Wing  Walls  of  Inlet 219 

165.  Section  of  Inlet  with  Ten  Feet  Fall..  220 


XX  LIST    OP    ILLUSTRATIONS. 

Number  of 

Figure  DESCRIPTION.  Page 

166.  Plan  showing  the  Relative  Position  of  the  Regulating  Bridges 

and  Escapes  at  Branch  Heads 221 

167.  Elevation  of  one  Span  of  Regulating  Bridge  at  Branch  Head..  221 

168.  Section  of  one  Span  of  Regulating  Bridge  at  Branch  Head.. . .  221 

169.  Kotluh  Branch  Head  at  Suranah,  Sutlej  Canal 225 

170.  Plan  of  Escape  Head  and  Regulator 227 

171.  Cross-Section  of  San  Antonio  Tunnel,  Ontario,  California 236 

172.  Cross-Section  of  Retaining  Wall 239 

173.  Drainage  Map,  showing  Arrangement  of  Distributaries 246 

174.  Plan  showing  Arrangement  of  Distributaries 247 

175.  Plan  showing  Arrangement  of  Distributaries 250 

176.  Section  of  Fall  on  Distributary  with  Aqueduct  Over  Tail 252 

177.  Plan  of  Fall  011  Distributary  with  Aqueduct  Over  Tail 252 

178.  Section  of  Syphon  Drain  for  passing  one  Distributary  under 

another,  or  under  a  Drainage  Channel 252 

179.  Plan  of  Distribution  System 253 

180.  Plan  of  Distribution  System 255 

181.  Cross-Section  of  Distributary  in  Four  Feet  Cutting 256 

182.  Cross-Section  of  Distributary  in  Five  Feet  Cutting 256 

183.  Cross-Section  of  Distributary  in  Seven  Feet  Cutting 256 

184.  Cross-Section  of  Distributary  in  Eight  Feet  Cutting 256 

185.  Cross-Section  of  Distributary  in  Ten  Feet  Cutting 256 

186.  Cross-Section  of  Distributary  in  Cutting 261 

187.  Cross-Section  of  Distributary  in  Embankment 261 

188.  Cross-Section  of  Distributary  in  Cutting 261 

189.  Cross-Section  of  Distributary  in  Embankment 261 

190.  Canal  Dredger 266 

191.  Plan  of  Irrigation  by  Flooding-Checks 280 

192.  Plan  of  Irrigation  by  Flooding-Checks 283 

193.  Cross-Section  of  Canal 283 

194.  Cross-Section  of  Distributary 283 

195.  Section  of  Country  showing  Two-Feet  Contour  Checks 283 

196.  Section  of  Country  showing  One-Foot  Contour  Checks 283 

197.  Plan  showing  Method  of  Furrow  Irrigation 287 

198.  Plan  of  Pipe  Irrigation  System,  Ontario,  California  . . . , 297 

199.  View  of  Water  Meter  or  Module,  by  A.  D.  Foote,  C.  E 342 

200.  Inlet  to  Module  in  use  on  Henares  Canal,  Spain 344 

201.  Longitudinal  Section  of  Module  in  use  on  Henares  Canal,  Spain  344 

202.  Plan  of  Module  in  use  on  Henares  Canal,  Spain 344 

203.  Cross-Section  of  Module  in  use  on  Henares  Canal,  Spain 344 

204.  Map  showing  the  Proposed  Works  of  the  Tulare  Irrigation 

District,  California 350 

205.  Cross-Sections  of  Canal  on  Sidelong  Ground 380 

206.  Cross-Section  of  Canal  in  Rock-Cutting,  with  Rubble  Wall  011 

Lower  Side. .  .  382 


RRIGATION    CANALS 


AND    OTHER 


Irrigation   Works. 


Article  i.     Canals  divided  into  two  Classes. 

Canals  are  divided  into  two  great  classes,  those  for 
irrigation  alone,  and  those  for  irrigation  and  naviga- 
tion combined.  The  conditions  required  to  develop  one 
of  the  former  class  successfully,  are: — 

1st.  That  it  should  be  carried  at  as  high  a  level  as 
possible,  so  as  to  have  sufficient  fall  to  irrigate  the  land 
for  a  considerable  distance,  on  one  or  both  sides  of  it. 

2d.  That  it  should  be  a  running  stream,  so  as  to  be 
fed  by  continuous  supplies  of  water  from  the  parent  river, 
to  compensate  for  that  consumed  in  irrigating  the  lands. 

The  conditions  of  a  canal  for  combined  navigation 
and  irrigation  are,  on  the  contrary,  that  it  should  be  a 
still-water  canal,  so  that  navigation  may  be  equally  easy 
in  both  directions;  and,  as  no  water  is  consumed  except 
by  evaporation  and  absorption,  and  at  points  of  transfer 
at  locks,  the  required  quantity  of  fresh  supply  is  com- 
paratively small,  and  it  is  thus  most  economically  con- 
structed at  a  low  level. 


25  IRRIGATION    CANALS    AND 

Article  2.     Systems  of  Irrigation. 

In  India  there  are  four  systems  of  irrigation  in  opera- 
tion, each  of  them  on  a  vast  scale.  They  are  Perennial 
canals,  Inundation  canals,  Tanks  or  Reservoirs,  and 
Wells.  The  inundation  canals  have  no  dam  in  the  river 
at  their  heads;  they  give  a  supply  only  during  floodtime, 
and  the  largest  and  greatest  in  number  aiu  situated  on 
the  river  Indus. 

Irrigation  from  wells  is  carried  on,  by  bullock  power 
and  manual  labor,  each  well  watering  from  three  to  ten 
acres. 

In  America  there  are  three  systems  of  irrigation,  Per- 
ennial canals,  Reservoirs  and  Artesian  Wells.  In  some 
instances  in  the  Western  States  of  America,  water  has 
been  developed  in  small  quantities  by  constructing  sub- 
merged dams,  in  the  beds  of,  and  below  the  surface  of  the 
ground,  of  streams,  and,  in  this  manner,  bringing  to  the 
surface,  for  purposes  of  irrigation,  water  that  before  had 
flowed  to  waste  under  the  bed  of  the  river.  In  other 
cases  tunnels  were  driven  to  bed  rock  through  the  gravel 
beds  of  rivers  and  through  hillsides,  to  develop  water  sup- 
plies. 

Pumping  is  sometimes  resorted  to  in  America,  but 
the  most  extensive  pumping  works  in  the  world  for  pur- 
poses of  irrigation  are  situated  in  Lower  Egypt. 

Article  3.     American  and  Indian  Irrigation  Canals 
Compared. 

In  a  paper  in  Volume  I,  of  the  Transactions  of  the 
Denver  Society  of  Civil  Engineers  and  Architects,  by 
Mr.  George  G.  Anderson,  C.  E.,  he  describes  the  Irriga- 
tion canals  of  Colorado.  This  description  is,  in  a  great 
measure,  applicable  to  the  majority  of  irrigation  canals 
in  existence  in  America.  Mr.  Anderson  states: — 

"  It  was  possible  to  design  works  on  sound  principles 


OTHER    IRRIGATION    WORKS.  O 

without  entering  into  too  minute  details  at  first,  and  it 
is  to  be  feared  that  this  has  not  been  done.  Regarded 
simply  on  the  question  of  construction,  it  is  too  appa- 
rent that  faults  are  numerous,  alignments  have  been 
bad,  grades  and  velocities  established  apparently  with- 
out any  consideration,  and  flumes,  headworks,  etc.,  con- 
structed, of  which  a  respectable  mechanic  would  be 
ashamed.  Still,  bad  as  the  conditions  are,  they  have 
their  value  to  the  engineer,  if  nothing  more  than  in 
showing  the  mistakes  to  be  avoided  in  entering  upon 
similar  works  in  new  countries. 

"  But  by  far  the  greater  number  of  mistakes  have  been 
due,  I  think,  to  haste  in  the  undertaking  of  the  enter- 
prise. Too  little  time  was  given  or  taken  by  the  engineer 
in  which  to  make  himself  thoroughly  familiar  with  the 
physical  conformation  of  the  country  to  be  supplied 
with  water.  Contracts  were  let  for  construction  almost 
"before  a  careful  preliminary  survey  had  been  made, 
and  the  energetic  contractor  kept  close  at  the  heels  of 
the  locating  engineer,  with  a  consequence  that  a  large 
percentage  of  necessarily  bad  alignment  was  made, 
which  it  is  now  utterly  impossible  or  impracticable  to 
correct.  Probably  the  best  thing  that  could  occur  to 
the  irrigation  system  of  northeastern  Colorado  to-day 
would  be  its  entire  blotting  out  from  the  face  of  the  map, 
and  reconstruction  begun  upon  sound  engineering  prin- 
ciples." 

Mr.  Walter  H.  Graves,  C.  E.,  in  a  paper  published  by 
the  Denver  Society  of  Engineers  in  1886,  states: — 

"To  determine  the  proper  form  of  channel,  the 
proper  grades,  slopes,  etc.,  requires  the  utmost  skill  and 
intelligence  on  the  part  of  the  engineer.  Mistakes  made 
in  the  construction  of  a  canal  may  not  appear  at  first, 
but  subsequently  develop  themselves  by  spreading  disas- 
ter and  ruin  on  all  sides.  A  thousand  farmers  depend- 


4  IRRIGATION    CANALS    AND 

ing  on  a  canal  for  their  water  supply,  at  a  critical  peri- 
od, when  the  canal  is  taxed  to  its  utmost  to  supply  their 
demands,  some  fatal  defect  suddenly  appears,  and  the 
canal,  for  the  time  being,  is  rendered  useless,  and  before 
repairs  are  completed  the  crops  are  ruined.  A  catas- 
trophe of  this  kind  would  be  almost  irreparable,  arid 
through  such  a  disaster  financial  ruin  might  overtake  an 
entire  community.  The  responsibility  of  the  engineer 
is  often  too  lightly  assumed  by  him,  and  too  carelessly 
and  cheaply  placed  by  the  company." 

The  above  descriptions  will  probably  apply  to  over 
ninety  per  cent,  of  the  irrigation  canals  and  ditches  in 
America.  The  weirs,  headgates,  bridges,  drops  and  other 
works  are  usually  temporary  structures  of  wood. 

Faulty  as  the  works  are,  it  must  be  admitted  that  they 
served  a  good  purpose  in  aiding  in  the  development  of 
the  country.  Without  them  millions  of  acres  of  land 
would  be  waste  that  now  bear  profitable  crops.  There 
is  a  good  field  for  Hydraulic  engineering  in  the  im- 
provement of  these  old  canals. 

A  great  change  for  the  better  has  of  late  taken  place 
in  the  design  and  construction  of  Irrigation  Canals  in 
this  country,  and,  in  some  new  canals,  works  of  a  more 
permanent  character  than  in  the  old  canals,  are  now  be- 
ing constructed. 

India  has  the  greatest  number  of  canals  that  can,  in 
many  respects,  be  quoted  as  good  examples.  It  may  be 
thought  that  Indian  canals  are  too  often  referred  to  in 
the  following  pages,  but  it  is  well  to  remember  that  the 
finest  examples  of  canal  construction  are  to  be  seen 
there,  that  in  length,  cross-sectional  dimensions,  dis- 
charging capacity,  number  and  aggregate  mileage,  the 
Indian  canals  are  the  greatest  in  the  world,  and  that 
their  structures  are  permanent,  that  is,  that  very  little 
wood  or  other  perishable  material  enters  into  their  con- 
struction. 


OTHER    IRRIGATION    WORKS.  5 

The  experience  gained  in  other  countries,  where  irri- 
gation has  been  practiced  from  time  immemorial,  is  use- 
ful, especially  in  showing  where  mistakes  have  been 
made  and  the  plans  adopted  to  rectify  them.  "Though 
the  designs  may  not,  on  the  whole,  suit  American  prac- 
tice, still  many  useful  hints  can  be  obtained  from  the 
study  of  the  published  descriptions  of  the  works  in  other 
countries. 

The  List  of  Irrigation  Canals  given  in  Article  10, 
shows  some  of  the  vast  works  carried  out  in  India. 

Article  4.     Diverting  the  Water  from  the  River  to  the 

Land. 

Irrigation  by  means  of  canals  is  chiefly  applied  to 
tracts  of  country  which  have  been  formed  by  the  gradual 
deposit  of  alluvial  matter,  from  rivers  in  a  state  of  flood. 
The  deposit  from  the  inundation  begins  to  take  place  at 
the  points  where  the  velocity  of  the  stream  is  checked; 
and  this  being  alongside  the  margin  of  the  channel,  an 
inundation  of  the  country  through  which  a  river  passes, 
will  leave  behind  it,  on  each  side,  a  stratum  of  silt  in 
the  form  of  a  wedge,  the  thick  end  of  which  is  on  the 
river  bank. 

In  the  course  of  time,  successive  annual  inundations. 
will  thus  have  formed  a  slope  away  from  each  of  the 
banks.  The  width  of  this  slope  will  vary  according  to 
the  nature  and  size  of  the  river.  It  may  be  only  two 
hundred  or  three  hundred  yards  wide,  or  it  may  extend 
to  the  distance  of  many  miles. 

The  feature  above  described  is  not  only  to  be  found 
along  the  main  channel  of  a  river,  but  also  along  its 
branches.  No  very  extensive  tract  of  country  has  been 
formed  by  the  inundation  and  consequent  deposit  from 
a  single  stream.  On  the  contrary,  it  must  have  been 
the  work  of  many. 


6  IRRIGATION    CANALS    AND 

The  channels  of  all  rivers,  unless  when  confined  by 
rocks,  are  more  or  less  liable  to  change  their  course. 
By  referring  to  a  map  of  any  delta,  the  reader  will 
observe  that  the  characteristics  of  the  delta  form,  is  that 
a  river,  as  it  approaches  the  sea,  should  split  up  into  two 
or  more  branches  or  arms,  which  again  may  be  subdi- 
vided into  smaller  ones.  This  is  well  exemplified  in  the 
delta  of  the  Nile,  a  diagram  of  which  is  given  in  the 
block-plan,  Figure  31. 

Each  branch  of  a  delta  has  a  tract  of  country  within 
its  influence,  and  serves  to  extend  the  amount  of  allu- 
vial deposit,  either  by  raising  its  banks  or  by  extending 
the  delta  seaward. 

It  is  a  common  occurrence  to  find  dry  beds  of  rivers  in 
alluvial  plains,  possessing  all  the  characteristics  of  the 
existing  channels.  In  some  cases,  channels  may  be 
found  of  such  capacity  as  to  show,  without  doubt,  that 
they  are  deserted  beds  of  the  main  stream;  in  others, 
there  may  be  indications  of  a  partial  and  gradually  di- 
minishing supply  having  reached  them,  which,  by  suc- 
cessive annual  deposits,  has  curtailed  their  section  to  such 
an  extent  as  to  admit  of  their  being  adopted  as  irriga- 
tion channels,  or  if  left  entirely  in  their  natural  state, 
such  channels  may  be  silted  up  completely,  by  successive 
deposits  from  flood  water  and  by  drifted  sand  and  dust, 
until  they  are  no  longer  perceptible,  and  all  that  is  left 
to  mark  their  course  is  a  ridge  of  high  land. 

It  will  thus  be  seen  that  an  alluvial  plain  is  not  made 
up  of  an  equable  deposit  of  alluvial  matter  to  the  right 
and  left  of  the  main  channel  of  a  river,  but,  on  the 
contrary,  by  that  from  a  number  of  channels,  some  of 
which  may  subsequently  be  obliterated.  The  fall  of  the 
country,  also,  instead  of  only  following  the  course  of  the 
main  channel,  will  be  affected  equally  by  all  the  others. 
Intermediate  between  the  channels,  the  ground  will  be 


OTHER    IRRIGATION    WORKS.  / 

low,  and  the  line  formed  by  the  intersection  of  the  two 
planes  sloping  away  from  their  respective  banks,  will 
evidently  indicate  the  course  in  which  the  drainage  from 
those  plains  will  tend  to  flow.  Such  lines  will  blTfoimd 
also  on  the  extreme  boundaries  of  a  delta,  receiving  on 
one  side  the  drainage  of  a  portion  of  the  delta,  and  on 
the  other  that  of  the  country  independent  of  it. 

After  these  remarks  it  is  time  to  explain  that  the  ir- 
rigation of  a  tract  of  country  is  based  on  very  simple 
principles.  Supposing  that  a  supply  of  water  is  re- 
quired for  the  land  near  the  bank  of  a  river,  which  has 
ceased  to  overflow  it,  but  which  may  rise  to  the  lip  of 
the  channel,  then  as  the  country  falls  away  from  the 
river,  it  will  be  readily  understood  that  a  cut  through 
the  bank  will  give  the  means  of  irrigating  the  ground 
beyond.  This  may  be  considered  the  simplest  form  of 
irrigation.  Again,  if  the  surface  of  the  river  falls  so 
considerably  below  the  lip  of  the  channel,  as  to  be  in- 
capable of  supplying  water  to  the  land  at  a  distance,  by 
means  of  a  cut  carried  at  right  angles  to  the  course  of 
the  river,  the  difficulty  may  be  surmounted  by  excavat- 
ing a  channel  in  an  oblique  direction;  for  the  course  of 
a  river  is  seldom  straight  for  a  few  miles,  and  an  artificial 
channel  may  be  formed  in  a  straight  line,  which  will 
carry  water  to  a  higher  level  than  that  of  the  surface  of 
the  river  at  any  point  opposite  to  it.  For  every  mile  of 
its  course,  it  thus  gains  something  on  the  surface  of  the 
level  of  the  river,  and  it  becomes  a  matter  of  simple 
calculation  to  find  how  far  it  will  have  to  be  carried  be- 
fore the  water  issues  011  the  surface.  For  example,  let 
the  plain  below  B,  Figure  1,  require  to  be  irrigated  from 
the  river  C  D. 

Suppose  that  the  surface  of  the  country  from  the 
foot  hills  at  A,  A,  A,  to  5,  falls  at  the  rate  of  two  feet  per 
mile.  Let  the  country  be  traversed  by  a  river,  CD,  and 


8 


IRRIGATION    CANALS    AND 


let  the  surface  of  the  water  in  this  river  throughout  its 
length  be  about  twenty  feet  below  its  banks.  If,  then, 
a  channel,  G  E,  be  excavated  with  a  horizontal  bed  and 
the  water  at  G  raised  very  slightly  by  a  weir  in  the  river 
at  this  point,  then  the  water  from  the  river  above  G 
would  flow  along  this  channel  until  it  reached^,  a  point 
at  right  angles  to  the  river  at  D,  whence  the  water  might 
be  conducted  to  irrigate  the  lower  portions  of  the  slope, 
E  B. 


In  like  manner  if  the  bed  of  the  channel  were  made 
to  fall  one  foot  per  mile,  it  would  at  ten  miles  be  only 
ten  feet  below  the  country  at  E,  and  at  twenty  miles, 
having  gained  a  foot  per  mile,  it  would  emerge  on  its 
surface  at  B. 


OTHER    IRRIGATION    WORKS.  9 

When,  however,  the  ground  falls  at  right  angles  to,  as 
well  as  with  the  course  of  the  river,  the  water  would 
come  to  the  surface  of  the  ground  at  a  less  distance  from 
C,  than  20  miles. 

The  case  is  more  unfavorable,  in  the  higher  reaches 
of  a  river  above  the  delta,  where  the  country  slopes  up- 
wards away  from  the  river.  In  this  case  the  water  for 
the  lands  farthest  from  the  river  must  be  brought  from 
a  part  of  the  river  nearer  to  its  source,  and  the  excava- 
tions must  be  deeper;  or,  as  will  often  happen,  the  ex- 
pense bearing  too  high  a  ratio  to  the  attainable  advan- 
tage, the  irrigation  must  be  restricted  to  those  lands 
which  lie  nearest  to  the  source  of  the  river,  and  at  the 
lowest  levels. 

It  is  the  depth  of  the  surface  of  the  water  below  the 
bank  of  the  river  at  the  head  of  the  channel,  and  the 
relative  slope  of  the  bed  of  the  channel  and  the  surface 
of  the  country  through  which  it  passes,  which  deter- 
mines the  least  length  of  the  channel. 

In  order  to  obtain  command  of  level,  and  in  order  to 
get  on  the  high  ground  without  much  heavy  digging,  it  is 
sometimes  necessary  to  locate  the  head  of  the  canal 
high  up  on  the  river's  course.  For  this  purpose  it  is 
sometimes  necessary  to  go  either  to  the  spot  at  which  the 
river  finally  leaves  the  hills  to  flow  through  the  plains, 
or  to  a  point  not  far  below  that  spot.  Moreover,  at 
this  point  the  water,  except  in  freshets,  is  comparatively 
free  from  silt,  the  great  enemy  of  canals,  and  the  course 
of  the  river  is  restricted  within  narrow  limits,  so  that,  by 
dams  thrown  across  the  river  bed,  we  can  easily  divert 
the  water  into  our  new  channel. 

The  above  considerations  are  so  important,  or  rather 
peremptory,  that  they  outweigh  the  disadvantages  of  the 
arrangement  which  are,  indeed,  very  serious.  For  the 
country  so  close  to  the  hills  having  generally  an  exces- 


10  IRRIGATION    CANALS    AND 

sive  fall,  and  being,  moreover,  intersected  by  hill  tor- 
rents, the  carrying  of  the  canal  through  such  irregular 
ground  entails  serious  difficulties,  which  require  the 
greatest  engineering  skill  and  a  large  expenditure  of 
money  to  overcome  them. 

Referring  to  the  canal  through  the  delta,  it  will  be 
readily  understood  that  the  high  ridges  and  the  old  chan- 
nels, above  described,  indicate  the  most  suitable  align- 
ment for  a  series  of  irrigation  channels.  The  object 
would  be  to  conduct  the  water  from  the  river  to  the  crest 
of  such  high  lands,  and  then  for  the  channels  along 
them,  to  arrange  as  far  as  may  be  practicable  that  the  ex- 
cavation shall  be  no  more  than  sufficient  to  furnish  the 
material  required  for  the  embankments,  which  should 
retain  the  water  at  as  high  a  level  as  possible,  consistent 
with  their  stability.  If  the  depth  of  water  admitted 
into  the  head  of  the  main  channel  is  materially  less 
than  what  is  due  to  the  river  at  its  full  height,  the  depth 
of  excavation  at  the  head  will  increase  in  proportion  to 
the  difference;  and  it  will  then  be  our  object  in  order  to 
make  the  cutting  as  inexpensive  as  possible,  tocarryvthe 
line  of  the  channel  through  low  ground,  until  the  water 
would  flow  011  the  surface.  The  irrigation  limit  is  then 
reached,  and  the  channels  should  be  continued  along  the 
highest  ground  that  will  allow  of  the  water  continuing 
on  the  same  level  with  it  or  above  it,  as  may  be  found 
most  suitable  for  the  locality.  If  the  ground  were  level 
on  both  sides  of  the  channel  it  would,  in  many  cases,  be 
indispensable  to  have  the  surface  of  the  water  above  it; 
but  on  the  other  hand,  the  soil  may  be  ill  adapted  for 
withstanding  pressure,  or  for  preventing  percolation; 
and  to  avoid  the  occurrence  of  breaches  it  may  be  desir- 
able to  keep  the  height  of  the  embankments  within  very 
moderate  limits. 

The  selection  of  the  exact  spot  for  the  head  of  a  canal 


OTHER    IRRIGATION    WORKS.  11 

is  a  task  requiring  much  careful  consideration.  This 
subject  will  be  again  referred  to  in  some  of  the  following 
articles. 

Article  5.     Quantity  of  Water  Required  for  Irrigation. 

The  source  of  supply  for  an  irrigation  canal  having 
been  fixed,  the  next  point  for  consideration  is  the  quan- 
tity of  water  required.  This  quantity  depends  upon: — 

1.  The  maximum  quantity  of  land  requiring  irriga- 
tion during  the  same  period. 

2.  The  duty  of  water  in  the  locality  irrigated  by  the 
canal. 

The  duty  of  water  is  the  area  irrigated  annually  by 
one  cubic  foot  of  water  per  second.  This  subject  is  dis- 
cussed in  the  article  entitled  Duty  of  Water. 

If,  after  an  examination  of  the  map  of  the  irrigation 
district,  we  find  that  96,000  acres  require  to  be  irrigated 
during  one  season,  and  we  also  find  the  duty  of  water  in 
this  district,  or  in  a  district  similarly  situated,  to  be  120. 
acres,  then  the  quantity  of  water  required  to  enter  the 
head  works  of  the  canal  is  -f  f £-  =  800  cubic  feet  per 
second. 

A  different  method  of  estimating  the  quantity  has  been 
adopted  in  the  projects  for  some  of  the  Indian  canals. 

For  the  Sone  Canals  in  India,  three-quarters  of  a  foot 
of  water  per  second  was  estimated  as  sufficient  for  every 
square  mile  of  gross  area,  but  this  area  included  land 
watered  from  existing  wells,  land  lying  fallow,  village 
sites,  roads,  etc. 

For  the  Upper  Ganges  Canal  in  India,  eight  cubic 
feet  per  second  wras  allowed  per  lineal  mile  of  main  canal, 
and  on  the  Sutlej  Canal,  six  and  seven  cubic  feet  have 
been  taken  on  the  same  basis. 

If  the  canal  is  to  be  a  navigable  one,  a  certain  mini- 
mum depth  of  water  must  be  kept  in  it  to  float  the  boats 


12  IRRIGATION    CANALS    AND 

as  far  as  the  navigation  extends,  and  this  must  be  in 
excess  of  the  quantity  required  for  irrigation. 

In  India  the  following  canals  have  provided  for  the 
purpose  of  navigation  alone,  in  addition  to  the  irriga- 
tion supply: — On  the  Sone  Canals  600  cubic  feet  per  sec- 
ond, on  the  Baree  Doab  Canal  130  cubic  feet,  and  on  the 
Ganges  Canal,  400  cubic  feet  per  second. 

In  fixing  the  area  available  for  irrigation,  all  swamp 
land,  sites  of  towns,  roads,  etc.,  not  requiring  water  have 
to  be  deducted,  and  only  the  remaining  area  computed, 
which  actually  requires  water. 

Having  determined  the  quantity  of  water  required, 
the  next  step  is  to  fix  the  dimensions  and  grade  of  the 
canal. 

Article  6.     Depth  to    Bed-width   of  Canal,  and  Dimen- 
sions of  Canals. 

The  form  of  cross-section  of  a  channel  is  determined 
in  a  great  measure: — 

1.  By  the  purpose  for  which  it  is  intended. 

2.  By  the  material  through  which  it  passes. 

3.  By  the  topography  of  the  country,  that  is,  whether 
it  passes  over  a  plain  or  along  a  steep  hillside. 

A  rectangular  channel  having  a  width  equal  to  twice 
the  depth,  has  a  maximum  discharging  capacity  for  the 
same  cross-sectional  area.  The  nearer  a  channel  ap- 
proaches this  form  the  less  will  be  its  sectional  area,  for 
the  same  discharge,  and,  therefore,  the  more  economical 
will  it  be. 

If  the  object  is  to  convey  water  to  a  certain  point 
without  expending  any  of  it  until  that  point  is  reached, 
and  if  the  material  cut  through  will  bear  a  high  veloc- 
ity, then  it  is  advisable  to  adopt  a  section  having  a  bot- 
tom width  equal  to  about  twice  or  three  times  the  depth, 


OTHER    IRRIGATION    WORKS. 


13 


and  with  such  side  slopes  as  may  be  required.  All  the 
fall  available  can  be  used  so  long  as  the  velocity  will  not 
erode  the  bed  or  banks,  or  endanger  the  works. 

On  steep  hillsides,  also,  this  form  of  channel  can,  in 
some  cases,  be  used  with  advantage,  where  the  material 
is  good,  as  already  explained.  In  this  case  the  upper 


CROSS    SECTIONS    OF    CANALS 

BY 
A.  D.  FOOTE,    M.  AM.SOC.  C.  E. 

FIG.  4 


__.  , ,    i <*- -r^-'f11 

^ ^j^  -4---g  g-:«)_-_-Jdr±iii  d 


FIG.  6 


side  is  usually  all  in  cut  and  the  lower  side  partly  in  cut 
and  partly  in  fill. 

If,  however,  the  channel  is  used  to  supply  other  minor 


14  IRRIGATION    CANALS    AND 

channels  with  water  for  irrigation,  its  depth  should  be 
small  in  proportion  to  its  width,  in  order  that,  when  the 
supply  fluctuates,  the  surface  of  the  water  may  be  near 
the  surface  of  the  land  to  be  irrigated. 

For  rectangular  channels,  constructed  of  masonry  or 
concrete,  the  maximum  discharging  channel  of  given 
area  is  one  with  a  bed- width  equal  to  twice  the  depth. 

The  diagrams,  figures  4  to  11,  show  cross-sections  of 
some  existing  canals  in  America,  India  and  Spain. 

In  the  List  of  Irrigation  Canals,  Article  10,  the  propor- 
tion of  depth  to  width  can  be  seen  by  inspection.  It 
will  be  noticed  in  the  Indian  canals  that  the  proportion 
of  depth  to  width  is  less  than  in  European  and  Ameri- 
can canals.  The  greater  number  of  the  Indian  canals 
flow  through  sandy  loam,  and  their  mean  velocity  sel- 
dom exceeds  three  feet  per  second.  In  order  to  arrange 
for  a  low  velocity,  and  also  to  keep  the  surface  of  the 
water  in  the  canal,  at  all  periods  of  ordinary  supply,  at 
such  a  level  as  to  be  able  to  irrigate  the  adjacent  land, 
the  depth  has  been  made  from  one-tenth  to  one-twentieth 
of  the  width,  except  in  the  case  of  the  Agra  Canal,  where 
it  is  one-seventh. 

On  the  Western  Jumna  Canal,  an  old  canal  in  India, 
the  water,  in  the  course  of  years,  formed  for  itself  a 
channel  whose  depth  was  found,  by  a  series  of  trials, 
to  be  about  one-thirteenth  of  its  width.  After  this, 
the  proportion  of  depth  to  width  fixed  on  construc- 
tion for  the  following  canals  in  India  was:  on  the  Baree 
Doab  Canal  1  in  15,  on  the  Sutlej  Canal  1  in  14,  and  on 
the  Sone  Canals  1  in  20. 

A  rule  has  been  proposed  to  make  the  bottom  width 
equal  in  feet,  to  the  depth  in  feet  plus  one,  squared. 

Mr.  T.  Login,  who  was  for  many  years  an  executive 
engineer  on  the  Ganges  Canal,  has  given  the  following 
table,  showing  approximately  the  sections  and  slopes, 


OTHER    IRRIGATION    WORKS. 


15 


probably  best  adapted  for  irrigation   canals   and  water 
courses  for  Northern  India. 

The  velocities  are  computed  by  Dwyer's 


Where  r  =  hydraulic  mean  depth  in  feet. 

tt      y_  fa]}  jn  fee^  of  surface  of  water  per  mile. 
"      v  =  mean  velocity  in  feet  per  second. 

TABLE  1.    Giving  dimensions  and  grades  of  canals. 


Cubic 

SECTIONS. 

SECTIONS. 

Side 

feet  of 

<s 

td 

y 

OQ 

W 

y 

GO 

dis- 
charge 

Mean  ve 
per  seco 

rg 

S  P- 

la 

S    "S- 

1  2, 

Hi 

o  i 

B  §. 
E? 

03 
C     O 

*H      ^ 

is! 

°  s 

M.      ° 

slopes 
of 

Ft 

>   P 

!         M.     05 

P 

w» 

§ 

1      I 

chan- 

per 

CD*    & 

P 

P      P 

(t> 

P 

P        P 

•  ^ 

CD     P 
5*"    P 

P  S 

O      *-i 

«• 

Pf 

&  2. 

nels. 

second. 

:    P' 

i    § 

S*  ^ 

•    »  s 

& 

*"    <J 

*   S 

':    I 

•    S- 

S-  S. 

:   Is, 

•r- 

2-  1 

'    P* 

1   2, 

50 

2. 

24 

4 

15 

2 

44       i       164 

1    tol 

100 

2.25 

44 

4|             144 

4 

5i 

16 

1     tol 

250 

2.5 

15 

5 

134 

134 

54 

14| 

1     tol 

500 

2.75 

274 

54 

13 

25 

6 

14* 

1     tol 

1000 

• 
3. 

50 

6 

13 

45 

6| 

14* 

1     tol 

2000 

3.25        774 

7 

13 

70 

7| 

14* 

14  tol 

j 

3000 

3.5          95 

8 

12| 

85 

8* 

14 

14  to  1 

4000 

3.5 

s& 

12f 

110 

9* 

14 

14  tol 

5000 

3.67 

1474 

8| 

124 

130 

9* 

isi 

14  to  1 

6000 

3.75 

170 

H 

124 

150 

9| 

134 

14  to  1 

While  the  dimensions  given  in  the  above  table  are, 
doubtless,  suitable  for  the  locality  mentioned,, still  the 
slopes  assigned  will  not  give  the  velocities  stated  in  the 


16  IRRIGATION    CANALS    AND 

table.     They  are  computed  by  a  formula  with  a  constant 
co-efficient  c  =94.5.     To  prove  this  we  have:  — 


substitute  this  value  of  /  in   Dwyer's  formula  and   we 
have:  — 


v  =  0.92  ]/2  X  5280  X  s  X  r 

.-,  v  =  94.5  i/rs 

It  is  now  admitted  that  a  formula  with  a  constant  co- 
efficient, such  as  Dwyer's,  is  suitable  for  only  a  small 
range  of  channels.  It  is,  however,  now  generally  ac- 
cepted that  Kutter's  formula  is  applicable  to  a  wide 
range  of  channels,  and  that,  of  all  the  existing  formulas, 
it  gives  the  closest  approximation  to  the  actual  flow  of 
large  open  channels. 

Assuming  a  value  of  n  =  .025  for  the  channels  given 
in  table  2  below,  we  find  the  corresponding  velocities. 
These  velocities  show  that  Dwyer's  formula  used  in 
computing  table  1  above,  gives  too  high  a  velocity  for 
all  the  channels.  This  subject  will  be  referred  to  at 
length  in  the  articles  on  the  Flow  of  Water  where  the  ap- 
plication of  Kutter's  formula  is  fully  discussed. 


OTHER    IRRIGATION    WORKS.  17 

TABLE  2.    Giving  velocities  of  Channels  by  Ku tier's  formula  with  n—  .025. 


Breadth  of  chan- 
nel at  bottom 
in  feet. 

Depth  of  water 
with  full 
supply  in  feet. 

Slope  of  surface 
of  water  in  inches 
per  mile. 

Side   slopes. 

Velocity  in  foet 
per  second. 

21 

4 

15 

1     to  1 

1.34 

*l 

4f 

14| 

1     to  1 

1.61 

15 

5 

13£ 

1     to  1 

1.98 

27| 

5| 

13 

1     to  1 

2.24 

50 

6 

13 

1     to  1 

2.53 

77i 

M 

/ 

13 

l|to  1 

2.87 

95 

8 

12| 

l|to  1 

3.12 

121J 

8| 

12| 

l|to  1 

3.30 

147  & 

8* 

12| 

l|to  1 

3.30 

170 

8f 

m 

litol 

3.39 

Article   7.     Side   Slopes „ 

The  side  slopes  usually  adopted,  on  the  water  side,  are 
within  the  limits  of  J  horizontal  to  1  vertical,  to  3  hori- 
zontal to  1  vertical.  For  most  soils  a  natter  slope 
than  2  to  1  will  not  be  required,  and  it  is  very  seldom 
that  as  flat  a  slope  as  3  to  1  is  required. 

The  outer  slopes  in  earthen  soils  may  have  an  inclina- 
tion regulated  by  the  stability  of  the  ground,  and  1J  to 
1  is  most  common. 

As  every  rule  has  an  exception,  so  we  find  that  Mr. 
Walter  EL  Graves,  C.  E.,  states  of  the  Grand  River  Canal 
system  of  Colorado: — 

"The  soil  of  this  locality  is  peculiar,  a  sort  of  argil- 
laceous adobe,  that  when  dry  resembles  ashes,  and  when 
thoroughly  wet  becomes  a  slimy  mud,  that  is  almost  iin- 
2 


18  IRRIGATION:  CANALS  AND 

possible  to  control  or  maintain  in  a  fixed  position.  In 
the  canal  banks  it  has  a  tendency,  when  soaked  with 
water,  to  melt  and  flatten  out,  and  to  preserve  in  good 
form  and  for  good  service  the  channel  has  proven  a  very 
difficult  and  expensive  matter." 

Long  experience  on  thousands  of  miles  of  large  and 
small  channels  in  northern  India  has  proved  that,  when 
a  flatter  slope  than  J  to  1  is  adopted  in  construction,  it 
cannot  be  maintained  with  economy  after  the  channel 
has  got  into  its  working  velocity. 

With  muddy  water  and  on  flat  slopes,  especially 
where  weeds  grow,  silt  is  deposited  on  the  sides  of  the 
channel  and  they  eventually  take  a  slope  of  about  J  to  1, 
It  is  found  advantageous  to  allow  this  slope  to  remain 
and  not  to  flatten  it  during  the  annual  repairs. 

The  same  thing  has  been  observed  in  America,  but, 
in  this  country,  the  recorded  observations  are  not  so 
full  as  in  India. 

Captain  Edward  L.  Berthoud,  of  Golden,  Colorado,  in 
a  paper  on  Irrigation,  published  by  the  Denver  Society 
of  Civil  Engineers,  is  quoted  as  having  stated: — 

"  I  find  that  cuttings  in  our  ditches  should  not  be  less 
than  1  to  1.  If  flatter  they  will  be  more  exposed  to  the 
wash  of  sudden  rains,  and  finally  reduced  to  1  to  1,  or 
even  steeper  slopes." 

With  reference  to  the  inner  side  slopes  of  canals, 
Major  W.  Jeffreys,  R.  E.,  in  a  note  in  the  Professional 
Papers  on  Indian  Engineering,  states: — 

11  Opinions  are  divided  as  to  the  pitch  with  which 
the  inner  slopes  of  distributaries  should  be  made.  In 
the  Punjab  a  slope  of  1J  to  1  is  adopted,  while  in  the 
Northwest  Provinces  1  to  1  is  preferred,  chiefly  for  eco- 
nomical reasons.  For  very  light  soils  the  former  of 
these  is,  of  course,  the  stronger  construction,  but  an 


OTHER    IRRIGATION    WORKS.  19 

officer  of  irrigation  experience  is  able  to  distinguish  be- 
tween a  rajbuha  (lateral  or  distributary)  newly  made,  and 
one  that  has  settled  down  into  an  irrigating  line.  ^What- 
ever slope  is  adopted  in  construction,  it  is  found  that 
this  cannot  be  advantageously  maintained  after  the 
channel  has  been  in  use  for  some  time.  A  distributary 
at  the  close  of  an  irrigating  season  invariably  assumes 
the  following  shape, except  when  the  soil  is  impregnated 
with  reh  (alkali). 


When  the  time  for  clearance  comes  round,  the  engi- 
neer in  charge,  if  he  is  wise,  will  not  attempt  to  restore 
the  original  section  which  is  opposed  to  the  form  that 
nature  adopts.  It  is  only  waste  of  money  to  dig  away 
the  long  slopes  which  are  soon  recovered  with  silt,  while 
in  theory  it  does  not  afford  a  maximum  hydraulic  depth 
which  it  is  the  great  object  to  attain  in  channels  with 
low  velocities.  The  custom  on  the  Ganges  Canal  Dis- 
tributaries is  to  trim  off  the  slope  at  J  to  1,  as  shown  by 
thick  dotted  lines,  a  b,  c  dy  in  Figure  7;  and  this,  in  prac- 
tice, is  found  to  conform  more  closely  to  the  average 
working  section  than  any  other.  To  arrive,  then,  ap- 
proximately, at  anything  like  the  working  results,  the 
discharge  tables  employed  by  the  rajbuha  (distributary 
or  lateral)  designer  should  be  based  on  these  conditions." 

The  following  canals  have  the  side  slopes  mentioned 
opposite  their  names.  More  information  relating  to 
these  and  other  canals  will  be  found  in  Article  10. 


20  IRRIGATION    CANALS    AND 

TABLE  3.    Giving  the  inner  side  slopes  of  canals  in  earth  and  sandy  loam. 

Ganges  Canal,  India 1J  (horizontal)  to  1  (vertical). 

Sone  Canals,  India 1 1  (horizontal)  to  1  (vertical). 

Sutlej  Canal,  India 1    (horizontal)  to  1  (vertical). 

Agra  Canal,  India 1    (horizontal)  to  1  (vertical) . 

Cavour  Canal,  Italy 1|  (horizontal)  to  1  (vertical). 

Henares  Canal,  Spain 1 J  (horizontal)  to  1  (vertical). 

Del  Norte  Canal,  Colorado 3    (horizontal)  to  1  (vertical). 

Citizens  Canal,  Colorado 3    (horizontal)  to  1  (vertical). 

Turlock  Canal,  California 2    (horizontal)  to  1  (vertical). 

Central  Canal,  California 2    (horizontal)  to  1  (vertical). 

TABLE  4.     Giving  the  natural  slopes  of  materials  with  the  horizontal  line. 

Degrees.  Degrees. 

Gravel,  average 40       Shingle 39 

Dry  sand 38       Bubble 45 

Sand 22       Clay,  well  drained 45 

Vegetable  earth 28       Clay,  wet 16 

Compact  earth 50 

Article  8.     Grade  or  Slope  of  Bed  of  Canal. 

The  method  of  finding  the  grade  of  a  channel  of  given 
dimensions,  in  order  that  it  may  have  a  certain  velocity 
or  discharge,  is  fully  explained  in  the  article  on  the 
Floiv  of  Water,  as  well  as  the  solution  of  all  the  other 
problems  relating  to  open  channels,  likely  to  occur  in 
practice. 

The  discharge  of  an  irrigation  canal  is  diminished 
in  proportion  to  the  quantity  of  water  expended  for 
irrigation  from  its  head  to  its  tail  end.  There  are 
three  methods  by  which  the  diminution  of  the  discharge 
is  regulated: — 

1.  By  diminution  of  sectional  area  and  an  increase 
of  slope,  so  proportioned  that,  though  the  discharge  is 
reduced  as  required,  still  the  velocity  is  not  diminished 
throughout  the  full  length  of  the  canal  channels. 

2.  By  keeping  the  same  sectional  area  and  diminish- 
ing the  longitudinal  slopes  or  grades. 

3.  By  maintaining  the  same  grade  and   diminishing 
the  sectional  area. 


OTHER    IRRIGATION    WORKS.  21 

An  example  of  the  first  method  is  herewith  given  in 
detail. 

Where  the  fall  of  the  country  is  tolerably  uniform, 
the  slope  of  the  bed  of  the  main  channel  should  be  Tess 
than  that  of  the  branches,  which  again  should  be  less 
than  that  of  the  minor  channels  and  cuts.  The  object 
of  this  is  to  secure,  as  far  as  possible,  a  uniform  velocity 
so  that  the  alluvial  matter  held  in  suspension  may  be 
carried  on  from  the  head,  and  deposited  uniformly  over 
the  lands  irrigated. 

There  are  two  important  reasons  why  the  silt  should 
be  carried  on  to  the  land,  the  first  is  that  the  annual  silt 
clearance  from  the  canal  may  be  lessened  as  much  as 
possible,  and  the  second  is,  that  the  silt,  if  it  has  fertil- 
izing qualities,  is  of  great  benefit  to  the  land.  The  ben- 
efit derived  from  this  is  fully  explained  in  the  article  en- 
titled Fertilizing  Silt. 

As  to  the  actual  fall  which  should  be  given  to  a  main 
canal,  of  say  bed  width  100  feet,  and  depth  of  water  6  to 
10  feet,  experience  shows  that  about  6  inches  to  1  foot  in  a 
mile  is  ample,  with  a  wetted  border  of  average  rough- 
ness. 

The  List  of  Carnals,  in  Article  10,  gives  the  grade  of 
the  principal  Irrigation  Canals  in  existence. 

Let  us  now  assume  that  a  canal  having  a  capacity  of 
1,700  cubic  feet  per  second  is  required  to  irrigate  a  certain 
district.  Experience  on  other  canals  in  the  district  has 
shown  that  a  mean  velocity  of  2.5  feet  per  second  will 
prevent  the  deposition  of  silt,  whilst  at  the  same  time  it 
will  not  erode  the  bed  or  banks.  It  is  therefore  deter- 
mined to  give  the  canal  a  bed-width  of  100  feet,  a  depth 
of  water  of  6.5  feet,  and  side  slopes  of  1  to  1.  By  Kutter's 
formula,  with  n  =  .025,  we  find  that  a  slope  of  10  inches 
per  mile  will  give  a  velocity  of  2.5  feet  per  second,  and 
that  therefore  the  discharge  is  1,730.6  cubic  feet  per 


22  IRRIGATION    CANALS    AND 

second  which  is  near  enough  to  the  required  discharge 
for  all  practical  purposes. 

Let  us  now  suppose  that  branches  are  drawn  off  to 
supply  water  for  irrigation,  and  that,  after  these  sup- 
plies are  drawn  off,  the  bed-width  and  depth  of  the  chan- 
nel are  reduced,  below  the  head  of  each  branch.  As 
the  mean  velocity  throughout  is  to  be  maintained  at 
what  the  channel  had  at  starting,  the  grade  of  the  canal 
will  have  to  be  increased  at  each  dimuiiition  of  dis- 
charge. For  example,  at  the  tenth  mile  from  the  head- 
work  an  irrigation  channel  takes  off  a  supply  of  550 
cubic  feet  per  second.  This  leaves  a  supply  of  1,150 
cubic  feet  per  second  in  the  main  canal.  Arranging 
the  dimensions  required  for  this  supply,  we  find  that  a 
bed  width  of  80  feet,  depth  of  water  of  5.5  feet,  side 
slopes  of  1  to  1,  and  a  grade  of  13  inches  per  mile,  will, 
by  Kutter's  formula,  with  n  =•  .025,  give  a  discharge  of 
1,175.6  cubic  feet  per  second,  and  a  velocity  of  2.50  feet 
per  second. 

These  agree  near  enough  to  the  required  velocity  and 
discharge  for  all  practical  requirements. 

At  the  10th  mile  a  branch  takes  off  550  cubic  feet  per 
second. 

At  the  19th  mile  a  branch  takes  off  350  cubic  feet  per 
second. 

At  the  31st  mile  a  branch  takes  off  300  cubic  feet  per 
second. 

At  the  40th  mile  a  branch  takes  off  260  cubic  feet  per 
second. 

At  the  54th  mile  a  branch  takes  off  140  cubic  feet  per 
second. 

At  the  60th  mile  a  branch  takes  off  50  cubic  feet  per 
second. 

The  channel  at  the  tail  of  the  canal  has  only  50  cubic 
feet  per  second  for  ten  miles. 


OTHER    IRRIGATION    WORKS. 


23 


The  table  given  below  shows  how  the  dimensions  and 
grades  of  the  channels  are  arranged  to  give  the  dis- 
charge required,  which  is  shown  in  the  sixth  column. 

It  will  be  seen  that  the  discharge  by  formula,  given  in 
column  seven  of  the  table,  differs  a  little  from  the  re- 
quired discharge  in  column  six,  but  a  slight  difference  of 
this  amount  does  not  affect  the  work  to  any  appreciable 
extent. 

TABLE  5.   Giving  full  details  of  channels  computed  by  Kutter's  formula  with 

n  =  .025. 


Bed, 
Width  in 
Feet. 

100 

Depth 
in   Feet. 

Side  Slopes 

Grade 
per  mile. 

Computed 
Mean   Veloc- 
ity in  feet 
per  second. 

Required 
Discharge  in 
Cubic  Feet 
per  second. 

Computed 
Discharge  in 
Cubic  Feet 
per  second. 

65 

1  to   1 

10  inches 

2.50 

1700 

1730.6 

80 

5.5 

ti 

13  inches 

2.50 

1150 

1175.6 

60 

5.0 

« 

15  inches 

2.48 

800 

806.0    . 

40 

4.5 

'< 

19  inches 

2.52 

500 

504.6 

20 

4.0 

(C 

2  feet 

2.43 

240 

233.3 

10 

3.0 

« 

4  feet 

2.64 

100 

103.0 

6 

2.5 

5  feet 

2.45 

50 

52.0 

From  the  length  of  the  different  reaches  of  the  canal 
and  the  fall  in  feet  per  mile  in  each  reach  we  find  that 
in  the  whole  distance  of  70  miles  the  total  fall  is  150  feet, 
being  an  average  fall  of  2.2  feet,  nearly,  per  mile.  If 
the  fall  of  the  country  did  not  admit  of  so  high  an  aver- 
age, it  might  be  easily  reduced  by  maintaining  a  greater 
depth  in  the  channels  and  diminishing  the  width.  A 
greater  depth  would  give  a  greater  hydraulic  mean  depth, 
and,  according  to  the  increase  of  the  hydraulic  mean 
depth,  the  slope  could  be  diminished. 


24  IRRIGATION    CANALS    AND 

The  above  will  be  sufficient  to  indicate  the  mode  in 
which  the  slope  of  the  channel  should  be  regulated,  in 
order  to  prevent  accumulations  of  silt.  In  practice,  a 
canal  is  never  perfectly  aligned  on  this  principle,  but 
every  endeavor  should  be  made  to  adhere  to  it,  in  de- 
signing a  system  of  irrigation  works,  so  far  as  local  pe- 
culiarities and  other  circumstances  will  permit. 

The  accumulation  of  silt  in  channels,  particularly  in 
the.  main  channel,  is  not  only  a  serious  impediment  to 
maintaining  a  supply  of  water  till  the  crops  are  matured, 
but  the  clearance  may  be  enormously  expensive.  Even 
if  the  silt  cannot  be  carried  on  to  the  fields,  as  in  a  per- 
fect canal,  at  least  one  step  in  advance  is  gained,  if  it  is 
prevented  from  accumulating  in  the  main  channel;  for 
the  maintenance  of  the  supply  in  it,  is  the  most  essen- 
tial point,  and  if  there  are  deposits  in  the  branches 
only,  it  may  be  possible  to  clear  them  in  turn,  without 
cutting  off  the  supply  from  the  river.  If  this  might  not 
be  feasible  with  the  branches,  it  would  be  so  at  all  events 
with  the  smaller  irrigation  channels;  and  it  would  not 
only  be  advantageous  to  throw  on  the  slit  to  them,  and 
to  clear  them  in  turn,  without  cutting  off  the  supply  of 
water  from  the  branches,  but  the  clearance  would  evi- 
dently be  much  less  costly  from  them  than  it  would  be 
from  the  larger  channels,  because  the  haul  would  be  less. 

When  the  fall  of  the  country  is  so  gentle  as  not  to 
allow  of  the  fall  of  the  channels  being  gradually  in- 
creased from  ten  inches  a  mile  it  would  be  necessary  to 
reduce  the  initial  slope  somewhat.  A  very  slight  reduc- 
tion, would,  as  it  affects  the  whole  of  the  channel  on- 
wards, in  the  aggregate,  amount  to  something  consider- 
able. 

If,  on  the  other  hand,  the  fall  of  the  country  be  too 
great,  the  initial  slope  may  be  increased,  with,  if  neces- 
sary, a  reduction  in  the  depth  of  water;  or,  if  the  fall  of 


OTHER    IRRIGATION    WORKS.  25 

country  is  rapid  at  first  and  afterwards  more  gentle,  the 
desired  result  may  be  obtained  by  constructing  perpen- 
dicular drops  at  intervals. 

Any  change  of  direction  causes  a  certain  loss  of  veloc- 
ity, and  the  water  thrown  into  branches  and  minor 
channels  would  lose  velocity  in  passing  through  head- 
sluices,  unless  they  possessed  the  full  water-way  of  the 
channel.  Due  allowance  would  have  to  be  made  for  this 
by  adding  somewhat  to  the  slope  at  the  heads  of  the 
branches  and  channels.  Where  the  water  supply  is 
drawn  from  a  river  highly  charged  with  silt,  the  princi- 
ple above  described  of  the  necessity  of  keeping  up  the 
velocity  to  the  point  of  delivery  of  the  water  is  very 
often  neglected,  and  as  a  result  canals  silt  up,  causing 
additional  expense  to  clear  them  out  and  a  loss  of  irri- 
gating capacity. 

With  reference  to  the  second  method  it  is  sometimes 
advisable,  when  there  is  little  silt,  to  give  a  uniform  rate 
of  fall  to  the  canal,  or  at  all  events  not  to  change  it  too. 
often.  It  will  be  sometimes  found  preferable  to  reduce 
the  gradient  instead  of  diminishing  the  cross-sectional 
area  in  proportion  to  distribution  of  water  along  its 
course,  and  as  the  requirements  for  carrying  the  volume 
of  water  became  lessened.  An  illustration  of  this  is 
found  in  the  Quinto  Sella  Canal,  in  Italy,  which  main- 
tains a  constant  section  for  about  fifteen  miles  of  its 
length;  and  although  in  this  distance  about  one-third 
of  its  waters  are  drawn  off  for  irrigation,  its  capacity 
for  the  carriage  of  water  is  diminished  solely  by  reduc- 
tion of  gradient,  the  slope  of  its  channel  being  1  in 
1,000  at  its  derivation  from  the  Cavour  Canal,  and 
which  is  gradually  reduced  to  0.3  per  1,000  at  the 
end,  according  as  its  requirements  become  lessened. 

An  example  of  the  third  method  is  supplied  by  the 
canal  of  the  Central  Irrigation  District  of  California,  of 
which  Mr.  C.  E.  Grunsky  is  the  Chief  Engineer. 


26  IRRIGATION    CANALS    AND 

The  main  canal  of  this  district  has  a  constant  slope 
of  1  in  10,000,  and  a  constant  depth  of  six  feet,  and  its 
discharge  is  diminished  by  contracting  the  bed  width 
of  the  canal. 

Sometimes  the  fall  of  the  ground,  that  is,  the  profile 
of  the  line,  will  determine  the  grade  of  the  canal,  after 
which  the  bed  width  and  depth  are  fixed. 

Mr.  T.  Login,  C.  E.,  has  stated  with  reference  to  the 
water  of  the  river  Ganges,  admitted  into  the  head  of 
the  Ganges  Canal  at  Hurdwar,  that  it  is  nearly  free  from 
silt  from  October  to  March;  but  as  soon  as  the  snow  be- 
'gins  to  melt  in  April,  the  water  is  highly  charged  with 
silt.  This  silt  is  carried  down  the  canal  in  the  hot  sea- 
son, that  is,  from  April  to  September,  and  is  deposited 
over  the  canal  bed,  to  be  again  picked  up  and  carried 
forward  in  the  cold  season,  that  is,  from  October  to 
March,  when  the  water  becomes  more  pure.  This  in- 
formation may  be  useful  in  other  works,  somewhat  sim- 
ilarly situated,  as  to  the  period  during  which  the  water 
supply  is  highly  charged  with  silt. 

Article  9.     Dimensions  of  Banks. 

The  top  of  the  canal  banks  is  generally  from  6  to  10 
feet  in  width,  according  to  the  material  and  depth  of 
water,  and  it  is  seldom  less  than  1J  feet  above  the  maxi- 
mum level  of  the  water.  This,  generally  speaking,  will 
be  sufficient,  as  irrigation  canals,  from  their  position, 
are  not  subject  to  floods,  and,  as  a  rule,  they 'do  not  re- 
ceive much  of  the  drainage  of  the  country  through 
which  they  pass,  and  for  this  reason,  the  effect  of  a  very 
heavy  rainfall  would  be  imperceptible. 

A  roadway  is  sometimes  made  on  one  or  both  banks, 
and,  in  this  case,  this  determines  the  top  width  of  the 
banks. 

The  top  width  of  the  bank  is  made  level,  or  slightly 


OTHER    IRRIGATION    WORKS. 


27 


lower  on  the  side  furthest  from  the  canal,  to  allow  the 
rain  waters  to  run  off  in  that  direction  as,  were  the  con- 
trary the  case,  during  storms  a  considerable  quantity  of 
earth,  especially  in  light  soils,  might  be  washed  inter  the 
canal. 

In  some  cases  the  top   of  the  bank  is  made  a  segment 
of  a  circle  with  a  slight  rise  in  the  center. 


When  the  channel  is  partly  in  cut  and  partly  in  fill,  a 
berm  of  from  2  to  6  feet  in  width  is  left  between  the  top 


28  IRRIGATION    CANALS    AND 

of  the  bank  in  cut  and  the  bottom  of  the  fill,  and  usually 
the  fill  has  a  flatter  slope  than  the  cut. 

In  deep  cutting,  where  the  excavated  material  is  run 
to  waste,  a  berm  of  at  least  10  feet  in  width  should  be 
left  between  the  top  of  the  cut  and  the  bottom  of  the 
slope  of  the  waste  bank,  and  the  waste  bank  should  be 
dressed  up  uniformly  along  the  line. 

In  side-hill  ground  an  open  drain  should  be  made  on 
the  high  ground  above  the  canal,  and  the  intercepted 
drainage  water  carried  to  the  nearest  water-course. 

In  some  of  the  large  canals  in  Colorado,  the  bed  has  a 
slope  from  the  sides  to  the  center  of  from  1  to  3  feet, 
and  this  is  called  the  sub-grade.  It  is  said  to  have  a 
tendency  to  keep  the  current  in  the  center  of  the  chan- 
nel. 


Another  peculiarity  of  some  canals  in  Colorado,  is 
mentioned  by  Captain  E.  L.  Berthoud,  already  quoted. 
He  states: — 

"  When  the  open  cutting  of  a  ditch  follows  around  a 
mountain  slope,  I  find  that  the  transverse  'slope'  of  the 
ditch  bottom  should  be  0.40  to  0.70  of  a  foot  lower  than 
the  '  bank  side  '  of  the  ditch,  thus  throwing  the  wear- 
ing force  of  the  current  near  the  mountain  side,  and 
largely  diminishing  the  tendency  in  bends  to  cut  the 
1  bank  ;  opposite  the  slope  of  cutting. 

"This  deepening  of  the  transverse  slope,  practically 
in  a  bend,  has  the  same  effect  as  the  elevation  of  the 
outer  rail  in  a  railroad  curve." 


OTHER    IRRIGATION    WORKS.  29 

In  silt  carrying  channels,  this  lowering  of  the  bed 
at  sub-grade  and  at  the  inner  slope  in  sidelong  ground, 
seems  of  doubtful  utility.  It  is  likely  that,-ln__tiiue, 
these  channels  would  make  a  working  section,  in  which 
the  low  parts  mentioned  would  not  be  very  apparent  nor 
be  very  likely  to  have  any  very  marked  effect  on  the  ve- 
locity at  these  parts. 

Article  10.     A    List   of   Irrigation  Canals,    Giving    Di- 
mensions, Grades,  Etc. 

The  following  list  gives  some  details  of  irrigation 
canals  in  the  principal  irrigating  countries  of  the  world. 
These  details  refer  to  the  greatest  discharging  part  of 
the  canals  mentioned,  that  is,  the  reach  immediately 
below  the  head  works. 

The  dimensions  of  the  main  canal  only  are  men- 
tioned., The  laterals  or  distributaries  are  not  included. 
For  instance,  the  length  of  the  Ganges  Canal  is  given 
as  456  miles.  This  is  the  length  o'f  the  main  canai 
alone.  It  has  in  addition  2,599  miles  of  distributaries 
or  laterals  and  895  miles  of  escapes  and  drainage  chan- 
nels, which  makes  its  total  length  of  drainage  channel 
3,950  miles. 

Again,  the  Sutlej,  also  known  as  the  Sirhind  Canal, 
has,  including  all  its  channels,  a  length  of  4,950  miles, 
but  of  this  only  503  miles,  the  length  of  the  main,  canal, 
is  given  in  the  list.  There  are  thousands  of  miles  of 
irrigation  canals,  in  the  different  countries  mentioned, 
not  included  in  the  above  list.  The  Inundation  canals 
of  the  single  province  of  Sind  in  India  are  over  5,000 
miles  in  length. 

The  mean  velocity  of  the  canals  varies  from  2  feet  per 
second  upwards  to  7  feet,  and  the  side  slopes  from  1  to  1 
to  4  to  1.  As  a  rule,  however,  the  side  slopes  of  irriga- 
tion canals,  when  first  constructed,  vary  from  1  to  1  to 


30 


IRRIGATION    CANALS    AND 


2  to  1,  but,  it  is  generally  found,  that  after  being  in  use 
for  some  time,  and  exposed  to  the  action  of  the  water, 
they  become  steeper  than  they  were  originally  con- 
structed. The  information  about  some  of  these  canals 
differs  considerably.  For  instance,  the  discharge  of  the 
Upper  Ganges  Canal,  and  the  Lower  Ganges  Canal, 
has  been  stated  by  some  authorities  to  be  5,100  cubic 
feet  per  second  and  by  others  as  high  as  7,000  cubic  feet 
per  second.  The  best  available  information  has,  how- 
ever, been  taken  with  reference  to  the  canals  included 
in  the  list. 

TABLE  6.     Giving  a  list  of  Irrigation  Canals. 


NAME  OF  CANAL. 

COUNTRY. 

Length  in  miles  

~s 

o     S 

3 

i 

5" 

Depth  in  feet  

Slope 

Discharge  in  cubic 
feet  per  second.  .  . 

Upper  Gauges.. 

India 

456 
531 

170 
216 

120 
190 
70 
180 
180 
90 
113 
174 
174 
20 
20 
20 
13 

131 

27.7 
53 

8.23 

10 

8 

5.5 
6 
10 
9 
9 
8 

LoisGi 

20 
10 

17 
10 
12 
6 

11 
4.9 

liii  4224 
1  in  10560 

lin  4800 
1  in  10560 
1  in  10560 
1  in  10560 
liii  3520 
1  in  16POO 
1  in  15000 
1  in  12000 
lin.  20633 
1  in  14000 
1  in  25641 
1  in  20000 
lin  1860 
lin  2000 

1  in  3067 

6000 
6500 
2372 
1068 
2500 
3500 
1100 
4500 
4500 
3000 

10846 
3943 
1138 
906 
981 
114 
1851 
3250 
700 
1760 
600 
2175 
738 
177 
89 

on 

Lower  Ganges  
Western  Jumna  
Eastern  Jumna  
Baree  Doab  

, 

433 
130 
466 
503 
137 
125 
170 
190 
170 

31 
53 
92 
102 
84 

28 
50 
25 

( 

Sutlej  or  Sirhind  
Agra 

( 

, 

Sone,  Western  
Sone,  Eastern  
Soonkasela  

, 

, 

< 

Ibrahimia  

Egypt  .  , 

Main  Delta  (Flood).  .. 
Main  Delta  (Summer). 
Sirsawiah  (Flood)  
Nagar               "       .... 
Sahel 
Subk                «       .... 
Grand  Canal  of  Ticino 
Cavour 

< 

( 

, 

< 

Italy  

Ivrea  .. 

'       '.'.'.'.'.'.'.'.'.'. 

Cigliano  

Botto  ... 
Muzza  

( 

Martesana.. 

( 

Henares. 

Spain  

Isabella  II. 

The  Eoval  Jucar  .  . 

OTHEK    IRRIGATION    WORKS. 


31 


TABLE    6. — Continued. 


g 

NAME  OF  CANAL. 

COTTNTBT. 

Length  in  miles  

«F 

^ 
Si 

5' 

u 

® 
*d_ 
c? 
5' 

if 

.<* 

Slope 

Discharge  in  cubic 
feelt  per  second.... 

Marseilles  . 

France 

52 

9  84 

7.87 

lin    3333 

424 

Ourcq..                    .... 

11.48 

4.92 

1  in    9470 

Crappone  

< 

33 

26 

6.5 

500 

Verdon  

. 

51 

1  in    5000 

212 

Alpines 

, 

480 

St.  Julien 

( 

18 

1  in    3333 

165 

Carpentaras 

, 

33 

lin    4000 

212 

Del  Norte 

Colorado,  U.S.  A. 

50 

65 

5  5 

1  in      660 

2400 

Citizens  . 

45 

40 

5  5 

1  in    1760 

1000 

Uncompahgre  

S9 

24 

1  in    1560 

725 

Fort  Morgan  

<>8, 

30 

3.5 

1  in    3300 

340 

Larimer  . 

45- 

30 

7  5 

720 

North  Poudre  

30 

20 

4.0 

1  in    2640 

450 

Empire  . 

32 

60 

5  5 

1400 

Grand  River  . 

35 

5  0 

1  in    2880 

High  Line. 

70 

40 

7 

1  in    3000 

1184 

Central  District   
Merced..  . 

California  

65" 

8 

60 

70 

6 

10 

1  in  10000 
1  in    5280 

720 
3400 

San    Joaquin    and 
Kind's  River 

it 

39 

55 

4 

1  in    5280 

Seventy-Six 

a 

100 

4 

1  in    3520 

Galloway 

(  t 

^ 

80 

3.5 

1  in    6600 

700 

Turlock 

it 

80 

20 

10 

1  in      666 

1500 

Idaho  Mining  and  Ir- 
rigation Co.'s  
Idano  Canal  Co  's 

Idaho  •.  . 
ii 

75 
4S' 

45 
40 

10 
4 

lin    2640 
1  in    3520 

2585 

Eagle  Eock  and   Wil- 
low Creek             .... 

<( 

50 

30 

3 

1  in      880 

Phyllis    .                 ..    .. 

<( 

54 

12 

5 

1  in    2640 

250 

Arizona.  . 

Arizona  

4f 

36  ' 

7.5 

lin    2640 

1000 

32 


IRRIGATION    CANALS    AND 


Article  n.     The  Surface  Slope  of  Rivers. 

TABLE  7.      Giving  the  surface  slopes  of  rivers  through  the  plains 


Name  of  River. 

s 

Fall  in 
inches 
per 
mile. 

Name  of  River. 

S 

FaU    in 
inches 
per 
mile. 

Mississippi  above  "1 

Neva 

0  000014 

9 

Vicksburg,    Miss.  / 
Bayou  Plaquemine. 

0.000050 
0.000170 

3 
11 

Ehine,  in  Holland.  . 
Seine,  at  Paris  

0.000150 
0.000137 

9* 

8| 

Bayou  Latorische  .  . 
Ohio,  Pt.  Pleasant. 
Tiber,  at  Eome  

0.000040 
0.000093 
0.000130 

2* 

6 

8 

Seine,  at  Poissy  .... 
Saone,  at  Eaconnay. 
Haiiie 

0.000070 
0.000040 
0  000100 

4^ 
2| 
6i 

Newka 

0.000015 

9J 

Article  12.     Safe  Mean  Velocities. 

Having  determined  the  quantity  of  water,  and  fixed 
the  proportion  of  depth  to  width,  and  a  minimum  for 
both,  and,  if  the  canal  is  to  be  navigable,  this  minimum 
is  to  be  fixed  chiefly  with  reference  to  navigation  facil- 
ities. After  this  there  still  remains  a  very  important 
question  to  be  determined  before  we  can  devise  the  sec- 
tion for  our  channel,  that  is,  the  slope  of  the  bed,  on  which 
the  velocity  depends. 

If  this  slope  is  too  great,  the  bed  of  the  canal  will  be 
torn  up,  and  the  foundations  of  all  bridges,  drops  and 
other  works,  will  be  endangered.  The  canal' bed  will  be 
cut  down  and  retrogression  of  levels  take  place,  until  the 
velocity  of  the  water  has  adjusted  itself  to  the  cohesion 
of  the  material  through  which  it  flows.  Also,  the  level 
of  the  surface  of  the  water  in  the  canal  will  be  lowered 
and,  furthermore,  the  difficulties  of  navigation  against 
the  stream  will  be  largely  increased. 

If,  on  the  other  hand,  the  slope  is  too  small,  a  larger 


OTHER    IRRIGATION    WORKS.  33 

section  of  channel  will  be  required  to  discharge  a  given 
quantity  of  water,  and  many  additional  works  will  be 
required,  in  the  shape  of  drops,  locks,  etc.  There  will 
also  be  danger  of  silt  being  deposited  in  the  bed,  or  of 
the  canal  being  choked  by  the  growth  of  aquatic  plants. 

In  order  to  provide  somewhat  against  the  deposition 
of  silt,  it  is  of  the  utmost  importance  that  the  grades 
and  dimensions  of  the  channels  should  be  so  arranged 
that  the  velocity  of  the  water  may  not  diminish  from 
the  time  it  enters  the  head  of  the  canal  until  it  is  de- 
posited on  the  land  to  be  irrigated. 

The  romoval  of  silt,  deposited  by  a  low  velocity,  has 
caused  a  great  deal  of  trouble  and  expense  on  some  of 
the  Indian  canals.  On  the  Sone  Canals  dredging  has  to 
be  resorted  to  in  order  to  keep  the  channels  clear.  In  1882 
the  Arrah  and  Buxar  canals  were  closed  to  allow  the  silt 
deposited  below  the  head-sluices  at  Dehri  to  be  cleared 
out  by  manual  labor.  It  was  estimated  that  about  forty 
thousand  dollars  would  be  expended  in  clearing  out  • 
some  five  or  six  miles  of  canal  below  the  headworks. 

On  the  Egyptian  canals  the  necessity  for  the  annual 
clearance  of  silt  from  the  irrigation  canals,  has  been 
one  of  the  greatest  evils  of  the  irrigation  system  in 
that  country. 

It  is,  therefore,  of  the  utmost  importance,  to  keep 
clear  of  both  extremes;  but  it  is  not  always  easy  to  do 
so,  and  in  general  a  compromise  has  to  be  made.  More- 
over as  the  velocity  increases  rapidly  with  the  depth,  it 
is  evident  that  a  slope  of  bed  which  might  be  a  very 
proper  one  for  water  of  a  certain  depth,  would  be  too 
great  if  it  were  necessary  to  increase  that  depth  so  as  to 
throw  an  extra  supply  into  the  canal. 

The  minimum  mean  velocity  required  to  prevent  the 
deposit  of  silt  or  the  growth  of  aquatic  plants  is,  in 
Northern  India,  taken  at  1J  feet  per  second. 


34  IRRIGATION    CANALS    AND 

It  is  stated  that,  in  America,  a  higher  velocity  is  re- 
quired for  this  purpose,  and  it  varies  from  2  to  3J  feet 
per  second. 

In  Spain  it  has  been  observed  that  a  velocity  of  from 
2  to  2J  feet  per  second  prevents  the  growth  of  weeds, 
but  does  not  scour  the  channel. 

In  the  Inundation  Canals  of  Sind,  in  India,  a  province 
watered  by  the  Indus,  it  is  found  that  with  a  velocity 
of  over  2  feet  per  second  the  silt  is  carried  on.  to  the 
fields,  and,  as  a  rule,  the  sand  is  deposited  in  the  canal 
and  this  sand  has  to  be  cleared  out  every  year,  in  order 
to  keep  the  canals  in  working  order. 

In  Egypt,  when  the  velocity  is  less  than  1.8  feet  per 
second,  silt  is  deposited  and  an  immense  quantity  of  it  has 
to  be  removed  every  year  from  the  irrigation  canals  there. 
A  velocity  of  over  two  feet  per  second,  however,  in  Au- 
gust and  September,  when  the  Nile  water  is  much  charged 
with  slime,  prevents  deposits,  not  only  of  slime  but  even 
of  sand.  During  summer  there  is  no  silt  as  the  water 
is  clear. 

Having  fixed  the  minimum  velocity  and  depth  of  chan- 
nel, the  required  slope  can  be  computed  as  explained  in 
the  examples  of  the  application  of  the  Tables  relating  to 
the  Flow  of  Water. 

The  maximum  mean  velocity  is  not,  however,  so 
easily  fixed.  It  must,  in  the  first  place,  vary  with  the 
nature  of  the  soil  of  the  bed.  A  stony  bed  will  stand  a 
very  considerable  velocity,  while  a  sandy  bed  will  be 
disturbed  if  the  velocity  exceeds  3  feet  per  second.  Some 
gravel  beds  will  bear  a  high  velocity.  Good  loam  with 
not  too  much  sand  will  bear  a  velocity  of  4  feet  per  second. 

It  is  better  to  give  too  great  than  too  small  a  velocity, 
as,  in  the  former  case,  measures  can  be  adopted  to  pro- 
tect the  side  slopes,  or  falls  can  be  made  in  the  canal 
and  the  longitudinal  slope,  and,  therefore,  the  velocity 


OTHER    IRRIGATION    WORKS.  35 

reduced.  In  the  latter  case  the  deposition  of  silt  will 
necessitate  an  annual  clearance  of  the  canal,  at  great 
expense,  and  the  loss  of  ground  along  the  canal-banks 
on  which  to  deposit  the  spoil. 

The  Cavour  Canal  in  Italy,  over  a  gravel  bed,  has  a 
velocity  of  about  5  feet  per  second. 

The  Naviglio  Grande  and  the  Martesana  canals  in 
Italy,  which  are  both  used  largely  for  irrigation,  have 
steep  slopes,  and  their  mean  velocities  are  not  less  than 
from  5  to  6  feet  per  second  in  their  upper  portions. 

On  the  Aries  branch  of  the  Crappone  Canal  in  the 
South  of  France,  the  mean  velocity  is  5.3  feet  per  sec- 
ond, and  on  the  Istres  branch  of  the  same  canal  the 
mean  velocity  is  6.6  feet  per  second. 

The  mean  velocity  of  the  Baree  Doab  Canal  in  India, 
when  carrying  its  supply,  3,000  cubic  feet  per  second, 
is  about  5  feet  per  second  over  a  gravel  bed. 

The  Del  Norte  Canal  in  Colorado,  has  a  discharge  of 
2,400  cubic  feet  per  second.  At  its  head  its  bed-width' 
is  65  feet,  depth  of  water  5J  feet,  and  side  slopes  3  to  1, 
therefore  its  velocity  must  be  over  5  feet  per  second,  but 
,as  the  channel  is  excavated  almost  entirely  from  a  coarse 
gravel,  drift  and  rock,  no  danger  is  anticipated  from  the 
erosive  force  of  the  current. 

Again,  if  the  navigation  requirements  are  to  be  con- 
sidered, the  maximum  velocity  at  which  a  boat  can  be 
navigated  against  the  current  at  a  profit,  is  evidently  a 
very  intricate  problem,  depending  on  such  varying  data 
as  the  moving  power  employed,  whether  steam,  animals 
or  man;  the  description  of  boat,  value  of  the  cargo,  etc. 
If  the  saving  thus  effected  on  the  total  traffic  annually 
conveyed  would  defray  the  interest  of  the  increased 
capital  required  for  the  proposed  reduction  of  slope,  then 
it  would  doubtless  be  desirable  to  make  that  reduction, 
looking  at  the  question  from  that  point  of  view  only. 


36  IRRIGATION    CANALS    AND 

But  there  is  a  limit  to  the  reduction  of  slope  beyond  a 
certain  minimum,  as  explained  above,  owing  to  the 
paramount  necessity  of  preventing  the  deposit  of  silt  in 
the  canal  channel,  and  though,  with  canals  carrying 
from  2,000  to  5,000  cubic  feet  per  second,  6  inches  per 
mile  may  be  taken  as  the  minimum  limit,  which  would, 
under  ordinary  circumstances,  interfere  seriously  with 
navigation;  still  it  must  depend  of  course  on  the  fall  of 
the  country  and  the  nature  of  the  soil,  and  so  difficult 
is  it  often  found  to  combine  the  requirements  of  the  two 
purposes,  irrigation  and  navigation,  that  it  has  been 
seriously  proposed  to  provide  for  the  latter  by  separate 
still-water  channels,  made  alongside  of  the  running  canal 
itself. 

In  the  irrigation  districts  in  this  country  there  are 
numerous  instances  of  canals  and  ditches  with  too  great 
a  slope.  In  other  cases  the  woodwork  of  the  drops  has 
been  washed  away  and  not  replaced,  and  by  retrogres- 
sion of  levels  the  fall  at  the  drops  has  been  added  to  the 
original  slope  of  bed,  and  in  this  way  a  velocity  suffi- 
cient to  erode  the  bed  and  banks  has  been  produced. 
The  deep  channeling  has  lowered  the  surface  of  the 
water  to  such  an  extent  that  the  distributing  channels 
have  to  be  deepened  at  their  offtake  in  order  to  obtain 
their  supply. 

In  some  of  the  Indian  canals,  including  the  Upper 
Ganges  and  Jumna  canals,  the  slope,  and  consequently 
velocity  was  too  great,  and  dangerous  erosion  took  place. 
To  prevent  dangerous  channeling,  expensive  repairs 
and  protective  works  had  to  be  undertaken,  with  the 
additional  loss  of  the  canal  for  irrigation  during  the 
period  that  this  work  was  going  on.  In  computing  the 
slope  for  the  Ganges  Canal,  Sir  Proby  Cantley  used  the 
formula  of  Dubuat.  This  formula  was  often  used  in 
canal  work  at  this  time,  but  it  is  now  known  to  be  unre- 


OTHER    IRRIGATION    WORKS.  37 

liable,  especially  for  large  canals.  After  the  admission 
of  water  into  the  canal  it  was  found  that  the  velocity 
exceeded  that  originally  contemplated.  It  was  dangerous 
to  the  works  and  a  great  hindrance  to  navigation.  Some 
years  after  the  canal  was  in  operation  Major  J.  Crofton, 
R.  E.,  was  appointed  to  prepare  plans  for  remodeling 
the  canal.  He  made  observations  on  the  velocity  in  the 
canal,  and  also  collected  data  on  the  same  subject,  which 
is  herewith  given  from  his  report. 

In  a  portion  of  the  channel  of  the  Eastern  Jumna  Canal 
lying  in  the  old  bed  of  the  Muskurra  torrent,  where  the  cur- 
rent seemed  perfectly  adjusted  to  a  light,  sandy  soil, 
Major  Brownlow,  the  Superintendent  of  the  canal,  found 
the  velocities  of  the  surface  to  be  from  2.38  to  2.28  feet 
per  second,  or  mean  velocities  (multiplying  by  0.81), 
1.928  to  1.847  feet  per  second. 

In  the  lower  district  of  the  same  canal,  near  Barote 
.and  Deola,  the  maximum  surface  velocities,  with  a  fair 
supply,  were  found  to  be  2.817  and  2.507  feet  per  second, 
or  mean  velocity  of  2.282  and  2.03  feet  per  second.  Silt 
is  constantly  being  deposited  here. 

About  1,000  feet  below  the  Ghoona  Falls,  on  the 
same  canal,  in  very  sandy  soil,  with  nearly  a  full  supply 
of  water,  the  maximum  surface  velocity  was  3.077  feet 
per  second;  no  erosion  from  bed  or  banks,  except  when 
-a  supply,  much  in  excess  of  the  maximum  allowed,  is 
passing  down. 

Below  the  Nyashahur  bridge  on  the  same  canal,  where 
the  soil  is  clay,  shingle  and  small  bowlders,  Lieutenant 
Moncrieff,  K.  E.,  found  the  mean  surface  velocity  to  be 
6.75  feet  per  second,  or  the  mean  velocity  about  5.47  per 
second.  The  same  officer  observed  the  surface  velocity 
at  some  distance  below  the  Yarpoor  Falls  in  the  new 
center  division  channel  of  the  Eastern  Jumna  Canal, 
and  obtained  a  mean  of  3.96  feet  per  second,  or  about 


38  IRRIGATION    CANALS    AND 

3.21  feet  per  second  mean  velocity  through  entire  sec- 
tion. The  soil  here  is  light  and  sandy,  and  the  channel 
has  been  both  widened  and  deepened  by  the  current. 

In  one  of  the  rajbuhas,  or  main  water-courses  of  the 
same  canal,  weeds  were  found  growing  in  the  bed  and 
on  the  sides  with  a  maximum  surface  velocity  of  2.12 
feet  per  second,  or  mean  velocity  of  about  1.72  feet  per 
second.  The  soil  is  sandy  with  a  fair  admixture  of  clay; 
silt  accumulates  to  a  troublesome  extent. 

In  another  rajbuha  (lateral  or  distributary),  in  the 
same  neighborhood,  a  surface  velocity  of  2.38  feet  per 
second,  or  mean  about  1.93  feet  per  second  was  found. 
Silt  deposits  here,  but  no  weeds  appear  to  grow. 

In  the  Mahmoodpoor  left  bank  rajbuha  of  the  Ganges 
Canal,  grass  and  weeds  were  found  growing  in  the  chan- 
nel with  a  maximum  surface  velocity  of  1.72  feet  per 
second,  or  mean  of  1.4  feet  per  second. 

In  the  Buhadoorabad  Lock  channel,  Ganges  Canaly 
weeds  appear  to  grow  wherever  the  maximum  surface 
velocity  is  2.38  feet,  or  mean  velocity  1.93  feet  or  under. 
Soil  generally  light  and  sandy. 

On  the  Ganges  Canal  velocities  were  found  as  follows: — 
Below  the  Roorkee  bridge  on  the  main  canal,  where  the 
deepened  bed  is  covered  with  silt,  and  erosion  from  the 
sides  has  ceased,  the  mean  velocity  in  the  entire  section 
was  2.92  feet  per  second;  the  soil  sandy  with  a  tolerable 
admixture  of  clay. 

In  the  widened  channel  at  the  Toghulpoor  sand  hills, 
36th  mile,  the  mean  velocity  with  full  supply  was  2.53 
feet  per  second. 

In  the  embanked  channel  across  the  Solani  valley, 
with  a  supply  of  two  inches  under  the  present  maximum 
on  the  Roorkee  gauge,  the  mean  velocity,  obtained  by 
calculation  from  the  area  of  the  water  section  there  and 
the  observed  discharge  through  the  masonry  aqueduct, 


OTHER    IRRIGATION    WORKS  39 

was  3.04  feet  per  second.  The  deepest  portions  of  the 
channeling  out  here  have  been  silted  up. 

At  the  50th  mile,  main  line,  below  the  Jaolee— falls, 
with  present  full  supply  in  the  canal,  the  observed  mean 
velocity  was  3.06  feet  per  second.  Erosion  from  the 
banks  has  ceased  here;  silt  on  the  deepened  bed,  soil 
sandy. 

Above  Newarree  bridge,  94th  mile,  in  a  stiff  clay  soil, 
with  full  supply  in,  the  observed  mean  velocity  was  4.12 
feet  per  second.  Erosion  trifling  here;  no  silt  deposit. 

Observations  communicated  by  Colonel  Dyas,   R.  E.,   Di- 
rector of  Canals,  Punjab. 

On  the  Hansi  branch  of  the  Western  Jumna  Canals, 
silt  was  deposited  with  mean  velocities  of  from  2  to 
2.25  feet  per  second.  The  deposition  of  the  silt,  how- 
ever, obviously  depends  on  the  quantity  and  specific 
gravity  of  the  matter  held  in  suspension  by  the  water 
coming  from  above,  and  the  ratio  of  the  current  veloc-1 
ities  at  different  points  along  the  channel.  He  states 
from  observations  on  the  channels  of  the  Baree  Doab 
Canal,  that  in  sandy  soil: — 

11  2.7  feet  per  second  appears  to  be  the  highest  mean 
velocity  for  non-cutting  as  a  general  rule,  for  there  are 
soft  places  where  the  bed  will  go  with  almost  any  veloc- 
ity; but  those  sorts  of  places  can  be  protected." 

Again  he  states: — 

. "  Bad  places  might  be  scoured  out  with  a  mean  velo- 
city of  2.5  feet  per  second,  but  better  soil  would  be  de- 
posited in  place  of  the  bad  with  a  slightly  smaller  velo- 
city than  2.5  feet;  and,  as  the  supply  is  not  always  full, 
there  would  be  no  fear  of  not  getting  that  slightly  smaller 
velocity  very  frequently.  The  good  stuff  thus  deposited 
would  not  be  moved  again  by  any  velocity  which  did 
not  exceed  2.5  per  second/' 


40  IRRIGATION    CANALS    AND 

In  Neville's  Hydraulics,  0.83  to  1.17  feet  per  second 
are  mentioned  as  the  lowest  mean  velocities  which  will 
prevent  the  growth  of  weeds.  This,  however,  will  vary 
with  the  nature  of  the  soil;  vegetation  also  is  much  more 
rapid  and  vigorous  in  a  tropical  climate  than  that  where 
Mr.  Neville  made  his  observations. 

In  Captain  Humphrey's  and  Lieutenant  Abbott's  re- 
port on  the  Mississippi,  1860,  it  is  mentioned  that  the 
alluvial  soil  near  the  mouth  of  the  river  cannot  resist  a 
mean  velocity  of  3  feet  per  second;  and  that  in  the 
Bayou  LaFourche,  the  last  of  its  outlets,  which  resembles 
an  artificial  channel  in  the  regularity  of  its  section  and 
general  direction,  and  the  absence  of  eddies,  etc.,  in  the 
stream,  the  mean  velocity  does  not  exceed  3  feet  per  sec- 
ond, and  the  banks  are  not  abraded  to  any  perceptible 
extent. 

From  the  foregoing  and  other  observations,  and  tak- 
ing into  consideration  that  the  higher  the  velocity  the 
less  the  works  will  cost,  the  following  may  be  taken  as 
safe  mean  velocities  with  maximum  supply  in  the  (re- 
modeled) Ganges  Canal  channels: — 

1.  In  the  Ganges  valley  above  Roorkee,   3  feet  per 
second. 

2.  In  the  sandy  tract  generally  between  Roorkee  and 
Sirdhana,  2.7  feet  per  second. 

3.  In  the  very  light  sand,  such  as   that  met  with  at 
the  Toghulpoor  sandhills,  not  higher  than  2.5  feet  per 
second. 

4.  And  for  the   channels  south   of  Sirdhana,  3  feet 
per  second. 

On  the  branches  the  same  data  to  be  assumed  accord- 
ing to  similarity  of  the  soil. 

There  are  soils,  as  Colonel  Dyas  has  noted,  such  as 
light  quicksand,  which  will  not  stand  velocities  of  even 
1  foot  or  1J  feet  per  second,  but  these  are  never  found 


OTHER    IRRIGATION    WORKS.  41 

to  any  great  extent  in  one  place;  erosion  there  can  only 
have  a  local  influence,  and  such  places  can  be  protected 
at  a  trifling  expense.  It  is  channeling  out  on  long  lines 
which  is  to  be  feared. 

Article  13.      Mean,  Surface  and  Bottom  Velocities. 

According  to  the  formula  of  Baziii — 


vb  =v— 10.87  i/rs.  In.  which  i;=mean 
velocity  in  feet  per  second. 

vmax  —  Maximum  surface  velocity  in  feet  per  second. 

t>b  r=  Bottom  velocity  in  feet  per  second , 

r  =  hydraulic  mean  depth  in  feet  and 

s  =  sine  of  slope. 

Rankine  states  that  in  open  channels,  like  those  of 
rivers,  the  ratio  of  v  to  v  is  given  approximately 
by  the  following  formula  of  Prony  in  feet  measures: — 

f<W-i-    7.71 

^"^max          :"~TT(T28 

The  least  velocity,  or  that  of  the  particles  in  contact 
with  the  bed,  is  almost  as  much  less  than  the  mean  ve- 
locity as  the  greatest  velocity  is  greater  than  the  mean. 

Rankine  also  states  that  in  ordinary  cases  the  veloci- 
ties may  be  taken  as  bearing  to  each  other  nearly  the 
proportions  of  3,  4  and  5.  In  very  slow  currents  they 
are  nearly  as  2,  3  and  4. 

The  deductions  of  Dubuat  are  that  the  relation  of  the 
velocity  of  the  surface  to  that  of  the  bottom  is  greatest 
when  the  mean  velocity  is  least:  that  the  ratio  is  wholly 
independent  of  the  depth:  the  same  velocity  of  surface 
always  corresponds  to  the  same  velocity  of  bed.  He 


42  IRRIGATION    CANALS    AND 

observed,  also,  that  the  mean  velocity  is  a  mean  pro- 
portional between  the  velocity  of  the  surface  and  that 
of  the  bottom. 

As  the  result  of  his  experience  on  rivers  of  the  largest 
class,  M.  Revy  arrived  at  the  following  conclusions: — 

1.  That,  at  a  given  inclination,  surface  currents  are 
governed  by  depths  alone,  and   are  proportional  to  the 
latter. 

2.  That  the  current  at  the  bottom  of  a  river  increases 
more  rapidly  than  that  at  the  surface. 

3.  That  for  the  same  surface  current  the  bottom  cur- 
rent will  be  greater  with  the  greater  depth. 

4.  That  the  mean  current  is   the  actual  arithmetic 
mean  between  that  at  the  surface  and  that  at  the  bottom. 

5.  That  the  greatest  current  is  always  at  the  surface, 
and  the  smallest  at  the  bottom;  and  that  as  the  depth 
increases,  or  the  surface  current  becomes  greater,  they 
become  more  equal,  until,  in  great  depths  and   strong 
currents,  they  practically  become  substantially  alike. 

Article    14.      Mean   Velocities   from   Maximum   Surface 

Velocities. 

Bazin  has  given  a  very  useful  formula  for  gauging 
channels,  by  means  of  which  the  mean  velocity  can  be 
found  from  the  hydraulic  mean  depth  and  the  observed 
maximum  surface  velocity.  For  measures  in  feet  this 
formula  is: — 

c  X  ^max 
=  c  +  2^4 

Now  let   ci  =         c         and 
c  -H  2o.4 

v  =  ci  X  vm&K 

The  following  table  will  be  found  of  great  service  in 
saving  time,  when  using  this  formula: — 

v=Ci  X  vma,. 


OTHER    IRRIGATION    WORKS. 

TABLE  8.     Giving  values  of  cr 


43 


Value  of  cx. 

Hydraulic 

~  •  —  =. 

mean  depth  in 

For  very  even  sur- 
faces, fine  plas- 

For   even    sur- 
faces, such  as  cut 

For  slightly  un- 
even surfaces, 

For  uneven  sur- 

feet r. 

tered  sides  and 

stone,  brickwork, 

such  as  rubble 

faces,  such  as 

bed,  planed 

unplaned  plank- 

masonry :  — 

planks,  etc:  — 

ing,  mortar,  etc.:  — 

earth:— 

0.5 

.84                        .81 

.74 

.58 

0.75 

.84                        .82 

.76 

.63 

1.0 

.85 

.82 

.77 

.65 

1.5 

.85 

.82 

.78 

.69 

2.0 

.85 

.83 

.79 

.71 

2.5 

.85 

.83 

.79 

.72 

3.0 

.85 

.83 

.80 

.73 

3.5 

.85 

.83 

.80 

.74 

4.C 

.85 

.83 

.81 

.75 

5.0 

.85 

.83 

.81 

.76 

6.0 

.85 

.84 

.81 

.77 

7.0 

.85 

.84 

.81 

.78 

8.0 

.85 

.84 

.81 

.78 

9.0 

.85 

.84 

.82 

.78 

10. 

.85 

.84 

.82 

.78 

11. 

.85 

.84 

.82 

.78 

12. 

.85 

.84 

.82 

.79 

13. 

.85 

.84 

.82 

.79 

14. 

.85 

.84 

.82 

.79 

15. 

.85 

.84 

.82 

.79 

16. 

.85 

.84 

.82 

.79 

17. 

.85 

.84 

.82 

.79 

18. 

.85 

.84 

.82 

.79 

19. 

.85 

.84 

.82 

.79 

20. 

.85 

.84 

.82 

.80 

Article  15.     Destructive   Velocities. 

Kutter  (translation  by  Jackson)  states: — 
"  The  maximum  velocities  determined  by  Dubuat,  as 
suitable  to  channels  in  various  descriptions  of  soil,  are 
taken  from  Morin's  'Aide  Memoire  de  Mecanique  Pra- 
tique', page  63,  1864.  The  first  column  in  the  follow- 
ing table  gives  the  safe  bottom  velocity,  and  the  second 
the  mean  velocity  of  the  cross-section;  the  formula  by 
which  these  are  calculated  is: — 


v  =  y ,  -j-  10.87  i   rs 


44  IRRIGATION    CANALS    AND 

TABLE  9.     Giving  safe  bottom  and  mean  velocities  in  channels. 


Material  of  Channel. 

Safe 
Bottom  velocity  vb, 
in  feet  per  second. 

Mean  velocity  v,  in 
feet  per  second. 

Soft  brown  earth  
Soft  loam  . 

0.249 
0  499 

0.328 
0.656 

Sand  .                                       ... 

1  000 

1.312 

Gravel  

1.998 

2.625 

Pebbles 

2  999 

3.938 

Broken  stone,  flint  

4.003 

5.579 

Conglomerate   soft  slate 

4.988 

6  564 

Stratified  rock  

6  006 

8.204 

Hard  rock.           

10.009 

13.127 

"  We  (Ganguillet  and  Kutter)  are  unable,  for  want  of 
observations,  to  judge  how  far  these  figures  are  trust- 
worthy. The  inclinations  certainly  have  no  influence 
in  this  case,  as  the  corresponding  velocities  are  mutu- 
ally interdependent,  but  the  variation  of  the  depth  of 
water  is  most  probably  of  consequence,  and  in  shallower 
depths  the  soil  of  the  bottom  is  possibly  less  easily  and 
rapidly  damaged  than  in  greater  depths,  under  similar 
conditions  of  soil  and  of  inclination.  Yet  this  effect  is 
not  very  large,  while  that  of  the  actual  velocity  of  the 
water  is  of  the  highest  importance.  Hence,  it  appears 
that  these  figures  may  be  assumed  to  be  rather  dispro- 
portionately small  than  too  large,  and  we  therefore  rec- 
ommend them  more  confidently." 

Mr.  John  Neville,  in  his  hydraulic  tables,  states  that 
for  the  materials  given  in  the  following  table  the  mean 
velocity  per  second  should  not  exceed — 

0.42  feet  in  soft  alluvial  deposits. 


OTHER    IRRIGATION    WORKS. 


0.67  feet  in  clayey  beds. 

1.0  feet  in  sandy  and  silty  beds. 

2.0  feet  in  gravelly  earth. 

3.0  feet  in  strong  gravelly  shingle. 
-  4.0  feet  in  shingly. 

5.0  feet  in  shingly  and  rocky. 

6.67  feet  and  upwards  in  rocky  and  shingly. 

The  beds  of  rivers  protected  by  aquatic  plants,  how- 
ever, bear  higher  velocities  than  this  table  would  as- 
sign, up  to  2  feet  per  second. 

Water  flowing  at  a  high  velocity  and  carrying  large 
quantities  of  silt,  sand  and  gravel  is  very  destructive  to 
channels,  even  when  constructed  of  the  best  masonry. 

The  Deyrah  Doon  water-courses  in  India  had  chan- 
nels of  sections  varying  from  5x2  feet  to  10  x  4  feet,  and 
with  slopes  varying  from  50  feet  to  80  feet  per  mile. 
They  were  almost  all  of  masonry,  and  had  numerous 
masonry  falls  from  5  to  6  feet  in  depth  on  them,  and 
they  passed  over  numerous  and  long  aqueducts.  The 
following  table  shows  the  mean  velocity  in  these  chan- 
nels, computed  by  Kutter's  formula  with  n  =.015. 

TABLE  10.     Giving  dimensions,  grades  and  velocities  of  masonry  channels. 


DIMENSIONS  OF  CHANNEL. 

Slope  in  feet 
per  rnile. 

Velocity  in  feet 
per  second. 

Width  in  Feet. 

Depth  in  Feet. 

5 

2 

50 

10.3 

5 

2 

80 

13.0 

10 

4 

50 

16.5 

10 

4 

80' 

20.9 

Before  measures  were  taken  to  protect  the  channels 
the  water  rushed  down  along  their  course  with  a  tre- 


46  IRRIGATION    CANALS    AND 

meiidous  velocity,  and  carrying  large  quantities  of  sand 
and  gravel,  and  the  abrasion  injured  all  the  masonry 
works  on  the  line.  The  silt-laden  water  acted  even  more 
injuriously,  as,  impelled  by  the  great  velocity,  it  cut 
into  the  masonry  with  an  action  like  that  of  emery 
powder.  Even  to  a  bed  laid  with  large  bowlders,  great 
damage  was  caused:  the  mortar  joints  were  washed  out, 
the  bowlders  lifted  out  of  their  places  and  then  rolled 
along;  the  bed  to  add  to  the  mischief.  But  it  is  to  brick- 

o 

work  that  the  greatest  damage  was  done.  In  fact,  it  re- 
quires but  time  to  make  all  brickwork  disappear  entirely 
in  the  presence  of  such  action.  In  some  of  the  old  canals 
there  was  a  flooring  of  brick  on  edge  over  the  arches  of 
the  aqueducts.  On  one  of  these  aqueducts  not  only  was 
the  foot  in  depth  of  the  brick  floor  entirely  cut  through, 
but  deep  ruts  were  formed  in  the  arch  itself.  But  it  was 
on  the  falls,  which  were  all  formerly  built  after  the  ogee 
pattern,  and  of  brick,  that  the  damage  was  greatest,  as 
might  be  expected.  Their  surfaces  were  cut  into  deep 
striae,  and  they  were  in  constant  need  of  repairs,  which 
were  difficult  to  execute. 

It  was,  therefore,  important  to  keep  the  silt  out,  and 
this  was  done  by  building  silt  traps  on  the  line  of  the 
canal.  * 

Except  in  storm  sewers,  which  flow  for  only  a  short 
period  every  year,  the  mean  velocity  in  sewers  is  usually 
kept  below  five  feet  per  second. 

Colonel  Medley,  R.  E.,  had  considerable  opportuni- 
ties of  observing  the  abrading  power  of  silt-laden  water 
on  the  Ganges  Canal,  India;  and  in  the  "  Roorkee 
Treatise  on  Civil  Engineering  "  he  writes  thus: — 

"  Brickwork  should  not  be  used  in  contact  with  cur- 


*  Mr.  R.  E.  Forrest,  iii  the  first  volume  of  the  Professional  Papers  on. 
Indian  Engineering. 


OTHER    IRRIGATION    WORKS. 


47 


rents  with  such  high    velocities   (15   feet   per  second). 
Even  the  very  best  brickwork  cannot  stand  the  Wear  and 
tear  for  any  length  of  time,  and  stone  should  he— used 
for  all  surfaces  in  contact  with  velocities  exceeding,  say, 
10  feet  per  second." 

Article  16.     Velocity  Increases  with  Increase  of  Depth 

of  Channel. 

The  following  table  is  given  in  order  to  show  that,  in 
the  channels  usually  adopted  for  irrigation,  the  velocity 
increases  with  the  increase  of  depth.  The  channel  50 
feet  wide  will,  with  a  depth  of  two  feet,  deposit  silt;  at  a 
velocity  of  about  1.6  feet  per  second,  but  with  a  depth  of 
five  feet  and  a  velocity  of  about  2.9  feet  per  second,  it 
will  keep  itself  clear  of  deposit. 

N  =.0275.     Side  slopes  1  to  1. 

TABLE  11.     Giving  dimensions,  grades  and  velocities  of  channels. 


Bed  Width  10  Feet. 

Bed  Width  50  Feet. 

Bed  Width  100  Feet. 

Depth  in  Feet. 

Slope  1  in  1000. 

Slope  1  in  2500. 

Slope  1  in  5000. 

Velocity  in  Feet  per 
Second. 

Velocity  in  Feet  per 
Second. 

Velocity  in  Feet  per 
Second. 

2. 

2.173 

1.582 

1.136 

3. 

2.756 

2.084 

1  .  520 

3.5 

3.002 

2.302 

1.692 

4. 

3.221 

2.511 

1.856 

4.5 

3.440 

2.701 

2.007 

5. 

3.634 

2.878 

2.150 

48  IRRIGATION    CANALS    AND 

Article  17.     Abrading  and  Transporting  Power  of  Water. 

Professor  J.  LeConte,  in  his  "Elements  of  Geology/' 
states: — 

"  The  erosive  power  of  water,  or  its  power  of  overcom- 
ing cohesion,  varies  as  the  square  of  the  Velocity  of  the 
current. 

"  The  transporting  power  of  a  current  varies  as  the 
sixth  power  of  the  velocity.  *  *  *  If  the  velocity, 
therefore,  be  increased  ten  times,  the  transporting  power 
is  increased  1,000,000  times.  A  current  running  three 
feet  per  second,  or  about  two  miles  per  hour,  will  move 
fragments  of  stone  of  the  size  of  a  hen's  egg,  or  about 
three  ounces  weight.  It  follows  from  the  above  law  that 
a  current  of  ten  miles  an  hour  will  bear  fragments  of 
one  and  a  half  tons,  and  a  torrent  of  twenty  miles  an 
hour  will  carry  fragments  of  100  tons.  We  can  thus 
easily  understand  the  destructive  effects  of  mountain 
torrents  when  swollen  by  floods. 

"  The  transporting  power  of  water  must  not  be  con- 
founded with  its  erosive  power.  The  resistance  to  be 
overcome  in  the  one  case  is  weight,  in  the  other,  cohe- 
sion; the  latter  varies  as  the  square;  the  former  as  the 
sixth  power  of  the  velocity. 

"  In  many  cases  of  removal  of  slightly  cohering  mate- 
rial, the  resistance  is  a  mixture  of  these  two  resistances, 
and  the  power  of  removing  material  will  vary  at  some 
rate  between  v2  and  v6." 

Silt,  sand,  gravel  and  stones  lose  as  much  weight  in 
water  as  a  volume  of  water  having  an  equal  cubic  con- 
tent, which  is  generally  about  equal  to  half  their  weight 
in  air.  They  are,  therefore,  easily  moved,  but,  with  the 
exception  of  silt,  their  velocity  is  less  than  that  of  the 
current,  and  the  nearer  their  specific  gravity  approaches 
that  of  water  the  nearer  their  velocity  approaches  that  of 
the  current. 


OTHER    IRRIGATION    WORKS. 


49 


The  English  Astronomer  Royal,  in  a  discussion  at  the 
Institution  of  Civil  Engineers,  said  that  the  formula  for 
the  transporting  power  of  water,  was  the  only  instance  in 
physical  science,  with  which  he  was  acquainted,  in  which 
the  sixth  power  came  really  into  application. 

Mr.  T.  Login,  C.  E.,  states  as  the  result  of  his  obser- 
vations for  several  years,  on  the  Ganges  Canal  and  other 
channels,  that  the  abrading  and  transporting  power  of 
water  increases  in  some  proportion  as  the  velocity  in- 
creases, but  decreases  as  the  depth  decreases. 

Umpfenback  gives  the  size  of  materials  that  will  be 
moved  in  the  botton  of  small  streams,  at  the  following 
figures: — 

TABLE  12.     Giving  the  transporting  power  of  water. 


Surface  Velocity 
in  Metres. 

Gravel,  Diameter  in 
Metres. 

Surface  Velocity 
in  Feet. 

Gravel,  Diameter  in 
Feet. 

0.942 

0.026 

3.091 

0.085 

1.569 

0.052 

5.148 

0.170 

Cubic  Metres. 

Cubic  Feet. 

2.197 

0.00515 

7.208 

0.182 

3.138 

0.209 

10.296 

0.738 

4.708 

0.618 

15.447 

21.826 

Chief  Engineer    Sainjon    made    observations    in   the 
River  Loire  in  France,  with  the  following  results: — 

Velocity  of  feet  per  second,       1.64       3.28       4.92     6.56 
Diameter  of  stone  in  feet,         0.034     0.134     0.325     0.56 

In  order  to  protect  the  foundations  of  the  Ravi  bridge, 

in  India,  15-inch  concrete  cubes  (1.56  cubic  feet),  were 

deposited  around  the  piers.     It   was   noted  in  one  case, 

that  with  a  velocity  of  probably  not  less  than  10  feet  a 

4 


50  IRRIGATION    CANALS    AND 

second,  the  blocks  were  moved  from  a  sandy  bottom  on 
to  a  level  brick  floor  protecting  the  bridge.  Although 
exposed  to  a  more  violent  current  they  were  not  moved 
off  the  flooring.  This  evidence  is  somewhat  in  proof  of 
Smeaton's  experience,  that  quarry  stones  of  about  half  a 
cubic  foot,  were  not  much  deranged  by  a  velocity  of  11 
feet  per  second,  although  the  soil  was  washed  from  under 
them. 

Experiments  made  by  Mr.  T.  E.  Blackwell,  C.  E.,  for 
the  British  Government,  in  the  plan  of  the  Main  Drain- 
age of  London,  show  very  clearly  that  the  specific  grav- 
ity of  materials  has  a  marked  effect  upon  the  mean  ve- 
locities necessary  to  move  bodies. 

For  example,  coal  of  a  specific  gravity  of  1.26,  com- 
menced to  move  in  a  current  of  from  1.25  to  1.50  feet 
per  second. 

A  second  sample  of  coal,  of  specific  gravity  1.33,  did 
not  commence  to  move  until  the  velocity  was  1.50  to 
1.75  feet  per  second. 

A  brickbat  of  specific  gravity  2.0,  and  chalk  of  specific 
gravity  2.05,  required  a  velocity  of  1.75  to  2  feet  per 
second  to  start  them. 

Oolite  stone,  specific  gravity  2.17;  brickbat,  2.12; 
chalk,  specific  gravity  2.0;  broken  granite,  specific  grav- 
ity 2.66,  required  a  velocity  of  2.0  to  2.25  feet  per  second 
to  start  them. 

Chalk,  specific  gravity  2.17;  brickbats,  specific  gravity 
2.18;  limestone,  specific  gravity  1.46,  required  a  veloc- 
ity of  from  2.25  to  2.50  feet  per  second  to  start  them. 

Oolite  stone,  specific  gravity  2.32;  flints,  specific  grav- 
ity 2.66;  limestone,  specific  gravity  3.00,  required  a  ve- 
locity of  2.5  to  2.75  to  start  them. 

It  was  shown  in  these  experiments  that  after  the  start 
of  the  materials  with  the  current,  in  no  case  did  the  ma- 
terials to  be  transported  travel  at  the  same  rate  as  the 


OTHER    IRRIGATION    WORKS.  51 

stream,  but  in  every  case  their  progress  was  considerably 
less,  as  a  rule,  often  more  than  50  per  cent,  less  than  the 
velocity  of  the  current. 

Mr.  Baldwin  Latham,  C.  E.,  in  the  course  of  his  ex- 
perience in  sewerage  matters,  has  found  that  in  order  to 
prevent  deposits  of  sewage  silt  in  small  sewers  or  drains, 
such  as  those  from  6  inches  to  9  inches  diameter,  a  mean 
velocity  of  not  less  than  3  feet  per  second  should  be 
produced.  Sewers  from  12  to  24  inches  diameter  should 
have  a  velocity  of  not  less  than  2^  feet  per  second,  and 
in  sewers  of  larger  dimensions  in  no  case  should  the 
velocity  be  less  than  2  feet  per  second. 

Sir  John  Leslie  gives  the  formula: — 

v  =  4  i/ a  for  finding  the  velocity  required  to   move 

rounded  stones  or  shingle,  in  which 

v  =  velocity  of  water  in  miles  per  hour,  and 

a  =  the  length  of  the  edge  of  a  stone  if  a  cube  in  feet, 

or  the  mean  diameter  if  a  rounder  stone  or  bowlder,  also' 

in  feet. 

This  formula  takes  no  note  of  specific  gravity.  Chailly 
has  supplied  this  omission,  and  he  has  derived  the 
following  formula,  which  is  just  sufficient  to  set  bodies 
in  motion: — 

v  =  5.67  i/ag,  in  which 

a  =  average  diameter  of  the  body  to  be  moved  in  feet, 

g  —  its  specific  gravity,  and 

v  =  velocity  in  feet  per  second. 

Experience  on  the  irrigation  canals  in  Northern  India, 
where  rapids  are  in  use,  has  proved  that  a  bowlder 
rapid,  with  a  flooring  composed  of  bowlders  not  less  than 
eighty  pounds  in  weight  each,  well  packed  on  end,  and 
at  a  slope  of  1  in  15,  will  not  stand  a  mean  velocity  of 
17.4  feet  per  second. 


52  IRRIGATION    CANALS    AND 

Article  18.     On  Keeping  Irrigation  Canals  clear  of  Silt. 

BY  E.  B.  BUCKLEY,  C.  E. 

(Extracted  from  Proceedings  of  the  Institution  of  Civil  Engineers, 
Volume  LVIII.) 

There  are  four  methods  by  which  it  is  possible  to  ex- 
clude more  then  a  desirable  proportion  of  silt  from  en- 
tering an  irrigation  system: — 

1.  By  works  in  the  river,  which  will  clear  the  water 
before  it  enters  the  canal. 

2.  By  so  constructing  the   head-sluice   of  the  canal 
that  only  water  bearing  the  desired  proportion  of  silt  is 
admitted. 

3.  By  constructing  a  depositing  basin  near  the  head 
of,  and  in  the  canal  itself,  to  be  cleared  either  by  dredg- 
ing or  by  hand  labor;  or,  what  is  practically  the  same 
thing,  by  making  two   supply  canals  from  the  river  to 
the  canal,  one  to  be  used  while  the  other  is  being  cleansed. 

4.  By  constructing  a  double  row  of  sluices,  with  a 
settling    tank  between,   so  arranged  that  the    water  is 
drawn    off    from   the   lower   row    carrying    the    desired 
amount  of  silt,  and  so  designed  that  the   deposit  in  the 
tank  can  be  flushed  back  again  into  the  river. 

These  systems  are,  of  course,  applicable  under  differ- 
ent circumstances.  The  first  can  be  rarely  used,  and 
only  when  the  local  conditions  are  suitable.  As,  for 
example,  when  the  bed  of  an  inundation  canal  is  per- 
haps 8  feet  or  10  feet  above  the  level  of  the  bed  of  the 
river,  and  which  canal  is  therefore  only  supplied  when 
the  river  is  in  flood.  In  such  a  case,  if  a  position  for 
the  head  of  the  canal  can  be  selected  behind  an  island 
covered  with  brushwood,  the  top  of  which  is  perhaps  a 
little  below,  or  even  slightly  above  the  high  flood  level, 
it  may  be  well  worth  the  cost  to  make  an  artificial  con- 


OTHER    IRRIGATION    WORKS.  53 

nection  between  the  head  of  the  island  and  the  main 
land,  so  that  all  the  water  entering  the  canal  will  first 
flow  through  the  bay,  found  between  the  island  anxLthe 
main  land,  entering  that  bay  from  below.  The  velocity 
of  water  in  the  bay  will  thus  be  diminished;  the  water 
will  deposit  silt  in  the  bay  instead  of  carrying  it  into 
the  canal;  and  if  the  bay  be  a  large  one  the  canal  may 
work  for  many  years  without  its  bed  silting  up. 

The  same  principles  can  be  employed  on  large  irriga- 
tion schemes,  by  altering  the  methods  now  generally 
adopted  on  these  works.  The  almost  invariable  arrange- 
ment is  that  the  weir  which  stretches  across  the  river, 
at  a  height  of  from  8  feet  to  15  feet  above  the  bed,  is 
cut  by  two  sets  of  under-sluices,  which  are  purposely  set 
as  close  as  possible  to  the  head-sluices  of  the  canal  im- 
mediately above  the  weir;  the  floors  of  the  head-sluices 
and  of  the  under-sluices  being  at  the  same  level.  The 
under-sluices  are  placed  in  this  position  so  that  silt  may 
not  accumulate  in  front  of  the  entrances  to  the  canal,' 
and  thus  impede  the  free  entrance  of  boats  to  the  lock, 
and  of  water  to  the  canal.  This  object  is  attained  by 
opening  the  under-sluices  during  floods,  thus  drawing 
down  a  rapid  stream  immediately  in  front  of  the  opening 
to  the  canals,  which  scours  the  channel  and  removes 
any  deposit  that  may  have  accumulated.  At  the  same 
time  that  the  action  of  the  under-sluices  clears  the  ap- 
proaches to  the  canal,  it  causes  the  canal  to  be  more 
deeply  silted,  for  the  higher  velocity  produced  by  the 
scour  of  the  under-sluices  removes  an  extra  quantity  of 
silt  from  the  bed  of  the  river,  and  it  is  from  this  rapid 
and  silt-bearing  stream,  impinging  directly  on  the  head- 
sluices,  that  the  canal  is  supplied.  But  if  the  weir  were 
constructed  with  a  double  set  of  under-sluices  at  each 
end,  one  set  being  in  the  line  of  the  weir,  and  about  200 
feet  from  the  river  bank,  and  the  other  set  some  dis- 


54  IRRIGATION    CANALS    AND 

tance  lower  down  the  river,  but  connected  to  the  upper 
set  by  a  flank  wall  parallel  to  the  river  bank,  and  if  the 
off-take  of  the  canal  were  placed  immediately  above  the 
lower  set,  the  stream  flowing  to  the  upper  set  would  not 
pass  in  front  of  the  off-take  to  the  canal.  The  silt-bear- 
ing water  would  pass  through  the  upper  set  of  under- 
sluices  with  full  velocity,  while  that  portion  of  the  river 
destined  for  the  canal  would  have  its  velocity  checked, 
immediately  opposite  the  flank  wall,  and  would  deposit 
its  silt  to  a  great  extent  before  it  reached  the  head- 
sluices  of  the  canal.  To  sweep  away  the  silt,  which 
would  be  deposited  between  the  weir  and  the  head- 
sluices,  it  would  be  necessary  to  close  the  upper  under- 
sluices  and  to  work  the  lower  ones.  This  plan  would 
be  rendered  most  effective  by  closing  the  head  of  the 
canal  for  a  few  hours  every  week,  while  the  lower  under- 
sluices  were  opened,  so  that  the  channel  might  be  kept 
clean  without  allowing  any  silt-bearing  water  to  have 
access  to  the  canal. 

In  almost  all  cases  the  head  sluice  of  a  canal  is 
formed  by  rows  of  single  shutters,  sliding  in  verti 
grooves,  so  that  water  is  always  first  admitted  to  the 
canal  from  below  the  shutters,  that  is,  at  a  level  of  the 
sluice  floor.  If  the  sluices  were  constructed  so  that  the 
water  was  drawn  from  the  top  instead  of  from  the  bot- 
tom of  the  river,  much  less  silt  would  be  carried  into 
the  canal.  In  rivers  which  rise  moderately  it  is  best  to 
have  a  single  opening  in  each  vent,  covered  by  three  or 
four  shutters  sliding  in  a  vertical  groove;  and  each  of 
these  shutters  should  have  independent  opening  gear. 
In  rivers  liable  to  floods  rising  30  feet  it  is  necessary  to 
have  in  each  vent  of  the  sluices,  several  openings  at  dif- 
ferent levels,  each  opening  being  fitted  with  an  inde- 
pendent shutter,  so  that  water  can  be  drawn  off  at  dif- 
ferent levels  as  the  flood  rises  or  falls.  This  way  of 


OTHER    IRRIGATION    WORKS.  55 

dealing  with  the  silt  can  at  most  be  but  partially  effect- 
ive, but  there  are  some  rivers,  carrying  a  small  amount 
of  silt,  to  which  this  system  may  be  applied  with- suffi- 
cient effect  to  render  the  clearance  of  silt  from  the  canal 
unnecessary. 

The  third  method  is  frequently  adopted  on  Indian 
canals.  The  first  half  mile  of  the  canal  is  excavated 
with  a  base  sufficiently  large  to  cause  a  great  diminution 
of  velocity;  the  silt  is  deposited  during  floods,  and  ex- 
cavated when  the  canal  is  closed  during  the  summer, 
or  perhaps  it  is  dredged  out  at  a  cost  even  more  exces- 
sive than  that  of  excavating  it  by  hand. 

The  fourth  method  is  peculiarly  suitable  for  rivers  with 
a  rapid  fall.  It  is  also  most  desirable  where  a  canal 
runs  alongside  of  the  river  for  some  distance  before 
branching  off  into  the  country.  If  this  method  be 
adopted,  the  channel  of  the  first  half  mile  or  so  must  be 
of  such  capacity  that  the  velocity  of  the  water  in  it, 
when  carrying  the  full  volume  required  for  the  canal, 
shall  not  exceed  that  which  will  allow  of  the  deposit  of 
the  matter  in  suspension;  so  that  the  water,  when  it 
reaches  the  end  of  this  length,  shall  contain  only  that 
proportion  of  silt  which  the  channels  below  are  arranged 
to  convey  to  the  fields.  At  the  end  of  this  broad  chan- 
nel a  sluice  will  have  to  be  built  to  carry  the  full  dis- 
charge required  in  the  canal  with  little  or  no  head  upon 
it.  The  head  sluice  on  the  river  bank  must  be  designed 
so  that,  with  only  a  moderate  flood  in  the  river,  a  suffi- 
cient quantity  of  water  can  be  introduced  into  the  canal 
to  generate  a  velocity  of  three  to  four  feet  per  second  in 
the  broad  reach,  the  flushing  sluices  leading  back  from 
this  reach  to  the  river  being  arranged  to  discharge  a  cor- 
responding quantity,  or  even  a  larger  quantity  of  water. 
These  sluices  might  be  fitted  with  falling  shutters.  The 
largest  flushing  sluice  should  be  about  150  feet  to  300 


56  IRRIGATION    CANALS    AND 

feet  from  the  head  sluice,  for  it  is  about  this  point  that 
the  heavy  sand  is  deposited  and  where  the  greatest  scour 
would  be  required.  This  system  is  the  most  effective  and 
the  least  expensive  for  large  schemes.  If  the  head  sluice 
on  the  river  bank  be  constructed  on  the  principle  of  tak- 
ing water  from  the  surface  of  the  river,  instead  of  from 
below,  the  minimum  amount  of  silt  will  enter  the  broad 
reach,  and  that  can  under  conditions,  be  cleared  away  by 
closing  the  sluices  at  the  extremity  of  the  broad  chan- 
nel for  a  short  time,  and  opening  all  the  shutters  of  the 
head  sluice  on  the  river  bank  and  the  various  flushing 
sluices. 

Article  19.     Fertilizing  Silt. 

The  quality  of  the  silt  carried  by  water  for  irrigation 
is  a  matter  of  great  importance.  Whilst  in  some  locali- 
ties it  is  of  no  use  to  the  land  as  a  fertilizer,  still,  in  a 
great  number  of  places,  it  acts  as  a  good  manure. 

It  is  well  known  that  for  ages  the  fertility  of  Egypt 
has  been  preserved  by  the  silt-laden  waters  of  the  Nile. 
Every  year  the  Nile  deposits  its  load  of  rich  slime  on 
the  land,  and,  in  consequence  of  this,  the  soil  retains 
the  fertility  for  which  it  has  been  famous  since  the 
earliest  date  of  history.  Such  muddy  water  furnishes 
not  only  moisture  to  bring  the  crop  to  perfection,  but  it 
also  brings  manure  to  the  land,  and  thus  prevents  it 
from  being  exhausted.  The  silt  annually  deposited  is 
merely  manure,  which  is  consumed  in.  bringing  the 
crops  to  maturity.  This  is  the  reason  that  the  land  has, 
for  so  many  centuries,  remained  within  reach  of  the 
Nile  flood. 

In  Upper  Egypt  large  depositing  basins,  to  retain  the 
Nile  silt,  have  been  in  use  from  time  immemorial,  with 
great  success. 


OTHER    IRRIGATION    WORKS.  57 

Sir  B.  Baker,  C.  E.,  states,  respecting  the  fertilizing 
properties  of  the  Nile  water: — 

"  1st.  That  the  fertility  of  the  Nile  is  due  to  thlTor- 
ganic  matter,  and  to  the  salts  of  potash  and  phosphoric 
acid  dissolved  and  suspended  in  it. 

"  2d.  That  these  constituents  are  most  abundant  in 
the  water  during  the  months  of  August,  September  and 
October,  wThen  the  river  is  in  flood;  and  that  it  is  during 
the  period  of  inundation  that  the  sedimentary  matter, 
or  mud,  deposited  from  the  water,  is  most  valuable  as  a 
fertilizing  agent." 

In  Lower  Egypt  these  basins  are  not  used.  The  land 
is  flooded,  but  the  water  flows  off  and  deposits  very 
little  of  its  silt. 

This  is  known  as  the  Improved  System. 

Mr.  "W.  Willcocks,  C.  E.,  in  his  account  of  Irrigation 
in  Lower  Egypt,  states  on  this  subject: — 

"  In  Upper  Egypt,  where  the  old  Pharaonic  system  of ' 
basin  irrigation  exists,  every  acre  of  land  is  cultivated, 
and  pays  revenue,  while  the  soil  is  as  rich  to-day  as  it 
was  thousands  of  years  ago.  In  Lower  Egypt,  on  the 
contrary,  where  the  improved  system  of  irrigation  pre- 
vails, and  a  triple  crop  is  gathered,  one-third  of  the  area 
is  uncultivated,  while  the  remaining  two-thirds  are  in- 
capable of  paying  a  higher  revenue  than  Upper  Egypt. 
The  improved  system,  besides,  has  only  lasted  fifty  years, 
and  yet  there  is  a  cry  of  deterioration  of  the  soil  and 
produce  from  one  end  of  the  country  to  the  other,  a  cry 
which  is  re-echoed  by  English  cotton-spinners.  Nature 
wants  the  slime  of  the  Nile  flood  to  be  deposited  on  the 
land;  it  is  now  forced  into  the  sea;  and  though  it  is  not 
necessary  to  go  to  the  full  extent  of  Napoleon's  state- 
ment, that  wrere  he  master  of  Egypt  he  would  not  allow 
an  ounce  of  slime  to  be  wasted;  yet  it  may  be  stated, 


58  IRRIGATION    CANALS    AND 

without  fear  of  contradiction,  that  for  every  one  pound 
(five  dollars)  of  profit  resulting  from  the  expenditure  of 
one  thousand  pounds  (five  thousand  dollars)  on  the  im- 
provement of  the  existing  irrigation  system,  ten  pounds 
(fifty  dollars)  would  be  the  return  on  money  spent  in  a 
partial  restoration  of  the  basin  system  where  the  lands 
are  cultivated,  and  a  complete  restoration  where  the 
lands  are  not  under  cultivation." 

In  respect  to  irrigation,  there  are  four  kinds  of  water:— 

First,  rain;  this  is  almost  pure,  and  supplies  nothing 
to  the  land  but  moisture.  The  land  dependent  upon  it 
must  be  continually  renewed  by  manure. 

Second,  well  water.  This  also  is  quite  pure,  being 
filtered  through  the  earth,  or,  what  is  worse,  it  is  often 
injured  for  irrigation  by  being  mixed  with  injurious 
minerals,  especially  at  the  end  of  the  dry  season. 

Third,  tank  or  reservoir  water.  This  generally  con- 
tains a  good  deal  of  nourishment  for  plants  in  a  state  of 
solution,  which  it  has  absorbed  in  the  lands  it  has  passed 
over,  but  what  it  has  held  in  suspension  is  almost  all 
deposited  in  the  bed  of  the  tank  before  the  water  is 
drawn  off  for  the  fields. 

Fourth,  river  water.  This  water  is  led  direct  from  the 
rivers  by  canals  to  the  fields.  It  deposits  in  the  chan- 
nels only  the  coarser  parts  of  the  silt  it  has  brought 
down  from  the  higher  lands  and  forests,  much  of  which 
is  only  sand.  A  large  quantity  of  its  most  fertilizing 
silt  is,  however,  conveyed  to  the  land.  80  complete  is 
the  effect  of  this  fertilization,  that  lands  so  supplied 
continue  to  bear  one  or  two  grain  crops  for  hundreds  of 
years  without  other  manure.  Thus  the  district  of  Tan- 
jore,  in  India,  is  believed  to  produce  as  large  crops  now 
as  it  did  2,000  years  ago. 

Different  rivers  are  more  or  less  fertilizing  according 


OTHER    IRRIGATION    WORKS.  59 

as  they  pass  through  different  rocky  strata.  Thus  the 
Kistnah  River,  in  India,  which  passes  through  a  lime- 
stone country,  has  a  delta  which  was  found  to  produce 
crops  50  per  cent,  larger  than  the  delta  of  the  Godavery, 
which  passes  chiefly  through  a  granite  country. 

In  Midnapore,  in  India,  the  rainfall  is  sometimes  as 
much  as  ten  inches  in  twenty-four  hours,  but  the  culti- 
vators are  not  satisfied  with  this.  In  order  to  gain  the 
advantage  of  the  manure  in  the  river  water,  they  drain 
off  the  rain  water  as  quickly  as  possible  and  admit  the 
former  water.  Long  experience  has  proved  to  them 
that  they  get  better  crops  by  irrigating  with  the  silt- 
laden  water  of  the  river  than  by  the  rain  water. 

The  water  of  the  river  Indus,  in  India,  is  preferred  to 
well  water,  owing  to  the  fertilizing  silt  which  it  con- 
tains. 

The  water  of  the  river  Durance,  in  France,  has  a  high 
reputation  for  irrigating  purposes.  In  addition  to  the 
sediment  mechanically  suspended,  it  also  holds  much 
valuable  agricultural  matter  in  solution,  which  is  con- 
sidered the  main  cause  of  the  waters  of  that  river  being 
so  valuable  for  irrigation. 

Mr.  Kilgour,  C.  E.,  in  the  Minutes  of  Proceedings  I. 
C.  E.,  vol.  27,  stated:— 

"  The  silt  in  suspension  in  the  waters  of  the  Punjab 
rivers  in  Northern  India  was  invaluable  as  a  manure  in 
the  district,  where,  owing  to  the  scarcity  of  timber,  the 
dung  of  the  cattle  was  mixed  with  clay,  sun-dried,  and 
employed  as  fuel." 

Mr.  George  Gordon,  C.  E.,  in  a  paper  on  the  storage 
of  water,  published  in  Minutes  of  I.  G.  E.,  vol.  33,  says: — 

"Land  irrigated  from  a  river  gives  a  better  return 
than  that  under  a  tank  by,  it  is  said,  25  per  cent,  in 
these  parts.  Whether  this  is  principally  due  to  the 


60  IRRIGATION    CANALS    AND 

brackish  quality  of  the  water  locally  collected,  or  to  the 
insufficient  supply  from  tanks,  the  author  cannot  say; 
probably  both  causes  contribute." 

General  Scott  Moncrieff,  R.  E. ,  states  that  the  price  paid 
for  the  water  of  the  Po,  in  Italy,  was  three  times  the 
amount  paid  for  the  water  of  the  Dora  Baltea,  the  extra 
value  of  the  water  of  the  Po  being  due  to  the  fact  of  its  allu- 
vial silt  being  considered  highly  fertilizing,  while  that  of 
the  Dora  Baltea  is  rather  the  reverse.  He  also  refers  to 
the  marked  difference  between  the  meadows  irrigated  with 
the  silt-bearing  waters  of  the  Durance  Canals  in  France, 
and  those  of  the  clear,  cold  Sorgues,  so  much  so,  that 
cultivators  prefer  to  pay  for  the  former  ten  or  twelve 
times  the  price  demanded  for  the  latter. 

Mr.  J.  H.  Latham,  C.  E.,  states,  as  the  result  of  his 
observations  in  the  Madras  Presidency,  in  India,  that 
river  channels  are  the  most  prized  of  all  the  sources  of 
supply  for  irrigation  as  they  are  stated  to  give  25  per 
cent,  more  crop  per  acre  than  either  wells  or  tanks. 

Mr.  Allan  Wilson,  C.  E.,  refers  to  the  great  superior- 
ity of  river  and  tank  or  reservoir  water  for  irrigation 
purposes,  as  compared  with  well  and  spring  water,  as  an 
argument  in  favor  of  the  formation  of  river  and  tank 
reservoirs.  He  ascertained  from  observation,  and  the 
experience  of  practical  authorities  in  India,  that  sugar 
cane  watered  from  tanks  and  rivers  yields  a  much  heavier 
crop  than  land  watered  from  wells  and  springs,  and  the 
molasses  produced  from  the  former  realizes  double  the 
price  of  the  latter. 

Mr.  Walter  H.  Graves,  C.  E.,  of  Denver,  Colorado, 
states  that  the  very  means  of  reclaiming  the  arid  land 
is  a  constant  source  of  its  fertilization.  By  irrigation 
the  pores  of  the  most  sterile  soil  can  be  filled  and  com- 
pacted by  the  infiltration  of  the  impalpable  silt,  and  con- 


OTHER    IRRIGATION    WORKS.  61 

verted  into  a  loam  of  prodigious  fertility.  Hence,  as  a 
general  statement,  all  lands  that  can  be  reached  and 
supplied  .with  water  for  irrigation  are  susceptible  ol  cul- 
tivation. 

Mr.  A.  D.  Foote,  C.  E.,  in  his  Report  on  the  Irrigating 
and  Reclaiming  of  Certain  Desert  Lands  in  Idaho,  gives 
full  and  interesting  details  of  crops  grown  on  lands  irri- 
gated by  silt-laden  water,  and  shows  very  plainly  its 
great  value  as  a  fertilizer.  And  in  a  discussion  on  irri- 
gation at  the  American  Society  of  Civil  Engineers  in 
1887,  Mr.  Foote  further  states: — 

"The  fertilizing  silt  which  swift  running  water  usually 
carries  is  eventually  nearly  as  valuable  as  the  water  it- 
self. Without  it  irrigation  in  this  country  would  soon 
be  a  failure.  No  land  can  stand  continual  production 
without  enriching,  and  it  will  be  many  years  before  our 
Far  West  can  afford  the  ordinary  artificial  manures.  The 
silt  with  which  our  western  rivers  is  loaded  in  the  spring 
and  summer  is  so  valuable,  that  the  land  irrigated  by  it 
improves  even  unto  the  heaviest  cropping." 

Mr.  E.  B.  Dorsey,  C.  E.,  quotes  an  Idaho  farmer  as 
having  said: — "  I  would  rather  give  two  dollars  an  acre 
for  muddy  water  than  one  for  clear." 

Mr.  C.  L.  Stevenson,  C.  E.,  Salt  Lake  City,  states  that: — 
"  The  waters  of  irrigation  from  the  mountains  annually 
carry  with  them  fresh  fertilizing  material,  so  that  prac- 
tically it  costs  the  average  Utah  farmer  less  to  keep  up 
his  ditches  and  apply  his  waters  of  irrigation  than  it 
does  the  eastern  farmer  to  manure  his  land.  One  field 
near  Farmingtoii,  at  first  producing  some  sixty  bushels 
per  acre,  was  kept  in  wheat  for  thirty  years  with  no 
other  fertilizer  than  what  was  brought  by  the  waters, 
and  there  was  after  the  second  or  third  year  a  general 
average  yield  of  over  forty  bushels  to  the  acre." 


62  IRRIGATION    CANALS    AND 

As  every  rule  has  an  exception,  so  we  find  an  exception 
to  the  almost  unanimous  opinion  as  to  the  value  of  silt- 
laden  water  for  irrigation. 

Major  J.  Browne,  R.  E.,  in  the  Transactions  of  the 
Institution  of  Civil  Engineers,  volume  33,  states  as  the 
result  of  his  observations  in  the  Punjab,  India,  that: — 
"  He  had  always  understood  from  such  cultivators  as  he 
had  spoken  to,  that  crops  raised  from  well  water  were 
of  a  better  quality  than  those  raised  from  canal  water. 
He  could  not  say  whether  it  was  due  to  the  higher  tem- 
perature of  well  water,  or  to  any  chemical  difference  in  the 
water  itself,  but  canal-raised,  were,  he  believed,  generally 
inferior  to  well-raised  crops." 

It  is  not  unlikely  that  the  cultivators  through  custom, 
as  has  often  been  found  in  India,  adhered  to  their  old 
method  of  well  irrigation. 

Article  20.     Silt  Carried  by  Rivers. 

It  is  sometimes  of  importance  to  know  not  only  the 
quality  of  the  silt  carried  in  suspension  by  a  river,  with 
reference  to  its  utility  as  manure,  but  also  its  quantity. 
This  quantity  varies  greatly  in  different  rivers,  and  also 
at  different  stages  of  the  flood  in  the  same  river.  In 
August  the  Nile  conveyed  three  hundred  times  more 
solids  in  suspension  than  in  May,  although  during  the 
former  month  the  volume  of  water  discharged  was  only 
ten  times  greater  than  in  May,  the  weight  of  solids  in 
suspension  to  the  weight  of  water  being  then  -g-yro-j 
whilst  in  August  it  rose  to  ^4r-  Although  the  volume 
of  water  discharged  in  August  was  one-quarter  less  than 
in  October,  the  suspended  sedimentary  matter  was  three 
times  greater.  In  August  the  weight  of  sediment  at- 
tained its  maximum  of  23,100,000  tons  and  in  October 
with  the  greatly  increased  discharge  the  sediment  de- 


OTHER    IRRIGATION    WORKS.  63 

creased  to  7,600,000  tons,  the  proportion  of  sediment  to 
water  in  August  being  ^T  an(^  in  October  ^Vir- 

The  perennial  flow  of  the  Nile  was  due  to  the  mag- 
nificent lakes  of  Central  Africa,  which  lay  at  its  source; 
while  its  annual  inundation  was  caused  by  the  flooding 
of  the  Atbara  and  Blue  Nile  during  the  rainy  season. 
These  two  tributaries  (although  almost  dried  up  from 
the  end  of  October  to  the  beginning  of  May,  when 
mountainous  Abyssinia  was  as  rainless  as  Egypt,)  were 
mighty  streams  from  the  beginning  of  June  to  the  end 
of  September,  and  the  undoubted  origin  of  the  period- 
ical inundations,  the  unfailing  deposits,  and  the  won- 
derful fertility  of  Lower  Egypt. 

The  Godavery  and  Mahanuddy  in  India  have  a  pro- 
portion about  TTV  m  but  this  is  much  less  than  that  in  the 
Kistiia  and  Indus,  the  quantity  in  the  latter  amounting 
to  nearly  ^  of  its  bulk. 

In  the  Durance  in  France,  with  a  flood  discharge  of 
210,000  cubic  feet  per  second,  the  quantity  of  sediment 
mechanically  suspended  increases  with  the  flow  of  the 
river.  The  ordinary  maximum  is  about  equal  to  ^  of 
the  water  by  weight.  In  exceptional  cases,  as  in  August, 
1858,  the  proportion  was  as  high  as  y1^-  of  the  water  by 
weight.  In  extreme  low  water  the  proportion  by  weight 
is  about  T-o-V(r-  The  average  proportion  for  the  nine 
years,  1867—75,  was  about  ^4o~.  It  is  estimated  that  the 
Durance  transports  annually  to  the  sea  seventeen  mill- 
ion tons  of  earthy  matter.  It  is  stated  that  in  the 
Vistula  in  floods  the  proportion  is  ^-  in  the  Garonne  in 
France  T^  Q-;  in  the  Rhine  in  Holland  T-J-g- ;  and  in  the 
P°  S^TT-  I*1  other  rivers  the  proportion  varies  from  that 
given  above  as  a  maximum  to  TT^TTIT  as  a  dry  weather 
flow. 

Sir  Charles  Hartley,  C.   E.,  has   given   the   following 


64 


IRRIGATION    CANALS    AND 


table  showing  the   principal  characteristics   of   four  of 
the  great  rivers  of  the  world: — 

TABLE  13.     Giving  length,  discharge,  etc.,  of  rivers. 


KlVER. 

Length 
in 

Drainage 
area  in 

Annual 
rainfall  in 

Mean 
annual 
discharge 

Mean 

Mean  weight 
of  dry  sedi- 
ment to 

miles. 

square 
miles. 

cubic 
miles. 

in  cubic 
miles. 

Ratio. 

•weight  of 
water. 

Nile  .  .  . 

3  300 

1  293  000 

892  1 

oo  7 

QO    Q 

i 

l&Off 

Ganges  

1,680 

588,000 

548.8 

43.2 

12.7 

Mississippi  . 

4,190 

1,244,000 

673.0 

132.0 

5.0 

itW 

Danube  .... 

1,750 

316,000 

198.0 

44.3 

4.5 

WsTT 

As  the  central  and  lower  parts  of  the  Nile  flowed 
through  an  exceptionally  dry  and  sandy  region,  it  dis- 
charged, as  shown  on  the  table,  ^¥  of  the  annual  rain- 
fall on  its  catchment  basin,  and  as  regarded  ratio  of 
rainfall  to  discharge,  compared  with  other  rivers,  it  was 
three,  eight  and  nine  times  greater  than  the  Ganges, 
Mississippi  and  Danube  respectively.  Again,  although 
the  Nile  had  about  the  same  drainage  area  as  the  Mis- 
sissippi, its  annual  rainfall  was  30  per  cent,  greater, 
whilst  its  annual  discharge  was  six  times  less  than  that 
of  the  "  great  Father  of  Waters."  Compared  with  the 
Danube,  the  annual  discharge  of  the  latter  was  double 
that  of  the  Nile,  although  the  annual  rainfall  of  the 
Nile  basin  was  four  and  a-half  times  that  of  the  Danube. 

An  irrigation  canal  drawing  its  supply  from  a  river, 
which  carries  fertilizing  silt  in  suspension,  and  which 
has  sufficient  velocity  to  carry  the  silt  on  to  the  land 
requiring  irrigation,  deposits  an  immense  quantity  of 
good  manure,  in  a  few  months,  in  a  thin  film,  over  the 
land.  For  example:  let  a  canal  have  a  bed  width  of 


OTHER    IRRIGATION    WORKS.  65 

60  feet,  a  depth  of  4  feet,  and  side  slopes  1  to  1,  and  a 
mean  velocity  of  2.5  feet  per  second.  Let  this  canal 
flow  for  four  months,  or  120  days,  and  during  tnisTlime 
let  its  supply  be  derived  from  a  river  which  holds  silt  in 
suspension  to  the  extent  of  -g-J-j-  of  the  bulk  of  water. 
The  discharge  of  the  canal  is  640  cubic  feet  per  second. 
There  are  86,400  seconds  in  one  day.  We  have  there- 
fore: — 

640  X  86400  X  120 

97  —       =307,200  cubic  yards  of  fertilizing 


silt  deposited  by  the  canal  on  the  land  in  120  days. 
From  this  a  good  idea  can  be  formed  of  the  great  ad- 
vantage of  manurial  silt  in  an  irrigation  supply. 

Article  21.     Improvement  of  Land  by  Silting  Up,  Warp- 
ing or  Colmatage. 

Silting  up  of  land,  warping  or  colmatage,  is  here  in- 
tended to  signify  the  improvement  of  land  before  this 
of  little,  if  any,  use,  by  the  deposition  of  silt.  Warping 
is  usually  applied  to  the  artificial  silting  up  of  land  on 
the  sea  coast,  in  bays  and  estuaries,  but  it  is  here  also 
applied  to  the  silting  up  by  river  water  of  land  not 
within  the  influence  of  the  tides.  Colmatage  is  a  French 
word  also  used  in  works  written  in  English  to  express 
the  same  thing  as  silting  up. 

When  water  containing  fertilizing  silt  is  not  required 
for  irrigation  it  can  be  usefully  employed  in  making 
good  land  out  of  a  sterile  waste.  There  are,  no  doubt, 
numerous  localities  in  the  United  States  where  land  can 
be  improved  in  this  way.  A  description  of  the  im- 
provement of  some  land  by  this  method  is  here  given.  * 

Above  Epinal  in  France  the  course  of  the  river  Mo- 
selle is  well  defined  and  regular.  Below  that  point  it 

>Irrigatiou  in  Southern  Europe  by  Lieut.  C.  C.  Scott  Moncrieff. 
5 


66  IRRIGATION    CANALS    AND 

used  to  flow  over  a  broad,  gravel  bed,  in  a  number  of 
separate  streams,  continually  changing.  A  scanty  crop 
of  miserable  pasturage  used  sometimes  to  spring  up  on 
the  best  parts  of  this  broad  channel,  the  rest  was  quite 
barren.  This  worthless  strip  of  bowlders  and  gravel  is 
now  being  transformed  into  extensive  stretches  of  green 
meadow,  yielding  plentiful  crops,  and  at  the  same  time 
confining  the  river  within  a  permanent  and  defined  bed 
in  a  way  no  series  of  expensive  embankments  could 
easily  have  affected.  The  result  of  river  embankments 
has  been  too  often  to  raise  the  bed  year  by  year,  so  that 
they  too  require  to  be  raised.  In  the  Moselle  valley,  on 
the  other  hand,  the  floods  are  allowed  to  flow  almost  un- 
checked over  the  whole  of  their  old  channel;  but  when 
they  retire  they  leave  beneficial  results  instead  of  injury 
behind  them,  and  resume  the  same  course  as  they  did 
before  they  rose. 

This  work  was  commenced  by  two  brothers,  Messrs. 
Dutac,  in  1827,  by  their  buying  fifty  acres  along  the  left 
bank  of  the  river's  bed  at  LaGosse,  a  little  below  Epinal. 
At  the  head  of  this  a  rough  bowlder  dam  was  thrown 
across  the  river,  turning  about  70  cubic  feet  per  second 
of  its  waters  into  a  channel  taken  along  the  left  of  the 
estate.  To  this  was  given  a  gentle  slope,  which  soon 
raised  it  above  the  river;  and  when  lately  seen  the 
whole  of  the  land  lying  between  the  river  and  the  canal 
was  a  fine  green  meadow.  The  masonry  works  on  the 
canal  are  all  of  the  simplest  kind,  and  require  no  re- 
mark save  to  notice  this  simplicity.  The  process  then 
is  as  follows: — Below  the  dam  there  is  erected  an  embank- 
ment at  such  points  as  are  required,  high  enough  to  pre- 
vent the  full  current  of  the  river  from  anywhere  sweep- 
ing over  the  land  to  be  reclaimed,  but  not  at  all  intended 
to  keep  it  from  being  flooded.  From  the  main  canal 
are  taken  out  little  branches,  and  the  land  to  be  irri- 


OTHER    IRRIGATION    WORKS 


67 


gated  by  them  is  carefully  leveled  in  a  succession  of  par- 
allel ridges  and  valleys  running  at  an  angle  to__ these 
branches.  About  every  25  feet  along  their  course  are 
little  openings,  admitting  a  stream  of  water  about  six 
inches  wide  and 'half  as  deep,  which  flows  along  and 
overflows  a  channel  made  on  each  ridge,  running  over 
the  slopes  into  a  similar  channel  in  the  depression  below. 
Along  this  it  runs  into  a  catch-water  drain,  which  col- 
lects all  these  little  separate  streams,  and  a  little  farther 
down  commences  to  give  the  water  out  again  to  irrigate 
a  fresh  piece.  Sometimes  the  irrigating  streams  are 
made  in  pairs,  back  to  back,  sometimes  they  run  singly. 


The  annexed  diagram,  Figure  12,  is  taken  from  a 
sketch  made  on  the  spot;  a  is  the  main  canal,  b  the 
distribution  channels,  from  which  the  water  flows  into 
the  minor  channels  c,  and  over  the  ground  on  each  side 
down  into  the  dips,  where  the  minor  drainage  lines  d, 
carry  it  off  to  the  main  drain  e,  which,  at  a  lower  level, 
becomes  in  turn  a  distributing  channel,  repeating  the 
operation.  The  main  line  ay  diminishes  at  last  into  a 
distribution  channel  b,  and  that  in  time  into  minor 
channels.  Of  course  it  requires  a  good  deal  of  labor  to 
bring  the  gravelly  bed  into  shape  for  this  method  of  wa- 
tering, but  once  done  there  is  very  little  further  outlay. 


68  IRRIGATION    CANALS    AND 

It  is  then  sown  with  grass  seed  (without  making  any 
attempt  to  clear  it  of  stones),  and  the  irrigation  is  at 
once  commenced.  A  light  deposit  of  mud  forms,  every 
flood  increases  it,  the  irrigation  is  carried  on  incessantly, 
and  the  grass  soon  begins  to  sprout. 

The  silt  deposit  proceeds  fast  at  first  where  the  water 
proceeds  directly  through  the  gravel,  which  acts  as  a  fil- 
ter. By  degrees  this  filtration  causes  a  nearly  imperme- 
able bed,  through  which  very  little  of  the  water  escapes, 
and  just  so  much  the  more  flows  by  the  drainage-lines , 
and  flows  off  without  having  entirely  divestod  itself  of 
its  particles  of  mud.  Were  it  not  for  this  the  meadows 
would  rise  higher  each  year  and  soon  be  above  the 
water's  reach,  but  it  is  found  that  after  a  few  years  there 
is  no  sensible  change  in  their  level,  and  what  fresh  silt 
is  deposited  only  makes  good  what  is  consumed  on  the 
vegetation. 

There  are  in  America  large  areas  of  alkali  land  within 
the  irrigation  districts,  which  would  be  benefited  by  this 
method  of  silting  up. 

Article  22.     Equalizing  Cuttings  and  Embankments. 

The  cross-section  of  the  water  channel  and  its  slope, 
or  grade  being  determined,  the  next  step  is  to  fix  the 
depth  of  digging. 

The  cross-section  of  the  canal  can  be  fixed  so  that  the 
surface  of  the  water  may  be: — 

1.  Within  soil,  or,  in  other  words,  all  in  cutting. 

2.  Above  soil,  so  that  all  the  water  is  carried  by  em- 
bankments. 

3.  Partly  in  cutting  and  partly  in  embankment,  or 
in  cut  and  fill. 

In  some  cases,  for  sanitary  reasons,  or  in  very  per- 
vious soil,  not  suited  to  make  good  banks,  where  the 


OTHER    IRRIGATION    WORKS. 


69 


loss  of  water  and  the  cost  of  repairs  to  banks  are  serious, 
it  may  be  necessary  to  keep  within  soil.  Care  must  be 
taken,  however,  by  sinking  trial  pits,  that  a  sandy^  stra- 
tum is  not  reached  by  deep  cutting,  as,  in  this  event, 
much  water  may  be  wasted  by  absorption,  and  the  for- 
mation of  swamps  may  seriously  affect  the  health  of  the 
district,  and  ruin  land,  by  water-logging,  for  any  useful 
purpose. 

In  the  second  case,  where  the  canal  is  all  in  embank- 
ment, there  is  always  danger  of  breaches  and  consequent 
damage,  and  also  the  stoppage  of  irrigation  when  ur- 
gently required.  In  some  soils  the  banks  may  require 
to  be  puddled. 

The  third  case  has  several  advantages.  "When  the 
canal  is  partly  in  cut  and  partly  in  fill,  the  water  has 
usually  sufficient  elevation  above  the  land  to  give  a  com- 
mand of  level  for  purposes  of  irrigation. 

It  is  also  the  most  economical  channel,  as  the  cross- 
section  can  be  arranged  so  that  the  earth  excavated  from 
the  channel  suffices  for  the  banks,  due  allowance  being 
made  for  shrinkage  and  waste. 

It  has  a  further  advantage,  where  saving  of  time  is  an 
object  in  completing  a  work,  as  there  is  less  material  to 
be  moved  than  when  the  canal  is  all  in  cut  or  all  in  fill. 


The  diagram,  Figure  13,  shows  a  cross-section  of  half 
of  a  canal,  not  drawn  to  scale,  where  the  excavation  is 
sufficient  to  make  the  banks,  due  allowance  being  made 
for  shrinkage. 

AB  shows  the  surface  of  ground  which  is  assumed  to 
be  level. 


70  IRRIGATION    CANALS    AND 

x  =  depth  of  digging  which  is  required. 

d  =  depth  from  top  of  bank  to  bed  of  canal. 

(d  —  x)  =  depth  from  top  of  bank  to  surface  of  ground. 

a  =  CD  =  half  bed-width  of  canal. 

m  =  ratio  of  slopes  CF  =  AE,  that  is,  the  ratio  of 
horizontal  to  vertical  distance  of  slope  as,  for  instance, 
2  horizontal  to  1  vertical,  then  m  =  2. 

b  =  EF  =  top  width  of  bank. 

As  the  area  of  the  excavation  is  to  be  equal  to  that  of 
the  embankments,  we  have:  — 

(x  X  a)-{-x  X  x  m=b  X  (d—x)-\-(d—x)  X  (d—  x)  m,  that  is, 

~~ 


Now,  let  a  =  40  feet,  6  =  6  feet,  d  =  7  feet,  and  side 
slopes  2  to  1,  that  is,  m  =  2,  and  substituting  these  val- 
ues and  reducing,  and  we  have:  — 

x2  —  74  x  =  140. 
.\  x  =  1.943  feet. 

Figure  14  shows  a  cross-section  where  a  berm  at  ME 
is  required. 


The  surface  of  the  ground  is  assumed  to  be  horizontal 
atHL. 

Let  a  =  BK  =  half  width  of  canal  bed. 

d  =  AB  =  depth  of  canal  from  surface  of  berm  to 
bed  of  canal. 


OTHER    IRRIGATION    WORKS.  71 

x  =  NB  =  required  depth  of  digging  to  give  sufficient 
material  to  make  the  bank. 

A=  area  of  bank  above  EC. 
B  =  area  of  canal  below  DE. 

Then,  whatever  the  position  of  the  natural  surface, 
A  and  B  are  constants. 

It  is  required  to  determine  the  depth,  BN,  or  x,  so 
that  the  area  of  excavation  BFLKB,  shall  be  equal  to 
the  area  of  embankment  EFHPQME,  that  is:— 

B  —  EFLDE  =  A  -f  EFHCE,  that  is:— 

ED  +  FL  EG  +  HF 

B-        —  -  --  x  (d—  a?)  =  A+-    —  o  --  X(d—  aj),thatis: 


(ED  +  FL)  +  (EC  +  HF)      ==  B  —  A 


Now  let  EC  —  Wj  and 

y?=  angle  of  BE  and  MQ  with  horizon,  and 
0  =  angle  of  HP  with  horizon. 
Then  HE,  =  CR.  cot  o  =  (d—x)  cot  o 
SF=(d  —x)  cot  /?,  and 
HF  =  w  -f  (d  —  x)  X  (cot  p  +  cot  o  ) 
.-.    EC  -f  HF  =  2w  +  (d  —  x)  X  (cot  ft  +  cot  e  ) 
Now  ED  =  AD  +  AE  =  a  +  d  cot  /? 
and  FL  =  NL  +  NF  =  a  +  x  cot  ? 
.'.      ED  +  FL  —  2a  +  (d  -f-  aj)  cot  /? 


72  IRRIGATION    CANALS    AND 

Substituting  the  values  of  (EC  -f  FH)  and  (ED  -f  FL) 
in  equation,  and  we  have: — 

d  —  x      /  i 

x 
.'.    ~n    cot  6  —  x  (a  -f  d  cot  ft  +  iv  -f-  d  cot  0) 

=  B  —  A  —  d  (a  -f  w)  —d2  cot  ft—  —  cot  0 

From  this  equation  the  value  of  x  can  be  found. 
Example: — Given  ft  =  0  =  45°  and  cot  £  =  cot  0=1 
Let  a  =  50  feet,  d  =  8  feet,  w  =  4Q  feet,  PQ  =  25  feet, 
QT  =  TM  =  6  feet  .  -.  CM  ==  37  feet. 

d2 
Then  B  =  ad  -f  -^  =  432 

25  +  37 
A  = s X  6  =  186  .*.   equation  becomes 

x2 

-^  —  106^c  =  432  —  186  —  720  —  64  —  32 

and  x  =  5.53  feet 

Having  determined  the  depth  x,  in  either  case,  then 
an  addition  to  that  depth  has  to  be  made,  in  order  to 
compensate  for  the  shrinkage  of  the  material  and  the 
waste. 


OTHER    IRRIGATION    WORKS.  73 

Article  23.     Canal  on   Sidelong  Ground. 

It  sometimes  happens  that  the  headworks  of  a  canal 
are  so  located  that  the  canal  before  it  reaches  the  ptems 
has  to  follow  along  steep  side-hill  ground. 

As  a  rule,  in  such  sloping  ground,  it  will  be  more 
economical  to  have  a  deep  narrow  channel  than  the 
usual  wide  and  shallow  channel  suitable  for  the  plains. 
A  section  with  bed  width  equal  to  or  about  twice  the 
depth  is  better  adapted  to  steep  ground  than  one  with 
a  greater  bed  width  to  depth. 


FIG    15 


The  cross-section  of  a  canal  in  sidelong  ground  is 
either  all  in  cut,  or  partly  in  cut  and  partly  in  fill.  In 
each  case  the  upper  part  of  the  cut  is  triangular  in 
shape  with  a  horizontal  base  as  shown  in  Figure  15.  The 
outer  side  of  the  triangle  has  the  slope  of  the  natural 
ground,  and  the  inner  side  the  slope  of  the  inner  side  of 
the  canal  in  cut. 

Table  14,  given  herewith,  will  facilitate  the  computa- 
tion of  the  triangular  portion. 

Let    B  =  width  of  base. 
A  =  area  of  triangle. 

x~  angle  of  natural  ground  with  horizon. 
y  =  angle  of  side  slope  of  cutting  with  horizon. 
k  =  co-efficient,  for  value  of  which  see  table. 

B 

cot  x  —  cot  y 


74  IRRIGATION    CANALS    AND 

TABLE  14.     Giving  Values  of  the  Co-efficient  K. 


Angle  of 
ground  x 
in  degrees 

Values  of  K  for  different  slopes. 

i  to  1 

|  to  1         1  to  1 

1J  to  1 

1 

.00877 

.00880 

.00888 

.00896 

2 

.01761 

.01777 

.01809 

.01842 

3 

.02655 

.02691 

.02765 

.02844 

4 

.03558 

.03623 

.  03759 

.03906 

5 

.04472 

.04575 

.04793 

.05035 

6 

.05397 

.05646 

.05873 

.06239 

7 

.06334 

.06541 

.06999 

.07525 

8 

.07283 

.07558 

.08176 

.08904 

9 

.08246 

.08600 

.09410 

.  10387 

10 

.09220 

.09670 

.  10700 

.11990 

11 

.10215 

.  10765 

.  12064 

.  13720 

12 

.11230 

.11900 

.13510 

.  15620 

13 

.  12250 

.  13050 

.  15008 

.17661 

14 

.  13290 

.  14240 

.16610 

.  19920 

15 

.14359 

.  15470 

.  18300 

.22404 

16 

.  15430 

.  16720 

.20080 

.25120 

17 

.  16551 

.  18045 

.22018 

.28241 

18 

.  17660 

.  19370 

.24070 

.31640 

19 

.18838 

.20797 

.26257 

.35617 

20 

.20000 

.22220 

.28570 

.40090 

21 

.21230 

.23753 

.31151 

.45261 

22 

.22520 

.25380 

.33890 

.51280 

23 

.23743 

.26942 

.35688 

.58445 

24 

.25000 

.28570 

.40120 

.67020 

25 

.26391 

.30405 

.43687 

.77624 

26 

.27770 

.32250 

.47610 

.90900 

27 

.29194 

.34186 

.51942 

1.08171 

28 

.30670 

.36200 

.56750 

1.31230 

29 

.32173 

.38340 

.62185 

1.64652 

30 

.33730 

.40580 

.68300 

2.15510 

32 

.37030 

.4545 

.8333 

34 

.4058 

.5091 

1.0373 

36 

.4440 

.5707 

1.3297 

38 

.4854 

.641 

1.7857 

40 

.5307 

.7225 

2.6041 

42 

.5807 

.8183 

44 

.6364 

.9345 

46 

.6983 

1.0729 

48 

.7692 

1.25 

50 

,   .8488 

1.475 

OTHER    IRRIGATION    WORKS.  75 

Article  24.     Shrinkage  of  Earthwork. 

In  the  construction  of  embankments  with  earthy  mat- 
ter, sandy  loam  and  similar  materials,  whether  for  can-afe 
or  reservoirs,  due  allowance  should  be  made  for  the 
shrinkage  or  settlement  of  the  material. 

The  following  extract,  on  this  subject,  is  from  a  paper 
by  the  writer,  on  the  Shrinkage  of  Earthwork,  published 
in  the  Transactions  of  the  Technical  Society  of  the 
Pacific  Coast  of  June,  1885: — 

"Books  of  reference  in  the  English  language  usually 
give  the  shrinkage  of  different  materials,  without  mak- 
ing any  allowance  on  account  of  different  methods  of 
construction  and  different  heights  of  bank.  For  in- 
stance, the  shrinkage  of  earth  in  general  is  given  at 
about  10  per  cent.  Now,  if  10  per  cent,  be  sufficient  for 
the  shrinkage  of  a  bank  of  that  material,  and  30  feet  in 
height,  constructed  from  the  end  of  bank  to  the  full 
height  by  "tipping"  from  wagons,  surely  a  similar  bank 
only  12  feet  high,  built  up  in  layers,  and  consolidated 
by  good  scraper  work,  will  shrink  much  less  than  10 
per  cent. 

"  In  no  other  branch  of  Civil  Engineering,  since  the 
time  when  railroads  were  first  commenced,  has  such  an 
immense  quantity  of  work  been  carried  out,  and  ex- 
penditures incurred,  as  in  earthworks;  and  in  no  other 
branch  of  engineering,  of  equal  importance,  have  so 
few  experiments,  on  a  scale  adequate  to  the  interests  in- 
volved, been  published.  In  other  branches  of  engineer- 
ing, long,  tedious  and  expensive  experiments  are  carried 
out  without  any  other  return  resulting  from  them 
than  the  information  they  give;  but.  experiments  on 
earthwork  could  be  carried  out  on  a  large  scale,  as  actual 
work,  and  with  little,  if  any,  additional  expense  more 
than  the  contract  price  of  the  work. 


76 


IRRIGATION    CANALS    AND 


"  Some  of  the  materials  are  mentioned  more  than  once, 
in  the  table  given  below,  with  a  slight  change  in  name, 
but  the  writer  deems  it  better  to  give  each  author's  own 
words  descriptive  of  the  material  than  to  make  a  selec- 
tion of  the  materials  under  a  fewer  number  of  names. 

TABLE  15.     Giving  Shrinkage  of  Different  Materials. 


MATERIAL. 

AUTHORITY. 

Percnt'ge  of 
Increase  + 
or  Dimin- 
ution —  of 
Embnkme't 
toexcv'tion 

REMARKS. 

Sand 

Hewson 

—  10 
—  10 
—  12.5 
—  11 

Q 

-8 

1-5  addition  to  height  of  bank 

Shrinkage  of  bank  10  %. 
Shrinkage  of  bank  15  to  17%. 

1-6  addition  to  height  of  bank 

Very  light  sand 

Graeff  

Light  sandy  earth 

Morris 

Molesworth 

Gravel  and  sand  
Sand  and  gravel 

Vose  
Trautwine—  Searle...  . 
Miss.  Levees,  1882.  . 

Earth  

Earth 

Simms  .  . 

—  10 

Earth  (scraper  work)  
Earth  (grading  machine). 
Earth  (carefully  tamped) 
Loam  &  light  sandy  earth 
Loam  

Canadian  Pacific  R.  R. 
Canadian  Pacific  R.  R. 
Graeff 

—  9  to  —  20 
—  12 
—  12 
—  10 
—  10 
—  8.5 
-8 

Vose  

Trautwine  —  Searle  .  .  . 
Vose  

Clay  and  earth  

Yellow  clayey  earth 

Morris                  .  .. 

Gravelly  earth  

Morris  
Molesworth—  Vose..  .  . 

Gravel  .... 

Clay  

Clay  

Trautwine  —  Searle...  . 
Molesworth  

—  10 
t-20 
g 

Clay  before  subsidence.  .  . 
Clay  after  subsidence  
Puddled  clay  

Trautwine  

—  25 
—  15 
—  15 
+  30 
+  50 
+  50to  -}  60 
+  25 
+  66  to  +  75 
+  60 

+  42 

+  60 
+  50 
+  70 
+  25  to  +  30 
+  20 
+  80 

+  90 
+  75 
+  60 
+  0 

Wet  soil  
Loose  vegetable  surf,  soil 
Chalk 

Searle  

Trautwine 

Molesworth 

Rock  

Vose  

Rock  .... 
Rock  

Graeff  
Rhine  Nahe  Railroad. 

Rock 

Rock,  large  fragments..  . 
Hard      sandstone     rock, 
large  fragments    .  . 

Searle  

Morris  

Blue   slate     rock,    small 
fragments  
Rock,  large  blocks  
Rock,  medium  fragments 
Rock,  medium  unselected 
Rock  (metal)         
Rock,  small  fragments.  .  . 
Rock     fragments     (loose 

Morris   

Molesworth     
Searle          

Molesworth 

Searle  

Rock  fragments  (careless- 
ly piled* 

Rock  fragments  (carefully 
piled)  

Trautwine  

Rock  with    considerable 

Graeff 

OTHER    IRRIGATION    WORKS.  77 

Article  25.     Works  of  Irrigation  Canals. 

The  works  of  irrigation  canals  include,  weirs,  dams^ 
regulators,  sluice-gates,  scouring-sluices,  movable  darns, 
bridges,  culverts,  aqueducts,  superpassages,  flumes,  in- 
verted syphons,  level  crossings,  inlets,  drops  or  falls, 
rapids,  tunnels,  escapes  or  wastes,  silt-traps  or  sand 
boxes,  retaining  walls,  modules  for  measuring  water,  cut- 
tings, embankments,  and,  on  navigable  canals,  locks. 
It  is  very  seldom,  however,  that  a  canal  has  all  the 
above  works.  These  works  are  described,  somewhat  in 
detail,  in  the  following  pages. 

Article  26.     Wells  and  Blocks. 

As  wells  and  blocks  are  frequently  referred  to  in  the 
descriptions  of  the  foundations  of  works  in  India,  a  brief 
description  of  them  is  herewith  given. 

Wells  for  foundations  are  usually  brick  cylinders, 
which  are  sunk  to  a  certain  depth  in  a  sandy  river. 
After  they  are  sunk  to  the  required  depth  they  are  filled, 
or  partly  filled,  with  concrete.  When  the  lower  part 
only  is  filled  with  concrete,  the  upper  part  is  filled  in 
with  sand  over  the  concrete.  In  addition  to  being  a 
foundation  for  weirs,  wells  also  diminish  the  cross-sec- 
tional area  of  the  bed  of  the  river  through  which  per- 
colation takes  place. 

A  block,  as  its  name  implies,  is  a  block  of  masonry 
having  one  or  more  vertical  holes  through  it.  Blocks 
answer  the  same  purpose  in  every  respect  as  wells.'  Fig- 
ures 16  and  17  show  a  plan  and  cross-section  of  one  of 
the  wells  under  the  walls  of  the  Sone  Weir,  shown  in 
Figure  37,  and  Figures  18  and  19  show  a  plan  and  cross- 
section  of  one  of  the  blocks  under  the  piers  of  the  Solani 
Aqueduct,  shown  in  Article  34. 

The  method  pursued  in 'sinking  them  is  as  follows: — 


78 


IRRIGATION    CANALS    AND 


.iiSI 


i 

S 

A 

1 

• 

j 

I 

V 

•i     ' 

~/G./ 

0 

«\l 

! 

|| 

-r 

*                       ~ 

—      * 

i 

i 

I 

i 

'i 

*--   g'  6! 


If  the  wells  to  b^  constructed  and  sunk  are  on  a  sand- 
bank in  the  river  bed,  which  is  dry,  the  sand  is  excavated 
until  water  is  reached,  then  the  well-curbs  are  placed  on 
the  level  of  the  water,  and  the  masonry  of  the  well  is 
commenced;  but  if  a  stream  has  to  be  crossed,  it  is 


OTHER    IRRIGATION    WORKS.  79 

diverted  from  that  part  of  the  river,  after  which  the 
water  is  dammed  and  stilled.  This  is,  of  course,  often 
a  very  difficult  operation  where  the  bed  of  a  river  "con- 
sists of  sand  to  a  depth  of,  perhaps  sixty  feet.  After  the 
water  is  stilled,  sand  is  thrown  in,  and  an  embankment 
formed  across  it,  sufficiently  wide  to  found  the  wells  on; 
they  are  then  built  on  it  and  afterwards  sunk. 

The  wells  are  allowed  to  stand  from  ten  to  fifteen  days 
after  being  built,  to  allow  the  masonry  to  set.  The  wells 
are  then  sunk  by  excavating  the  sand  from  within  them, 
it  being  generally  found  that  the  quantity  of  excavation 
is  about  double  the  cubic  area  of  the  well  sunk.  The 
wells  under  the  walls  of  the  Sone  Weir,  Figures  16  and 
17,  are  six  feet  wide  on  exterior  diameter,  and  are  sunk 
from  eight  to  twelve  feet  below  low  water  mark.  These 
wells  are  sunk  in  single  rows,  each  well  being  separated 
from  the  next  one,  in  the  line  crossing  the  river,  by  a 
space  of  about  six  inches.  The  inside  of  the  wells  and 
the  craters  all  around  them  are  then  filled  in  with  rubble 
stone,  the  surface  to  a  depth  of  two  feet  inside,  and  be- 
tween, the  wells  being  filled  with  concrete.  Large  stone 
slabs  are  then  placed  over  the  top  of  the  wells,  binding 
the  walls  to  the  hearting,  and  also  bonding  them  to  one 
another,  and  the  masonry  of  the  well  is  then  com- 
menced. 

Wells  have  been  sunk  for  foundations  of  bridges  in 
sandy  rivers,  to  a  depth  of  over  seventy  feet. 

Article  27.     Headworks  of  Irrigation  Canals. 

The  works  at  the  head  of  a  canal,  for  regulating  and 
controlling  the  quantity  of  water  required  to  be  admit- 
ted to  it,  consist  of  a  Weir  across  the  river,  by  which  the 
water  is  checked  and  diverted  into  it,  and  a  Regulator 
across  the  head  of  the  canal,  by  which  the  proper  quan- 
tity of  water  is  admitted. 


80  IRRIGATION    CANALS    AND 

In  the  Regulator  are  fixed  sliding  gates,  or  some  other 
device,  to  control  the  supply  of  water  to  the  canal,  and 
in  the  weir  and  near  the  .head  gate  is  placed  a  Scouring 
Sluice  to  control  somewhat  the  flow  of  water  in  the  river 
past  the  head  gate. 

The  operation  of  the  Weir,  Scouring  Sluices  and  Reg- 
ulator is  so  intimately  connected,  that  a  description  of 
one  of  them  applies  more  or  less  to  the  others;  therefore, 
the  descriptions  given  below,  in  the  articles  entitled  Di- 
version Weirs,  Scouring  Sluices  and  Regulators,  are  only 
descriptions  of  different  parts  of  the  Headworks. 

The  requirement  for  good  headworks  for  an  irrigation 
canal  are  the  following — but  these  are  seldom  to  be 
found  in  one  place: — 

1.  Permanent   banks,   and  bed,    which  will   prevent 
the  river  from  eroding  the  banks  and  endangering  the 
regulator,  etc. 

2.  A  straight  reach  of  the  river  for  say  half  a  mile 
up  and  down  the  river  from  the  weir. 

3.  A  velocity  in   the  river   as  low  as,  or  not  much 
greater  than,  the  velocity  in  the  canal.     The  nearer  the 
velocity  in  the  canal  approaches  to  that  of  the  river,  the 
less  silt  will  be  deposited  in  the  former. 

4.  That  the  current  of  the  river  should  flow  at  right 
angles  to  the  center  line  of  the  canal  at  its  head. 

5.  That  the   river  at  the   headworks,  and  after  the 
construction  of  the  weir,  shall  not  overflow  its  banks. 

6.  That  the  bank  of  the  river  at  the  regulator  is  not 
very  high,  so  as  not  to  involve  very  heavy  digging  for  the 
first  few  miles  of  the  canal. 

With  reference  to  the  third  requirement  mentioned 
above,  Mr.  C.  E.  Fahey,  M.  Inst.  C.  E.,  states:* 

"Transactions  of  the  Institution  of  Civil  Engineers,  Vol.  71. 


OTHER    IRRIGATION    WORKS.  81 

"  If  the  velocity  (in  the  river)  across  the  mouth  of  a 
canal  exceeds  the  proposed  velocity  in  the  canal,  the 
result  must  be  that  the  latter  will  soon  silt  up.  Of  course 
some  silt  will  deposit  in  all  but  the  largest  canals,  in 
which  a  high  velocity  can  be  kept  up;  but  if  a  canal  is 
led  off  from  a  point  in  the  river  where  the  velocity  is 
from  five  to  six  feet  per  second,  the  water  (in  the  Indus) 
at  this  point  will  have  its  full  proportion  of  silt  in  sus- 
pension, and  the  heaviest  part  of  this  silt,  namely  the 
sand,  which  the  above  velocity  was  able  to  keep  in  sus- 
pension, will  drop  in  the  mouth  of  the  canal,  where  the 
velocity  is  suddenly  reduced  to  about  three  feet  per 
second.  This  fact  admits  of  no  dispute.  It  is  proved 
every  year  in  the  Sind  Canals.  If  a  canal  is  in  fair 
order,  that  is,  if  it  has  a  properly  regulated  width  and 
bed-slope,  the  sandy  deposit  will  be  distributed  along  the 
upper  third  of  the  canal,  the  heavier  sand  in  the  first  mile 
or  so,  the  finer  lower  down,  and  the  clay  at  the  extreme 
tail,  while  the  central  portion  will  seldom  or  never  re- 
quire cleaning.  Although  the  velocity  in  the  canal  is 
not  sufficient  to  carry  on  the  sand,  it 'is  sufficient  to 
carry  on  the  clay,  and  if  only  escapes  could  be  provided 
at  the  tails  of  all  canals,  which  is  not  practicable  in 
Sind,  there  would  be  no  clay  to  be  annually  removed." 

Article  28.     Diversion  Weirs. 

WEIRS DAMS ANICUTS BARRAGES. 

A  Diversion  Weir  is  a  weir  built  across  a  river  to  divert 
the  water  into  the  canal.  At  certain  times,  and  always 
during  floods,  the  water  flows  over  part  or  the  whole  of 
this  weir. 

A  Reservoir  Dam  is  used  to  impound  water,  and,  ex- 
cept in  very  rare  cases,  no  water  flows  over  its  top.  In 
engineering  literature  the  terms  weir,  dam,  anicut  in 
6 


82  IRRIGATION    CANALS    AND 

Madras,  and  barrage  in  Egypt,  are  also  used  to  designate 
a  weir  across  a  river. 

The  cross-sections  of  diversion  weirs  are  as  different 
in  form  as  the  materials  of  which  they  are  constructed. 
The  drawings  in  this  article  give  several  examples,  show- 
ing the  sections  adopted  in  different  countries,  to  suit 
the  material  available  for  their  construction,  and  their 
foundation  in  the  beds  of  the  rivers  across  which  they 
are  constructed. 

Canals  have  frequently  been  taken  off  from  rivers 
without  weirs,  but  where  these  rivers  are  liable  to  change 
their  beds  by  erosion  of  their  banks,  or  where  they 
carry  large  quantities  of  silt  in  suspension,  it  has  been 
found  impossible  to  regulate  both  the  river  channel  and 
also  the  supply  of  water  into  canals  on  their  banks, 
without  a  weir  built  right  across  the  stream. 

Some  canals,  without  weirs,  have  their  beds  at  the 
off-take,  much  lower  than  the  beds  of  the  river  from 
which  they  derive  their  supply,  with  a  view  of  obtain- 
ing a  supply  at  the  low  stage  of  the  river,  but  this  is 
objectionable  for  several  .reasons,  one  is  the  great  quan- 
tity of  sand  and  silt  likely  to  be  carried  into  the  canal 
and,  therefore,  the  difficulty  and  expense  of  keeping  the 
deep  channel  open. 

In  some  cases,  in  Northern  India,  the  canal  is  taken 
out  of  a  branch  of  the  main  river;  and  the  permanent 
diversion  weir  is  thrown  across  the  branch  only,  the 
water  being  diverted  from  the  main  stream  into  the 
branch  by  temporary  dams  constructed  of  bowlders, 
which  are  swept  away  on  the  rise  of  the  river,  and  an- 
nually replaced.  This  arrangement  has  chiefly  been 
due  to  the  very  heavy  expense  which  would  be  incurred 
in  throwing  a  permanent  dam  across  the  main  river 
itself.  An  example  of  this  method  was  in  operation  a 
few  years  since  at  the  headworks  of  the  Upper  Ganges 
Canal  shown  in  Figure  26. 


OTHER    IRRIGATION    WORKS.  83 

Dams  in  rivers  are  made  solid,  except  at  the  scouring 
sluices,  when  they  are  called  weirs.  Of  these,  Figures 
37,  39  and  43  are  good  examples. 

When  they  are  provided  with  openings  through  their 
whole  length,  or  the  greater  part  of  their  length,  they 
are  called  dams  in  India.  Indeed  the  term  dam  is 
always,  in  Northern  India,  understood  to  mean  an  open 
dam,  or  one  partly  open  and  partly  closed.  Examples 
of  this  latter  class  of  dam  are  to  be  found  in  the  Kern 
River  dam,  Figure  20,  the  Myapore  dam,  Figure  27,  and 
the  Barrage  of  the  Nile,  Figure  32. 

The  advantage  of  the  Weir  is  that  it  is  self-acting,  re- 
quiring no  establishment  to  work  it,  and  if  properly 
made  ought  to  cost  little  for  repairs.  It  is  also  a  stronger 
construction,  better  able  to  withstand  shocks  from  float- 
ing timbers,  etc.  Its  disadvantages  are,  that  it  causes  a 
great  accumulation  of  silt,  bowlders,  etc.,  above  it,  and 
interferes  far  more  than  an  open  dam,  with  the  normal 
regimen  of  the  river.  It  is  possible,  that  in  certain 
cases,  this  might  result  in  forcing  the  whole  or  part  of 
the  river  water  to  seek  another  channel,  and  the  possi- 
bility of  this  should  always  be  taken  into  account;  but 
if  the  river  has  no  other  channel  down  which  it  could 
force  its  way,  the  accumulation  of  material  above  the 
weir  would  be  an  advantage  rather  than  otherwise,  as 
adding  to  its  strength. 

The  advantage  claimed  for  the  open  dam  is  that  the 
interference  with  the  normal  action  of  the  river  is  re- 
duced to  a  minimum,  the  strong  scour  obtained  by  open- 
ing its  gates  effectually  preventing  any  accumulation  of 
silt  above. 

A  dam,  in  India,  consists  of  a  series  of  piers  at  reg- 
ular intervals  apart,  on  a  masonry  flooring  carried  right 
across  and  flush  with  the  river  bed,  protected  from  ero- 
sive action  by  curtain  w;alls  oi  masonry  up  and  down 
stream. 


84  IRRIGATION    CANALS    AND 

The  piers  are  grooved  for  the  reception  of  sleepers  or 
stout  planks,  by  lowering  or  raising  which  the  water 
passing  down  the  river  is  kept  under  control.  The  in- 
tervals between  the  piers  may  be  six  to  ten  feet,  which 
is  a  manageable  length  for  the  sleepers.  If  the  river  is 
navigable  at  the  head,  one  or  two  twenty  feet  openings 
fitted  with  gates  must  be  provided  to  enable  boats  to 
pass. 

The  flooring  must  be  carried  well  into  the  banks  of  the 
river  on  both  sides,  to  prevent  the  ends  of  the  dam  being 
turned,  and  the  banks  and  bed  of  the  river  will  gener- 
ally require  to  be  artificially  protected  for  some  distance, 
above  and  below  the  dam,  to  stand  the  violent  action  of 
the  water  when  the  gates  are  partially  closed. 

The  two  flanks  of  the  dam  for  some  length  are  gen- 
erally built  as  weirs;  that  is,  instead  of  having  piers 
and  gates,  the  masonry  is  carried  up  solid  to  a  certain 
height  so  that  when  the  water  rises  above  that  height,  it 
may  flow  over  the  top  of  it.  The  advantage  of  this  ar- 
rangement is,  that  it  affords  an  escape  for  water  in  case 
of  a  sudden  flood  when  the  dam  may  be  closed,  while, 
when  the  water  is  low,  they  keep  it  in  the  center  of  the 
river  and  away  from  the  flanks,  and  thereby  create  a 
more  perfect  scour. 

When  the  river  is  subject  to  sudden  and  violent  floods, 
damage  might  be  done  before  the  sleepers  could  be  all 
raised,  one  by  one;  it  is  better  therefore  to  employ  flood 
or  drop-gates  in  such  a  case;  that  is,  gates  which  turn 
upon  hinges  in  the  piers  at  the  level  of  the  flooring  and 
which  v/hen  shut  are  held  up  by  chains  against  the  force 
of  the  water.  In  case  of  flood,  the  chains  are  loosened, 
the  gates  drop  down,  and  the  water  flows  over  them. 
Should  the  intervals  between  the  piers  be  over  ten  feet, 
there  would  be  a  difficulty  in  hauling  the  gates  up  again. 

A  bridge  of  communication  may  be  made  between  the 


OTHER    IRRIGATION    WORKS.  85 

piers  of  the  dam  if  required.  But  as  it  is  not  desirable 
to  have  it  obstructed  with  traffic,  it  may  be  merely  alight 
foot-bridge,  or  the  intervals  may  be  spanned  temporally 
with  spare  sleepers. 

The  dam  and  regulator  are  generally  close  together 
and  connected  by  a  line  of  revetment  wall,  as  shown  in 
Figures  28,  31,  40  and  48.* 

In  some  cases  iron  or  stone  posts  were  fixed  on  the 
crest  of  the  weir.  Planks  laid  horizontally  are  fixed  in 
grooves  in  these  posts  to  raise  the  water  about  two  feet 
higher  than  the  crest  of  the  weir.  These  planks  are 
removed  before  the  occurrence  of  floods. 

The  greater  number  of  the  weirs  or  dams  across  Indian 
rivers,  and  almost  all  those  of  modern  date,  are  located 
at  right  angles  to  the  general  direction  of  the  rivers.  It 
is  well  known  that  the  tendency  of  oblique  weirs  is  to 
divert  the  strongest  stream,  and  consequently  the  deep- 
est channel  towards  the  bank  on  which  the  upper  end  of 
the  oblique  weir  is  situated.  It  was,  no  doubt,  quite 
true  that,  in  rivers  where  a  good  foundation  could  be 
obtained,  there  would  be  very  little  objection  to  oblique 
weirs;  but  in  rivers  such  as  those  which  had  to  be  dealt 
with  in  India,  with  sandy  beds  and  difficult  foundations, 
they  were  very  objectionable,  for  three  reasons: — 

Firstly,  they  induced  currents  parallel  to  the  weir; 

Secondly,  they  caused  a  deepening  of  the  channel 
above  the  weir,  near  the  up-stream  end,  which  was  dan- 
gerous; and 

Thirdly,  they  raised  the  level  of  the  water  in  the  river 
at  the  lower  end  of  the' weir. f 

Another  reason  is  that  they  cost  more  than  the  straight 

*Roorkee  Treatise  on  Civil  Engineering. 

tR.  B.  Buckley,  C.  E.,  in  Proceedings  of  I.  C.  E.,  Volume  60. 


86  IRRIGATION    CANALS    AND 

weir,  and,  therefore,  for  all  these  reasons  the  latter  weir 
is  preferred  in  India. 

The  location  of  the  dam  should  be  studied  with  a  view 
to  the  avoidance  of  flooding  the  country  above  the  dam 
in  the  high  stages  of  the  river.  To  prevent  flooding, 
long  and  heavy  embankments  had  to  be  made  above  the 
Narora  weir. 

In  order  to  reduce  the  first  cost  of  construction,  it  has 
become  a  custom  to  build  bridges  and  dams  across 
streams  at  the  narrowest  point  available,  or  to  contract 
the  stream  for  that  purpose.  This  frequently  involves 
great  difficulties  to  the  engineer  in  laying  the  piers  and 
abutments,  and  also  brings  in  an  element  of  danger  by 
adding  to  the  scouring  effect  of  the  waters  in  the  con- 
tracted channel.  Moreover,  it  generally  produces  evil 
effects  by  the  formation  of  shoals  below  the  scoured-out 
channel. 

The  proper  location  for  such  works,  and  especially  for 
dams  across  a  river  with  unstable  banks,  where  the 
highest  factor  of  safety  is  desired,  is  in  the  broad  reaches 
of  the  stream,  where  the  depth  of  water  is  usually  less, 
and  especially  in  places  where  a  "  bar  "  has  already  been 
formed  across  the  river  by  natural  causes. 

The  dam  across  a  river  is  not  only  analogous  to  a 
"  bar"  formed  by  natural  causes,  but  in  the  scheme  of 
irrigation  by  gravitation  it  is  a  "bar,"  and  should  be 
located  and  treated  as  such.  If  this  is  done  at  a  broad 
passage  of  the  stream,  or  where  it  has  its  average  width, 
the  first  cost  of  material  and  workmanship  may  possibly 
be  increased  beyond  a  similar  work  at  a  contracted  pas- 
sage; but  this  is  not  an  absolute  necessity,  as  many  of 
the  ordinary  difficulties  to  be  overcome  by  the  engineer 
are  much  lessened,  and  danger  to  the  work  in  progress, 
and  when  finished  is  much  reduced  during  floods  and 
ice-gorges.  The  adjacent  banks  are  less  liable  to  be  torn 


OTHER    IRRIGATION    WORKS.  87 

away,  wing-dams  are  avoided,  the  levees  are  less  expen- 
sive and  less  liable  to  abrasion  and  to  crevasses,  there  is 
less  cost  for  protecting  works,  and  less  cost  of  subsequent 
supervision  and  repairs  * 

With  three  exceptions,  none  of  the  weirs  described  in 
this  article  raise  the  water  higher  than  fourteen  feet. 
Indeed,  all  the  weirs  in  the  wide,  sandy  rivers  of  India 
are  low  weirs  of  the  type  of  the  Okhla  Weir,  Figure  39, 
in  Northern  India,  and  of  the  Godavery  Anicut,  Figure 
44,  in  Madras. 

The  high  weirs,  the  Turlock  Weir,  Figure  45,  and  the 
Henares  Weir,  Figure  46,  have  a  cross-section  not  in 
favor  in  India.  It  is  very  likely  that  an  Indian  engineer 
would  reverse  these  cross-sections  and  place  the  vertical 
side  down-stream,  with  a  water-cushion  on  the  lower 
side,  to  receive  the  falling  water  and  diminish  its  de- 
structive effect.  This  will  be  referred  to  when  describ- 
ing the  dams  mentioned. 

The  Cavour  Canal  weir  has  a  cross-section  similar  to 
the  Ogee  falls  first  constructed  on  the  canals  in  North- 
ern India.  These  falls  destroyed  themselves,  and  they 
had  to  be  replaced  by  vertical  falls  with  water-cushions. 
This  is  referred  to  in  the  article  entitled  Falls.  Two  of 
the  weirs  have  vertical  drops,  the  Streeviguntum  Anicut, 
Figure  41,  and  Narora  Weir,  Figure  43.  The  latter,  how- 
ever, has  a  water-cushion  three  feet  in  depth  at  the  low 
stage  of  the  river,  while  the  apron  of  the  former  is  laid 
at  the  level  of  the  low-water  of  the  river. 

In  America  there  are  numerous  dams  of  a  temporary 
character  which  are  made  of  brush  and  bowlders.  At 
Phoenix,  Arizona,  dams  are  formed  of  stakes,  brush 
and  bowlders,  rendered  water-tight  by  filling  in  up 
stream,  with  gravel  and  sand.  Stakes  are  first  driven 

*Irrigatioii  in  India,  Egypt  and"  India,  by  Professor  George  Davidson. 


88 


IRRIGATION    CANALS    AND 


across  the  channel,  and  between  these,  bundles  of  fas- 
cines of  willow  trees,  about  three  inches  in  diameter  at 
their  butts, are  laid,  with  butts  down  stream,  and  weighted 
with  a  layer  of  bowlders;  tule  reeds  in  bundles  are  also 
used,  mixed  with  willow  and  cottonwood  tree.  In  al- 
ternate layers  the  dam  is  built  up  to  the  height  of  five 
feet.  The  willows  sprout  and  the  whole  forms  a  mass 
of  living  brush  and  bowlders.  When  the  current  is  too 
strong  for  a  man  to  withstand  while  driving  stakes, 
cribs  are  made  and  floated  out  and  sunk,  as  was  done 
with  the  fascine  dam  at  Merced  Canal  head,  in  Cali- 
fornia. 

The  cross-section  of  the  weir  of  the  Galloway  Canal, 
across  the  Kern  River,  California,  is  shown  in  Figure 
20.  The  plan  of  the  head  works  of  this  canal  is  shown 
in  the  article  entitled  Methods  of  Irrigation. 

FIG  20 


The  Calloway  Canal  is  diverted  from  the  right  bank  of 
the  Kern  River,  a  few  miles  above  Bakersfield.  The 
average  maximum  discharge  during  the  rainy  season  is 
probably  over  19,000  cubic' feet  per  second.  The  water 
of  the  canal  is  diverted  from  the  river  by  a  very  light, 
open,  wooden  weir,  extending  at  right  angles  to,  and  en- 
tirely across,  the  river  from  bank  to  bank.  The  length 


OTHER    IRRIGATION    WORKS.  89 

of  this  diversion  weir  is  400  feet.  The  weir  rests  on 
three  rows  of  4"xl2"  anchor  piles  at  right  angles  to  the 
course  of  the  river,  and  two  rows  of  4"xl2"  sheet  piHng-, 
at  the  wings  parallel  to  the  course  of  the  stream.  The 
piles  are  driven  ten  feet  into  the  bed  of  the  river.  On 
the  bed  of  the  river  and  resting  on  the  tops  of  the  piles, 
and  on  the  mud  sills,  to  which  it  is  securely  spiked,  a 
flooring  of  plank  two  inches  thick  is  fixed.  This  floor 
is  about  thirty  feet  in  length  in  the  direction  of  the  river. 

The  trestles,  A,  B,  C,  D,  Figure  20,  are  about  four  feet 
from  center  to  center.  These  trestles  support  the  plank- 
ing, A,  B,  two  inches  thick,  which  holds  up  the  water 
and  thus  diverts  it  into  the  canal.  There  are  two  light 
foot-bridges  on  the  weir  shown  at  B}  and  C.  All  the 
planking,  A,  B,  are  shown  in  position.  When  this 
happens  the  water  on  the  up-stream  side  of  A,  B}  is 
level,  but  as  shown  in  Figure  20  some  of  the  planking, 
not  on  the  line  of  the  cross-section  are  assumed  to  be 
out  and  water  is  flowing  through  the  weir. 

One  man,  standing  on  the  foot-bridge,  operates  the 
two-inch  flash-boards  with  an  iron  hooked  rod.  The 
total  height  of  the  weir  is  ten  feet  above  the  floor. 

The  Head-Sluice  or  Regulator,  at  the  head  of  the  Gal- 
loway Canal,  is  of  similar  construction  to  the  weir  just 
described,  but  exceeding  it  by  one  foot  in  height. 

These  head-works  are  in  use  seven  years  and  they  are 
reported  to  give  satisfaction.  As  the  whole  weir  is  open 
in  flood  time  the  river  bed  above  it  has  not  silted  up. 

There  is  not,  probably  in  the  world,  a  lighter  or  cheaper 
weir,  of  an  equal  length,  and  situated  on  the  sandy  bed 
of  a  river,  that  has  acted  so  efficiently,  and  that  costs  less, 
for  its  operation  and  maintenance.  It  was  a  bold  under- 
taking to  attempt  to  control  such  a  river,  having  a  flood 
discharge  of  over  19,000  cubic  feet  per  second,  with  such 
a  light  structure,  and  it  well  exemplifies  one  of  the  Pecu- 
liarities of  American  Engineering. 


90  IRRIGATION    CANALS    AND 

The  cross-section  of  the  weir  of  the  Bear  River  Canal, 
in  Utah,  is  shown  in  Figure  21. 


•       3&-  •> 

Cross  Section  Bear  River  Weir. 

Its  location  is  well  selected,  as  it  has  high  rock  abut- 
ments and  a  rock  foundation.  It  is  constructed  of  crib- 
work  of  sawn  lumber.  Between  the  crib-work  it  is 
filled  in  with  earth  and  loose  rock,  and  the  up  stream 
side,  which  has  a  slope  of  two  to  one,  is  filled  in  with 
rock.  The  down  stream  side  has  a  slope  of  one-half  to 
one.  The  lowest  sills  of  the  crib,  ten  inches  by  twelve 
inches,  are  drift  bolted  to  the  bed  rock  and  on  these 
planking  is  spiked,  on  the  down  stream  side,  to  protect 
the  foundation  from  the  effect  of  the  falling  water.* 

The  weir  across  the  North  Poudre  River,  at  the  head  of 
the  North  Poudre  Irrigation  Canal  in  Colorado  is,  in  the 
center,  thirty  feet  six  inches  high,  and  150  feet  wide  on 
the  top,  and  it  is  formed  in  two  parts.  The  down-stream 
division,  or  face,  which  gives  the  necessary  stability 
against  floods,  consists  of  crib-work  and  stones;  the  up- 
stream or  back,  which  renders  the  weir  water-tight,  being 
a  vertical  panel  or  diaphragm  of  timber,  backed  with 
earth,  small  stones,  gravel  and  mud,  thrown  in  without 
puddling. 

The  crib-work  is  formed  of  round  logs,  ten   inches  at 

*  American  Irrigation  Engineering  by  Mr.  H.M.  Wilson,  M.  Am.  Soc.  C. 
E.,  in  Transactions  of  the  American  Society  of  Civil  Engineers,  Vol.  24. 


OTHER    IRRIGATION    WORKS. 


91 


CRIB  DAM  ON  NORTH  POUDRE IRRIGATION  CANAL 

FIG  22 


I     BED  OF  RIVER 

SECTIONAL\ELEVATION 

JO   .5    0         10        20        30   j     40        30        (JQ        7Q 
SCALE\OF  FEET 


SECTIONAL  PLAN 

least  in  diameter,  joined  at  the  ends,  as  in  ordinary  log 
huts,  with  dovetail  or  tongue  joints.  Figures  22,  23,  24 
and  25,  give  plans  and  sections  of  the  weir.  Each  crib 
is  ten  feet  long  on  the  face,  and  is  fastened  together  with 
eighteen-inch  treenails,  two  inches  in  diameter.  The 
cribs  are  radiated  so  as  to  form,  when  laid  close  together 
across  the  stream,  curved  tiers  of  200  feet,  216  feet,  and 
232  feet  radius  on  the  face.  There  are  three  of  these 
tiers,  of  different  heights,  six  feet  asunder.  The  inte- 
rior of  the  cribs,  and  the  spaces  between  the  tiers,  are 
filled  with  stones,  and  the  exterior  surfaces  are  faced  with 


92 


IRRIGATION    CANALS    AND 


large  selected  blocks  of  stone,  carefully  laid  so  as  to 
overlap  each  other  like  the  slates  or  tiles  of  a  house,  and 
without  mortar.  The  arrises  are  protected  by  twelve- 
inch  square  blocks,  securely  bolted  to  the  cribs.  The 
timber  diaphragm  is  carried  four  feet  higher  than  the 

CRIB  DAM  NORTH  POUDRE  IRRIGATION  CANAL 


Scale  32Feet  to  one  Inch 


FIG.  24 


SECTION  THROUGH  CENTER  OF  CRIBS 

cribs  and  stonework  of  the  tallest  tier,  to  form  a  "  slash 
board,"  which  can  be  removed  in  sections  in  case  it  is 
found  liable  to  be  damaged  by  ice.  The  center  portion 
of  the  weir  for  a  length  of  sixty  feet,  is  carried  two  feet 

CRIB  DAM  NORTH  POUDRE  IRRIGATION  CANAL 
Scale  32Feet  to  one  Inch- 


HG.  25 


SECTION  AT  ENDS  OF  CRIBS 

higher  than  the  sides,  to  throw  the  bulk  of  tne  stream 
on  to  natural  benches  of  solid  quartz  rock  on  the  sides, 
and  thereby  to  protect  the  greater  part  of  the  face,  and 
especially  the  toe  in  the  center  of  the  stream  from  the 
abrading  power  of  the  water. 


OTHER    IRRIGATION    WORKS. 


93 


The  weir  was  founded  011  stone  and  debris,  the  depth 
of  which  had  not  been  sounded,  but  it   was   hoped   that 

PLAN  OF  HEADWORKS  OF  UPPER  GANGES  CANAL. 


the  clay  thrown  into  the  back  of  the  weir,  combined 
with  the  silting  up  of  the  river,  would  have  the  effect  of 
putting  a  stop  to  the  flow  of  the  water,  and  the  result 
has  justified  the  expectation.  At  first  the  water  leaked 


94 


IRRIGATION    CANALS    AND 


through  and  there  was  some  difficulty  in  stopping  it,  but 
it  was  finally  arrested.  The  weir  was  simply  for  the 
purpose  of  lifting  the  water  high  enough  to  enter  the 
canal.* 

I 


Irrigation  in  New  Countries,  by    Mr.   P.  O'Meara,   M.   Inst.,   C.  E.,  in. 
Transactions  of  the  Institution  of  Civil  Engineers,  Vol.  73. 


OTHER    IRRIGATION    WORKS.  95 

The  Myapore  Headworks  of  the  Upper  or  Original 
Ganges  Canal  are  shown  in  the  general  plan,  Figure  26, 
and  in  detail  in  Figures  27,  28,  29  and  30. 

This  weir  is  an  example  of  an  "  open  dam,"  differing 
from  the  unbroken  "  anicuts  "  of  Madras,  and  the  solid 
weirs  with  scouring  sluices,  such  as  the  Sone,  Okhlaand 
Narora  weirs,  built  in  later  years  in  Northern  India. 
As  stated  by  the  designer,  Sir  P.  Cautley,  in  the  follow- 
ing extract,  this  dam  is  "  in  fact  a  line  of  sluices  with 
gates  or  shutters,  which  are  capable  of  being  laid  en- 
tirely open  down  to  the  bed  of  the  river  during  the 
period  of  flood."  This  weir  is  designed  somewhat  on 
the  plans  of  the  Barrage  of  the  Nile,  a  description  of 
which  is  given  below. 

This  dam  differs  also  from  the  weirs  now  generally 
constructed  in  regard  to  its  position  in  relation  to  the 
head  sluices  of  the  canal,  which  are,  at  Myapore, 
placed  in  a  "regulating  bridge,"  situated,  not  on  the 
flank  revetments  immediately  adjoining  the  weir  abut- 
ment, but  two  hundred  feet  or  more  down  the  canal. 
This  is  a  defective  arrangement,  as  the  pocket  thus 
formed  between  the  regulator  and  the  actual  commence- 
ment of  the  canal  channel  is  filled  by  an  almost  still 
back-water,  when  the  flood-waters  are  pouring  over  the 
dam;  and  this  pocket  becomes  shingled  up,  with  seven 
or  eight  feet  in  depth  of  bowlders  and  sand,  marked 
*  *  *  on  Figure  28,  and  the  supply,  especially  at  low 
water,  is  reduced  until  this  accumulation  is  cleared 
away. 

The  left  flank  of  the  dam  abuts  upon  an  island,  in 
which  nearly  one-half  of  its  full  width  is  excavated. 

The  flooring  of  the  dam  and  of  the  regulating  bridge 
are  laid  on  one  level,  and  the  front  line  of  the  latter  is 
the  zero  to  which  the  whole  line  of  the  canal  is  refer- 
able, as  to  levels  and  length.  The  zero  point  for  levels 


96  IRRIGATION    CANALS    AND 

was  fixed  at  the  level  of  the  bed  of  the  river  at  the  loca- 
tion of  the  regulator. 

The  dam  itself,  which  is  517  feet  between  the  flanks, 
is  pierced  in  its  center  by  fifteen  openings  of  ten  feet 
wide  each;  the  sills  or  floorings  of  each  opening  being 
raised  two  and  a-half  feet  from  the  zero  line.  These 
floorings  are  so  constructed,  that,  if  necessary,  they  may 
be  removed,  and  a  flush  waterway  be  obtained  as  low  as 
zero.  The  piers  between  the  above  openings  are  eight 
feet  in  height,  so  that  the  elevated  flooring  leaves  the 
depth  of  sluice-gate  equal  to  five  and  a-half  feet.  The 
piers  are  fitted  with  grooves  for  the  admission  of  planks. 

The  Regulating  Bridge,  at  the  head  of  the  canal,  has 
ten  bays  or  openings  each  twenty  feet  in  width  and  six- 
teen feet  in  height,  each  bay  being  fitted  with  gates  and 
the  necessary  apparatus  for  opening  or  closing  them. 

The  narrowness  of  the  platform,  only  forty-four  feet, 
contrasts  strangely,  at  this  time,  with  the  width  of  other 
weirs,  as  for  example  the  Sone,  the  Okhla  and  the  Lower 
Ganges,  shown  in  Figures  37,  39  and  43,  but  it  must  be 
remembered  that  the  bed  of  the  Ganges  at  Myapore  con- 
sists of  large  and  small  bowlders,  forming  a  natural  talus 
or  apron  below  the  weir;  and  that  owing  to  the  back- 
water of  the  other  open  channels  of  the  river,  which 
form  a  water-cushion  below  the  weir,  the  bed  of  the 
Myapore  channel  below  it  has  a  tendency  to  rise  instead 
of  being  scoured  away.  The  above  arrangement  is 
given  to  illustrate  what  kind  of  headwork  was  adopted 
when  the  Original  Ganges  Canal  was  projected,  but  of 
late  years  a  new  weir,  across  the  whole  Ganges  River, 
has  been  constructed,  two  or  three  miles  above  the  Mya- 
pore dam,  which  somewhat  modifies  the  above  arrange- 
ments.* 

*Koorkee  Treatise  on  Civil  Engineering 


OTHER    IRRIGATION    WORKS. 


97 


The  Barrages  of  the  Nile,  at  its  bifurcation  at  the  Ro- 
setta  and  Damietta  branches,  are  open  weirs  or  dams, 
provided  with  openings  along  their  entire  length. 

PLAN  OF  PART  OF  THE  NILE  DELTA 

SHOWING   LOCATION    OF  BARRAGES   AND   CANALS. 


the  Nile  in  Egypt  during  flood,  is  considerably  above  the 
level  of  the  country,  which  is  protected  by  embankments 
from  inundation,  it  would  have  been  dangerous  to  build 

7 


98  IRRIGATION    CANALS    AND 

a  solid  barrage,  which  would  have  still  further  raised 
the  water  surface,  unless  a  length  of  barrage  could  have 
been  obtained  much  in  excess  of  the  normal  width  of  the 
river. 

A  plan  of  the  head  of  the  Delta  of  the  Nile,  showing 
the  positions  of  the  barrages,  is  given  in  Figure  31,  and 
Figures  32,  33  and  34  give  the  plan  and  longitudinal  and 
cross-sections  of  the  barrage  of  the  Rosetta  Branch.  A 
view  of  the  barrage  is  given  in  Figure  35. 

The  Egyptians  call  the  barrage  the  "  Bridge  of  Bless- 
ings," for  the  reason  that  it  has  considerably  extended 
the  area  of  irrigation  during  the  period  when  it  is  ur- 
gently required  in  Lower  Egypt.  The  barrage  crosses 
the  Nile  about  twelve  miles  below  Cairo,  at  the  point 
where  the  river  divides  into  two  branches.  The  length 
of  the  western  or  Rosetta  branch,  following  the  sinuosi- 
ties of  its  course,  is  about  116  miles,  and  of  the  eastern 
or  Damietta  branch,  124  miles.  The  plain  which  they 
traverse,  termed  the  Delta,  presents  a  front  to  the  Medi- 
terranean of  about  180  miles,  and  forms  by  far  the  most 
valuable  portion  of  the  lands  of  Egypt. 

To  form  an  idea  of  the  barrage,  with  the  aid  of  the 
drawings,  imagine  a  bridge  or  viaduct  of  solid  propor- 
tions established  at  the  head  of  the  delta,  on  each  of  the 
two  branches  of  the  river,  and  above  these  bridges  the 
headworks  of  three  great  canals,  destined  to  traverse  in 
their  course  the  Eastern,  the  Central  or  Delta,  and  the 
Western  Provinces  of  Lower  Egypt.  If  the  arches  of 
these  bridges  were  closed  by  sluices,  the  water  would  of 
course  be  backed  up  and  inundate  the  valley,  unless  it 
were  carried  off  by  the  canals  fed  from  the  river  and 
restrained  by  the  banks  formed  to  control  its  overflow. 
The  water  thus  raised  and  thrown  into  the  three  canals, 
of  which  mention  has  been  made,  could  then  be  dis- 
charged at  will,  on  any  of  the  lands  of  Lower  Egypt 


OTHER    IRRIGATION    WORKS.  99 

through  openings  made  in  the  canal  banks.  When  the 
-Nile  commenced  to  rise,  the  sluices  in  the  arches  of  the 
bridge  would  be  opened  gradually,  until  at  the-time-al. 
the  great  floods,  there  would  be  110  obstruction,  except  the 
piers  of  the  bridges,  to  the  passage  of  the  waters.  By 
this  system  it  would  be  possible  to  regulate  the  height 
of  water  as  desired,  to  increase  the  height  of  feeble  floods, 
and  to  diminish  somewhat  the  effect  of  violent  floods  by 
discharging  water  through  the  three  main  canals. 

M.  Mougel,  an  able  French  engineer,  designed  the 
barrages,  and  constructed  them  under  great  difficulties. 
During  his  absence  from  Egypt  they  were  condemned  as 
unsafe,  and  for  twenty  years,  from  1862  to  1882,  they 
were  never  used  to  raise  the  Nile  water  to  anything  like 
the  height  originally  contemplated.  About  the  latter 
date,  General  Sir  C.  C.  Scott  Moiicrieff,  K.  E.,  took 
charge  of  the  work,  and  since  then  he  has  so  thoroughly 
repaired  and  strengthened  the  foundations  of  the  bar- 
rages, that  they  now  retain  a  head  of  water  never  at- 
tempted before  he  took  charge  of  the  works.  After 
making  a  partial  success  of  the  barrages,  General  Moii- 
crieff publicly  acknowledged,  in  the  most  generous 
manner,  the  great  ability  of  M.  Mougel,  the  original 
designer  of  the  works. 

The  following  description  explains  the  barrages  as 
they  existed,  before  the  construction  of  the  works  to 
reinforce  the  foundations,  carried  out  by  General  Moii- 
crieff. 

The  Xile  barrages  are  two  open  weirs  thrown  across 
the  heads  of  the  Kosetta  and  Damietta  branches,  at 
the  apex  of  the  Delta.  Of  the  two  branches  the  Kosetta 
has  nearly  twice  the  flood  supply  of  the  Damietta,  while 
its  bed  is  some  six  feet  lower.  The  Damietta  branch 
feeds  eight  important  canals.  The  Kosetta  barrage  is 
l,4,S7  feet  between  the  ftaiiks,  arid  the  Damietta  1.709. 


100 


IRRIGATION  CANALS  AND 


JL.-JL 


OTHER    IRRIGATION    WORKS.  101 

These  barrages  are  separated  by  a  revetment  wall  3,280 
feet  in  length,  in  the  middle  of  which  is  situated  the 
head  of  the  Main  Delta  Canal.  The  platform  7)1  "the 
Rosetta  barrage  is  flush  with  the  river  bed,  being  29.8 
feet  above  mean  sea  level.  Its  width  is  151  feet  and 
depth  11.5  feet,  and  it  is  composed  of  concrete  overlaid 
with  brick  and  stonework  as  shown  in  Figure  34. 

Down  stream  of  the  platform  is  an  irregular  talus  of 
rubble  pitching,  varying  in  places  from  150  to  ten  feet 
in  width,  and  from  fifty  to  two  feet  in  depth.  The  left 
half  of  the  platform  is  laid  011  loose  sand,  the  right  half 
on  a  barrier  of  rubble  pitching  overlying  the  sand. 
This  loose  stone  barrier  is  thirty  feet  high,  200  feet  wide 
at  the  deepest  part,  and  tapers  off  to  zero  at  the  ends. 
It  closes  the  deep  channel  of  the  river,  and  its  only 
cementing  material  is  the  slime  deposit  of  the  Nile. 
This  deposit  is  so  excellent  that  the  barrier  is  practically 
water-tight.  The  platform  supports  a  regulating  bridge 
with  a  lock  at  each  end.  This  bridge  consists  of  sixty- 
one  openings  each  16.4  feet  wide.  The  lock  on  the 
left  flank  is  39.4  feet  wide,  while  that  on  the  right  is 
49.2  feet.  Fifty-seven  of  the  piers  are  6.6  feet  wide, 
while  three  of  them  are  11.6  feet  wide;  their  height 
being  32.2  feet.  The  lock  walls  are  9.8  feet  and  14.8 
feet  wide.  The  piers  support  arches  carrying  a  road- 
way. The  waterway  of  the  barrage  is  34,359  square 
feet,  while  the  high  flood  discharge  is  225,000  cubic  feet 
per  second,  causing  a  banking  up  or  afflux  of  0.8  foot. 

During  the  floods  of  1867  the  floor  of  ten  openings  of 
the  Rosetta  Barrage  settled  0.4  foot,  producing  a  deflec- 
tion in  the  superstructure  both  horizontally  and  vertical- 
ly, and  after  this  time  no  attempt  was  again  made  to 
raise  the  water  so  high  until  after  the  completion  of  the 
remodeling  of  the  foundations  by  General  Moncrieff. 

The  Damietta   Barrage   has  ten  openings  of  16.4  feet 


102 


IRRIGATION    CANALS    AND 


each,  more  than  the  Rosetta  Barrage.  The  platforms  and 
superstructures  are  on  the  same  level,  and  exactly  sim- 
ilar. 


FIG.  35.     VIEW  OF  NILE  BARRAGE. 

The  Okhla  Weir,  on  the  River  Jumna,  Figure  o(J,  is  a 
mass  of  loose  rubble  stone  with  absolutely  no  founda- 
tion, and  holds  up  annually  ten  feet  of  water,  when  the 
water  pressure  per  lineal  foot  bears  to  the  weight  of  the 
dam  a  proportion  of  il'j/Joo-  or  /0.  Nile  sand  is  much 
finer  than  that  in  the  Jumna,  and  will  therefore  require 
a  lower  co-efficient. 

Considering  the  barrage  a  thoroughly  unsound  wo-rk 
as  to  its  foundations,  and  relying  only  on  friction,  it 
was  determined  to  make  the  submerged  weight  of  ma- 
sonry bear  a  ratio  of  fifty  to  the  pressure  of  the  water 
going  to  be  brought  on  it.  Springs  might  cause  a  slight 
subsidence  of  any  part  of  the  barrage,  but  it  could  not 
be  moved  as  a  whole.  The  pressure  of  a  head  of  ten 
feet  of  water  would  be  8, 125  pounds  per  lineal  foot.  The 


OTHER    IRRIGATION    WORKS. 


103 


submerged  weight  of  the  platform,  as  first  constructed, 
was  103,983  pounds  per  lineal  foot.  The  co-efficient  was 
-sV  That  this  proportion  might  be  --10,  it  was  nBeef^a-ry 
to  make  the  rubble  talus  everywhere  131  feet  wide  and 
ten  feet  deep,  with  a  submerged  weight  per  lineal  foot 
of  51,668  pounds.  This  made  the  submerged  platform 
and  talus  together  .155,651  pounds  as  compared  to  the 
pressure,  3,125  pounds.  Since  only  one-third  of  the 
talus  was  completed  in  1884,  the  barrage  was  not  re- 
quired to  hold  up  more  that  7.2  feet  of  water,  but  on  the 
completion  of  the  talus  in  1885,  ten  feet  of  water  were 
held  up.* 

The  headworks  of  the  Sono  Canals,  taken  from  the 
river  Soiie,  in  India,  shown  in  plan  in  Figure  36,  is  a 
good  illustration  of  the  headworks  of  a  modern  canal, 
taken  from  a  river  in  the  plains  of  India,  and  having 
scouring  sluices  with  movable  shutters. 


FIG.  36.     PLAN  OF  HEADWORKS  OF  SONE  CANALS. 

The  length  of  the  weir  between  the  abutments,  on  the 
right  and  left  banks  of  the  river,  is  12,550  feet,  or  2.35 
miles,  and  its  crest  is  eight  feet  higher  than  the  bed  of 
the  river.  As  two  canals  are  taken  off  above  this  weir, 
one  from  each  bank  of  the  river,  there  are  two  sets  of 
end  weir  scouring  sluices,  one  at  each  extremity  of  the 

"Irrigation  in  Lower  Egypt,   by  Mr.  W.  Willeocks,  C.  E.,   in  Vol.  88  of 
Transactions  of  the  Institution nf  Civil  Engineers. 


104 


IRRIGATION    CANALS    AND 


weir.  There  is  also  a  central  set  of  scouring  sluices  to 
provide  a  greater  control  over  the  regimen  of  the  river, 
and  to  assist  in  keeping  open  a  navigable  channel  across 
it,  between  the  locks  of  the  two  canals.  However,  after 
an  experience  of  several  years,  they  have  been  found 
insufficient  for  this  purpose.  The  pool  above  the  weir 
silted  up  so  much  that  when  the  water  was  level  with 
the  crest  of  the  latter,  that  is,  when  the  water  was  eight 
feet  above  what  used  to  be  the  bed  of  the  river,  it  was 
with  difficulty  that  a  boat  drawing  three  feet  of  water 


FIG.37 


SECTION 


^_^_^  £ed  of  ki  re  i 


WEIR  AT  DEHREESONE  CANALS 

could  be  got  across  from  the  canal  on  one  side  to  that  on 
the  other.  Many  islands  were  formed  one  foot  or  two 
feet  above  the  level  of  the  crest  of  the  weir,  and  were 
yearly  increasing.  To  facilitate  navigation,  and  to  raise 
the  level  of  the  pool  with  the  object  of  obtaining  a 
greater  depth  of  water  upon  the  head  sluices  of  the 
canals,  it  was  decided  to  put  a  movable  dam  two  feet 
high,  along  the  whole  length  of  the  weir.  Four  men 
can  raise  these  shutters,  when  a  deptli  of  six  or  eight 
inches  of  water  is  flowing  over  the  crest  of  the  weir 
almost  as  quickly  as  they  walk. 


MOVABLE  DAM  TO  BE  ERECTED  ALONG  THE  CREST  OF  THE  SONE  WEIR. 


Each  set  of  scouring 
sluices  is  made  up  of 
twenty-five  movable 
shutters  of  a  width  of 
twenty  feet  each,  that 
is,  each  set  is  500  feet 


OTHER    IRRIGATION    WORKS.  105 

in  length.  These  movable  shutters  are  explained  in  the 
article  entitled  Sluices  and  Movable  Dam.s. 

Before  the  construction  of  the  weir  the  mean  depth  trf 
the  river  at  time  of  high  flood  was  found  to  be  11.64 
feet,  and  the  breadth  between  the  banks  12, 400  feet. 

The  river  in  Hood  rises  eight  and  one-half  feet  over 
the  crest  of  the  weir,  and  discharges  about  750,000  cubic 
feet  per  second.  Colonel  Dickens  estimated  the  flood 
discharge  at  1,020,000  cubic  feet  per  second,  but  his  es- 
timate was  too  large.  The  catchment  basin  of  the  Sone 
is  about  23,000  square  miles. 

The  weir  is  composed  mainly  of  dry  rubble,  and  is- 
similar  in  cross-section  to  the  Okhla  weir,  Figure  39,  but 
differing  from  that  structure  in  having  foundations  to 
its  three  parallel  masonry  walls,  which  traverse  the  mass 
of  dry  rubble  from  end  to  end,  and  keep  this  mass  to- 
gether. 

An  ample  supply  of  good  stone,  both  for  rubble  and 
ashlar,  is  obtainable  from  quarries  about  five  miles  dis- 
tant. The  Sone  differs  from  the  Himalayan  rivers  gen- 
erally, in  being  confined  within  a  permanent  channel, 
so  that  no  flank  defenses  of  any  importance  are  neces- 
sary 011  the  banks  of  the  river.  The  three  parallel  walls 
of  the  dam  are  founded  on  shallow,  hollow  blocks,  sunk 
with  the  aid  of  Fouracre's  excavators.  These  blocks 
have  thin  walls;  for  blocks  of  six  feet  interior  width  a 
single  brick  thick  was  sufficient,  \vhile  for  fourteen  feet 
blocks  the  walls  were  built  from  one  and  one-half  or  two 
brick  thick.* 

In  the  Bengal  Revenue  Report  of  the  Public  Works 
Department  for  1889-90,  it  is  stated  that: — 

"  For  many  years  after  the  construction  of  the  Sone 
Weir,  the  recurring  failures  of  the  piers  of  the  river 

* Indian  Weirs,  by  Major  A.  M.  Lang,  K.  E.,  Professional  Papers  on  In- 
dian Engineering,  Vol.  VT.  Second  Series. 


100  IRRIGATION    CANALS    AND 

sluices,  owing  to  the  inherent  weakness  of  their  design, 
were  a  constant  cause  of  expenditure  in  repairs,  and  in 
1885  it  was  decided  to  build  them  011  a  stronger  model. 
The  work  is  now  completed." 

The  Okhla  Weir,  Agra   Canal  in    India,  is   shown  in 
cross-section  in  Figure  39.     This  is  a  remarkable  work, 

FIG. 39  SECTION 


AGRA  CANAL  OKHLA  WEIR, 


in  which  the  engineers  of  Northern  India  have  exceeded 
the  Madras  engineers  in  the  shallowness  of  foundation, 
in  which  the  so-called  "  Madras  system  "  was  supposed 
to  differ  widely  from  the  practice  of  other  parts  of 
India.  In  this  case  foundation  may  be  said  to  be  en- 
tirely dispensed  with.  The  lowest  cold  water  level,  649 
feet  above  Kurrachee  mean  sea  level,  was  adopted  as 
the  datum,  and  a  trench  was  made  for  2,438  feet  across 
the  dry  sandy  bed  of  the  Jumna,  eight  miles  below 
Delhi,  at  this  level;  and  in  this  trench  was  built,  in  the 
winter  of  1869-70,  a  wall  four  feet  thick  and  five  feet 
high  of  quartzite  rubble  masonry,  laid  in  lime  cement; 
a  sloping  apron  of  dry  quartzite  rubble  extended  five 
feet  above  this  wall,  and  a  sloping  talus  of  similar 
material  was  laid  for  100  feet  below  it;  the  floods  of  1870 
were  allowed  to  pass  over  this  weir,  and  left  it  unharmed. 
During  the  next  winter,  the  wall  was  raised  to  its  full 
height,  of  nine  feet,  and  the  talus  was  lengthened  to 
180  feet.  The  floods  of  1871  overtopped  the  weir  by 
five  and  a-half  feet,  more  than  1,000,000  cubic  feet  per 
second  sweeping  over  it,  while  40,000  cubic  feet  broke 
over  the  left  shore  eubankmeiit  and  inundated  a  large 
tract  of  country.  The  greatest  velocity  was  18.6  feet 


OTHER    IRRIGATION    WORKS. 


107 


per  second,  and  was  found  to  be  at  forty-two  feet  below 
the  crest.  Stone  was  worked  out  of  the  talus,  and  deep 
holes,  twenty  feet  deep,  were  scoured  out  on  the 


stream  edge.       During  the   next    winter,   1871-72,    the 
embankments  were  heightened  and  strengthened;    and 


108  IRRIGATION    CANALS    AND 

1,000,000  cubic  feet  of  stone  were  expended  in  filling  up 
the  holes  below  the  talus.  In  1872-73,  a  second  wall — 
the  true  crest  wall  of  the  weir,  parallel  to,  and  thirty  feet 
above  the  one  first  built — was  raised  to  a  height  of  nine 
feet;  the  interval  between  the  two  walls  being  filled  with 
dry  rubble.  A  third  wall,  four  feet  thick  and  four  feet 
deep,  was  inserted  in  the  talus,  forty  feet  below  the  lower 
wall;  this  has  quite  stopped  all  movement  in  the  upper 
part  of  the  talus;  this  wall  is  at  the  line  of  maximum 
velocity  in  floods.  In  March,  1874,  the  canal  was  opened. 
The  total  quantity  of  stone  in  the  weir  is  4,660,000 
cubic  feet.  The  stone  is  the  quartzite  of  the  ridge  of 
Delhi,  and  of  similar  outcropping  ridges  in  the  country 
around.  The  right  flank  of  the  Okhla  weir  abuts  on  to 
a  ridge  of  this  rock,  which  has  furnished  an  inexhaust- 
ible supply  of  material  on  the  spot.  The  stone  contains 
a  large  proportion  of  quartz,  a  little  feldspar,  and  pro- 
toxide of  iron.  It  is  very  durable  and  excessively  hard, 
rendering  it  unsuitable  (owing  to  the  labor  and  expense) 
for  finely  dressed  ashlar  work.  The  river  bed  has  silted 
up  to  the  crest  level;  but  at  the  canal  head  a  clear  chan- 
nel is  kept  open  by  the  scouring  action  of  the  river 
sluices  placed  at  the  right  end  of  the  weir,  similarly 
situated  to  those  of  the  Narora  Weir,  as  described  below. 

This  weir,  and  also  the  Sone  and  Narora  weirs,  have 
long  aprons  of  dry  rubble,  and  this  seems  to  be  the 
section  selected  for  the  modern  dams,  in  sandy  rivers, 
by  Indian  engineers.  As  the  sandy  beds  of  these  rivers, 
except  in  the  vicinity  of  the  scouring  sluices,  were  al- 
ways raised,  on  the  up-stream  side,  to  the  level  of  tlio 
crest  of  the  weir,  consequently  that  portion  of  the  work 
would  be  free  from  scour,  and  it,  therefore,  was  given  a 
steeper  slope  than  the  apron  on  the  down-stream  side. 

The  Streeviguntum  Weir  or  Aiiicut,  over  the  Tam- 
brapoorney  River  in  Madras,  is  shown  in  cross-section 


OTHER    IRRIGATION    WORKS.  109 

in  Figure  41.      This  weir,  and  also  that  across  the  Goda- 
very,   Figure   44,   are   located  in  Madras,   and  they  are 
there  called  anicuts.     The  Streeviguntum  Weir  is  of  the- 
same  type  as  the  Narora  Weir,  though  on  a  smaller  scale. 


It,  however,  has  no  water  cushion,  while  the  Norora 
Weir  has  a  water  cushion  of  at  least  three  feet  at  the  low 
stage  of  the  river.  The  scouring  sluices  of  this  weir,  as 
in  the  greater  number  of  the  old  weirs  of  the  Madras 
Presidency,  have  a  small  span.  In  this  case  there  are 
nine  vents,  and  each  vent  is  only  four  feet  in  width  by 
nine  feet  high.  These  small  vents  have  not  the  scour- 
ing capacity  of  the  large  ones  of  Northern  India. 

The  Streeviguntum  Weir  is  1,380  feet  in  length  be- 
tween the  wing-walls,  raised  six  feet  above  the  average 
level  of  the  deep  bed  of  the  river,  and  the  width  at  the 
crown  is  seven  and  one-half  feet;  there  is  a  front  slope 
of  one-half  to  one,  and  in  rear  a  perpendicular  fall  on 
to  a  cut-stone  apron  twenty-four  feet  wide,  and  four  and 
one-half  feet  in  depth;  beyond,  there  is  a  rough  stone 
talus  of  the  same  depth,  and  thirty-six  feet  in  width, 
protected  by  a  retaining  wall.  The  foundation  of  the 
body  of  the  work,  and  of  the  cut-stone  floor  in  rear,  is  of 
brick-in-linie,  laid  on  wells  sunk  ten  and  one-half  feet 
in  the  sand,  and  raised  four  and  one-half  feet  above 
the  wells,  including  the  cut-stone  covering;  the  retain- 
ing wall  is  built  of  stone-in -lime,  and  rests  on  a  line  of 
wells,  sunk  to  the  same  depth,  ten  and  one-half  feet. 
The  body  of  the  aiiicut  is  of  brick-in-lime,  faced  through- 


110  OTHER    IRRIGATION    WORKS. 

out  with  cut  stone,  and  furnished  with  a  set  of  under- 
sluices  at  each  extremity  of  the  work,  to  let  off  sand 
and  surplus  water.* 

The  Narora  Weir,  Lower  Ganges  Canal  in  India,  is 
shown  in  cross-section  in  Figure  43.  This  canal  gets 
its  supply  from  the  river  Ganges.  It  is  the  most  recent 
of  the  large  and  important  weirs,  built  across  wide  rivers 
with  sandy  beds,  and  from  the  volume  of  the  floods,  the 
sandy  nature  of  the  river  bed,  and  the  absence  of  material 
on  the  site  suitable  for  a  weir  of  this  description,  the  diffi- 
culties to  be  contended  with  have  been  very  great.  The 
dam  proper  is  a  solid  wall  of  brick  masonry  3,700  feet  in 
length ;  the  floor  below  is  of  concrete,  three  feet  thick,  cov- 
ered over  with  brick  work,  one  foot  thick,  and  then  with 
one  foot  of  sandstone  ashlar;  and  the  talus  below  is 
formedfof  very  large  masses  of  block  kunkur,  a  kind  of 
nodular  limestone,  brought  from  the  quarries  at  thirty 
miles  distance.  The  up-stream  side  of  the  weir  is 
backed  with  clay  puddle,  pitched  011  its  outer-  slope 
with  an  apron  of  block  kuriker. 

The  length  of  the  weir  was 
settled  by  Major  Jeffreys,  R. 
|c  E.,  as  4,000  feet,  on  the  fol- 

.*<**  <#•  *„**._   lowing  data:     See  Figure  42. 

&— afflux =1.5  feet,  when  the  river  was  at  its  highest 
was  accepted  as  perfectly  safe. 

((( — b)  =(>  feet---  maximum  flood  level  above  sill  of 
weir. 

Q— -maximum  flood  volume  flowing  over  weir  of  200,000 
cubic  feet  per  second. 

Z-=  length  of  crest  of  weir  in  feet. 

w  -6  feet  per  second  —  xnvfiwe  velocity  of  approach. 


*  Indian    Weirs,  by  Major  A.  M.  Lang.     Professional  Papers  on  Indian 
Engineering.     Vol.  VI,  Second  Series. 


OTHER    IRRIGATION    WORKS.  Ill 

The  figures  applied  in  D'Aubiiison's  formula  give: — 


Q  —  3.49  I  h  i  h  +  .035  w*    ;    4.97  I  (a  —  b)  yh  +  .01  -it? 
Computing  this  we  find  the  value  of  ^length  of  weir 
=3,776  feet. 

FIG.  43.     NARORA   WEIR,   LOWER  GANGES  CANAL. 


Colonel  Brownlow,  R.  E.,  in  reviewing  the  project  and 
deprecating  a  proposed  reduction  of  the  length  settled 
by  Major  Jeffreys,  showed  that  a  maximum  flood  of  230,- 
000  cubic  feet  might  not  unreasonably  be  expected,  and 
that  taking  into  consideration  the  circumstances  of  the 
site,  the  light  and  friable  nature  of  the  soil  of  the  coun- 
try, and  the  lowness  of  the  ridge  which  intervenes  be- 
tween the  present  channel  of  the  river  and  the  broad 
parallel  trough  of  the  Mahewah  Valley,  it  would  be  very 
dangerous  to  contract  the  weir  and  raise  flood  levels. 

The  necessity  for  well  foundations,  especially  for  a 
strong  line  of  deep  blocks,  along  the  lower  end  of  the 
stone  floor,  and  also  for  staunching  all  leakage  by  a  pud- 
dle of  clay  above  the  drop  wall — with  a  view  of  holding 
up  all  the  water  possible,  and  thus  losing  none  of  the 
supply  when  the  river  is  at  its  lowest — of  stopping  all 
flow  under  the  floor  to  the  risk  of  undermining  arid  de- 
stroying it — and  also  of  resisting  retrogressive  action 
below  the  weir,  was  strongly  urged  in  Colonel  Brown- 
low's  review  of  the  project,  as  will  be  seen  from  the  fol- 
lowing extract  from  his  report: — 

"  My  reasons  are,  first,  that  all  our  experience  in 
Upper  India  shows  that  where  velocity  of  a  stream  is 
largely  augmented  by  the  construction  of  a  barrier 
across  it,  permanent  deepening  of  the  channel  below  in- 
variably takes  place;  and  secondly,  that  leakage  will 


112  IRRIGATION    CANALS    AND 

•occur  through  the  sandy  bed  underneath  a  dam  with 
shallow  foundations. 

11  Deepening  of  the  bed  has  taken  place  on  all  the  tor- 
rents across  which  weirs  have  been  thrown  on  the  East- 
ern Jumna  Canal,  and  it  is  now  occurring  at  Okhla. 
It  occurred  below  the  Dhanowrie  Dam,  011  the  Ganges 
-Canal,  until  the  obstruction  caused  by  the  dam  was  re- 
duced, so  that  the  normal  velocity  of  the  torrent  was 
nearly  restored,  when  the  channel  below  partially  silted 
up  again. 

11  This  fact  alone  is  a  very  strong  argument  against  the 
proposed  reduction  of  length  of  weir,  but  as  our  weir  at 
Narora  will,  in  any  case,  greatly  accelerate  the  mean 
velocity  of  the  Hoods,  we  must  be  prepared  both  for  re- 
trogression of  levels,  and  the  formation  of  very  deep 
holes  immediately  below  the  talus  of  heavy  material. 
Those  at  the  tail  of  the  Okhla  Weir,  Figure  30,  after  the 
floods  of  last  season,  were  from  IV)  to  20  feet  deep;  but 
whereas  at  Okhla  the  materials  for  filling  them  up,  and 
thus  resisting  further  retrogression,  are  readily  available, 
we  shall  at  Narora  have  nothing  but  a  scanty  supply  of 
block  kunkur  brought  from  long  distances,  or  blocks  of 
beton  manufactured  at  considerable  expense. 

"  In  the  latter  case,  a  strong  line  of  deep  blocks,  sup- 
ported by  the  ruins  of  the  talus,  would  stoutly  resist 
any  retrogressive  action,  whilst  the  materials  for  repair 
were  being  collected  and  prepared;  while  the  work  on 
shallow  foundations  would  run  the  greatest  risk  of 'being 
undermined  and  destroyed. 

"  It  is  stated  that  the  leakage,  prevented  by  deep  well 
foundations,  is  more  imaginary  than  real,  because  long 
before  the  volume  entering  the  canal  is  likely  to  be  util- 
ized, the  bed  of  the  river  will  have  become  silted  up 
nearly  to  the  crest  of  the  dam,  and  the  upper  layers  of 
silt  will  have  become  more  or  less  clayey,  because  leak- 


OTHER    IRRIGATION    WORKS.  113 

age  takes  place  through  the  banks  as  well  as  through 
the  bed,  and  finally  because  little  or  no  leakage  has  been 
detected  through  the  Okhla  weir  which  has  shnilow 
foundations. 

"  I  cannot  admit  that  the  upper  layers  of  silt  deposited 
in  the  bed  of  the  river  above  are  deposited  by  falling 
floods,  and  are  swept  out  again  by  the  full  current  of  the 
next  succeeding  high  flood.  The  scour  which  takes  place 
immediately  above  any  marked  contraction  of  a  stream,  is 
a  matter  of  common  experience,  and  is  easily  explained 
by  the  great  relative  increase  in  the  bottom  velocity  re- 
sulting from  the  contraction. 

"  The  banks,  on  the  contrary,  will  become  permanent, 
if  the  flanks  of  the  weir  are  not  turned,  and  they  may 
ultimately  become  staunched  by  the  clay  brought  down 
by  the  flood  water.  Besides,  the  effect  of  the  pressure  of 
the  water  011  the  banks  is  not  worth  mentioning,  when 
compared  to  that  011  the  sand  underlying  the  weir.  I 
think,  therefore,  that  any  consideration  of  the  leakage 
through  the  banks  may  safely  be  neglected.  But,  even 
if  it  could  not  be,  I  do  not  see  why  we  should  not  try 
and  stop  the  leakage  through  the  bed,  because  the  banks 
are  supposed  likely  to  leak  also. 

"  The  latter  argument  applies  equally  to  the  objection 
commonly  urged  against  deep  block  foundations,  viz: 
that  aline  of  them  cannot  be  made  perfectly  water-tight. 
It  is  surely  better  to  block  up  TWtns  of  the  area  through 
which  leakage  can  occur,  than  to  leave  it  all  open  be- 
cause a  perfectly  water-tight  partition  cannot  be  made. 

"  Apart  from  any  consideration  of  the  value  in  money 
of  the  water  saved  by  a  strong  water-tight  dam,  the 
strongest  necessity  is,  to  my  mind,  laid  upon  us  to 
economize  every  drop  of  the  low-water  supply  in  the 
river,  owing  to  its  insufficiency  for  the  requirements  of 
the  years  of  drought.  Common  justice  to  the  cultivating 
8 


114  IRRIGATION    CANALS    AND 

community,  dependent  on  the  canal,  seems  to  me  to  dic- 
tate the  adoption  of  every  reasonable  precaution  for 
rendering  the  whole  of  the  short  supply  available  for 
purposes  of  irrigation. 

"  I  have  placed  the  deep  line  of  blocks  at  the  tail  of  the 
cut-stone  apron,  because  I  think  that  the  latter,  if  built 
at  the  proper  level,  and  of  a  proper  section,  will  perfectly 
protect  the  blocks  from  any  fear  of  action  on  the  up- 
stream side,  and  that  the  real  danger  to  be  guarded 
against  is  the  cutting  back  and  permanent  deepening  of 
the  bed  of  the  river  below  the  weir.  I  have  allowed  only 
shallow  foundations  for  the  drop  wall,  because  I  consider 
the  line  of  blocks  underneath  it  sufficiently  protected  by 
the  cut-stone  apron  and  deep  foundations  on  the  down- 
stream side,  and  by  the  mass  of  heavy  material  on  the 
up-stream  side.  The  velocity  of  the  current  above  the 
weir,  although  amply  sufficient  to  sweep  away  the  loose 
sand  of  the  bed,  has  been  proved,  by  the  experience  at 
Okhla,  insufficient  to  move  the  heavy  material  of  the 
apron." 

To  hold  the  talus  together,  it  is  traversed  from  end  to 
end  by  solid  concrete  walls  at  intervals  of  thirty  feet  and 
forty  feet  as  shown  in  Figure  43.  This  plan  was  found 
to  be  necessary  at  Okhla,  Figure  39,  where  the  third  wall 
of  four  feet  square  section  was  adopted  as  necessary,  in 
order  to  check  the  movement  in  the  blocks  in  the  upper 
part  of  the  talus,  although  it  formed  no  part  of  the  orig- 
inal design. 

The  level  of  the  cut-stone  floor  of  the  weir,  as  also  of 
the  floor  of  the  under-sluiee,  is  three  feet  below  low 
water  level;  and  as  the  floor  is  five  feet  thick,  the  laying 
of  it  entailed  excavation  to  a  depth  of  eight  feet  below 
low  water.  To  effect  this,  the  upper  row  of  blocks  and  lower 
row  of  wells  were  sunk  to. full  depth,  and  hearted  with  con- 
crete. This  was  done  by  filling  the  hole  below  the  curb,  and 


OTHER    IRRIGATION    WORKS.  115 

the  lower  one  or  two  feet  of  the  block  or  well  by  hydraulic 
cement  let  down  in  skips;  when  this  had  set,  it  formed 
a  water-tight  plug,  and  enabled  the  well  or  block  To~be 
pumped  dry.  The  concrete  core  of  the  well  or  block 
was  then  put  down  in  layers,  and  rammed  in  the  ordi- 
nary manner.  The  interval  between  each  pair  of  con- 
tiguous wells  and  blocks  was  closed  by  wooden  piles,  and 
the  interval,  included  between  piles  and  well,  cleared  of 
sand  and  filled  with  concrete.  Clay  puddle  was  also 
packed  above  the  upper  row  of  blocks.  The  space, 
thirty-three  feet  in  width  intervening  between  the  upper 
row  of  blocks  and  the  lower  line  of  wells,  was  then  di- 
vided into  compartments  of  about  forty  feet  in  length, 
by  cross  lines  of  shallow  blocks,  sunk,  hearted  and  con- 
nected as  above  described.  Thus  large  coffer-dams  were 
formed,  which  were  excavated  to  a  depth  of  eight  feet  below 
low  water  level,  and  the  water  pumped  out  by  Gwynne's 
pumps,  so  as  to  allow  of  a  three  feet  thick  concrete  floor 
being  laid.  On  this  a  layer  of  brick- work  one  foot  thick 
was  added;  and  this  in  its  turn  was  covered  by  an  ash- 
lar floor  of  cut  sandstone  blocks  one  foo't  in  thickness. 

The  under-sluices,  forty-two  vents  of  seven  feet  each, 
are  at  the  extreme  right  abutment  end  of  the  weir,  so  as 
to  keep  a  clear  channel  open  along  the  front  of  the  im- 
mediately adjoining  head-sluices  of  the  canal,  whose 
floor  is  three  feet  above  that  of  the  weir  sluices,  and  this 
allows  the  lowest  three  feet  of  silt-laden  water  to  pass  by 
without  entering  the  canal.  The  crest  of  the  weir  stands 
seven  feet  above  low  water  level,  which  is  the  level  of 
the  floor  of  the  head-sluices,  thus  allowing  seven  feet  in 
depth  of  water  to  pass  into  the  canal/"" 

The  Dowlaiswaram  Branch  of  the  Godavery  Aiiicut 
or  Weir  is  shown  in  cross-section,  in  Figure  44. 

*  Indian  Weirs,  by  Major  A.  M.  Lang.     Professional  Papers  on  Indian 
Engineering,  Vol.  VI,  Second  Series. 


116  IRRIGATION    CANALS    AND 

The  total  length  between  the  extreme  flanks  of  the 
weir  is  20,570  feet.  It  is  broken  Into  four  sections 
separated  by  islands,  and  the  total  length  of  the  anicut 
on  these  four  sections  is  11,866  feet. 


GOOAVERV       ANICUT 

The  longest  section  is  the  Dowlaiswaram,  and  the  fol- 
lowing description  of  this  section  is  taken  from  Colonel 
Baird  Smith's  work,  "  Irrigation  in  Southern  India:" 

The  bed  of  the  Godavery  throughout  is  of  pure  sand, 
and  in  such  soil  are  the  whole  of  the  foundations  laid. 
Commencing  from  the  eastern  or  left  bank,  the  first 
portion  of  the  work  is  the  Dowlaiswaram  branch  anicut 
or  dam.  The  total  length  of  this  is  4,872  feet.  The 
body  of  the  dam  consists  of  a  mass  of  masonry  resting 
on  front  and  rear  rows  of  wells,  each  well  being  six  feet 
in  diameter,  and  sunk  six  feet  below  the  deep  bed  of  the 
stream.  The  masonry  forming  the  body  is  composed: — 

1st.  Of  a  front  curtain  wall  running  along  the  whole 
length,  seven  feet  in  height,  four  feet  in  thickness  at  the 
base,  with  footings  one  foot  broad  on  each  side  10  cover 
the  tops  of  the  wells  on  which  the  curtain  wall  rests, 
and  three  feet  thick  at  the  summit. 

2d.  Of  a  horizontal  flooring  or  waste-board  nineteen 
feet  in  breadth  and  four  feet  in  thickness. 

3d.  Of  a  masonry  counter-arched  fall  twenty-eight 
feet  in  breadth  and  four  feet  thick,  of  which  the  curve 
is  so  slight  that  the  form  may  be  considered  practically 
as  that  of  an  inclined  plane.  The  waste-board  and  tail 


OTHER    IRRIGATION    WORKS. 


117 


slope  are  protected  against  the  action  of  the   stream  by 
a  covering  of  strongly  clamped  cut  stones  over  all. 

4th.  Of  a  rough  stone  apron  in  rear  formed  ~oi~the 
most  massive  stones  procurable,  and  extending  about 
seventy  or  eighty  feet  down  stream.  Figure  44  does  not 
show  the  apron  extended  so  far,  but  it  is  now  extended 
to  about  150  feet,  and  further  secured  by  a  masonry  bar. 

The  apron,  protects  the  rear  foundation  against  the 
erosive  action  of  the  stream  passing  over  the  dam.  The 
body  of  the  dam  rests  merely  on  a  raised  interior  or 
core  of  the  common  river  sand,  and  no  precautions  to 
strengthen  this  in  anyway  have  been  considered  neces- 
sary. On  the  extreme  left  flank  of  the  dam  is  a  series 
of  works,  consisting  of  a  lock  for  the  passage  of  craft, 
a  head  sluice  for  an  irrigation  channel,  and  an  under 
sluice  for  purposes  of  scour  and  clearance  from  deposits. 


FIG.   45.     CROSS-SECTION  OF  TURLOCK  WEIR. 

The  Turlock  Weir  in  California,  across  the  Tuolumne 
River,   is   shown  in   cross-section,  in   Figure   45.      The 


118  IRRIGATION    CANALS    AND 

original  design  for  this  weir  was  made  by  Mr.  Luther 
Wagoner,  C.  E.,  but  the  water  cushion  was  added  by 
Mr.  E.  H.  Barton,  the  present  Chief  Engineer  of  the 
Turlock  Irrigation  District.  The  flood  discharge  of  the 
river  will  pass  over  the  weir.  The  low  weir  on.  the  down- 
stream side  backs  up  the  water  and  forms  a  water  cushion 
to  receive  and  break  the  shock  of  the  flood-water  when  it 
flows  over  the  weir.  The  water-cushion  has  been  found 
in  India  to  be  a  most  effective  protection  to  the  bed  of 
the  river  from  the  erosion  caused  by  falling  water. 

The  length  of  the  weir  on  top  is  330  feet,  its  max- 
imum height  to  foundation  108  feet,  and  the  maximum 
height  of  the  overfall  of  water  ninety-eight  feet.  Its 
width  at  base  is  eighty-three  feet,  and  the  maximum 
pressure  6.3  tons  per  square  foot.  The  weir  is  curved 
in  plan,  the  radius  to  up  stream  face  being  300  feet, 
and  the  angle  60°.  Bed  and  sides  of  channel  is  meta- 
morphic  (quartzite  after  slate)  rock  of  exceeding  hard- 
ness. 

On  the  removal  of  an  old  dam,  near  the  site  of  this 
weir,  an  inspection  of  the  bed  rock,  where  the  fall  had 
been  ten  to  thirty  feet  over  said  dam  for  eighteen  years, 
showed  hardly  any  appreciable  wear.  Calculated  for  the 
highest  flood  known,  that  of  1862,  the  flow  over  the 
crest  of  the  weir  is  130,000  cubic  feet  per  second. 

The  subsidiary  weir  is  located  200  feet  below  the  main 
weir.  It  is  120  feet  long  on  top,  twelve  feet  in  width, 
and  twenty  feet  in  maximum  height,  and  it  backs  the 
water  to  a  depth  of  fifteen  feet  on  the  toe  of  the  upper  or 
main  weir,  giving  a  water-cushion  of  that  depth;  but, 
during  floods,  there  will  be  a  depth  on  the  toe  of  over 
forty-five  feet.  The  volume  of  the  dam  will  be  about 
33,000  cubic  yards. 

Vertical  falls,  with  water-cushions,  are  preferred  in 
India  to  sloping  or  curved  faces  on  the  down-stream  side 


OTHER    IRRIGATION    WORKS. 


119 


of  works  over  which  water  falls.  For  stability  to  resist 
water  pressure  dams  or  weirs,  with  a  curved  profile  ac- 
cording to  the  French  plan,  are  the  most  suitable-pbttt, 
in  order  to  avoid  the  erosive  and  destructive  action  of 
the  falling  water  on  the  curved  face,  vertical  walls  with 
water-cushions  are  preferred. 

Numerous  instances  of  vertical  falls  are  to  be  found 
on  the  canals  in  Northern  India,  and  011  two  important 
modern  works,  the  Bhim  Tal  Dam  and  the  Betwa  Weir. 
Doubtless  instances  can  be  found  also  in  modern  works 
of  dams  with  curved  faces  on  the  down-stream  side  over 
which  water  flows — for  example,  the  Vryiiwy  Dam  for 
the  Liverpool  water  supply,  and  the  concrete  dam  for 
the  Geelong,  Australia,  water  supply. 

The  dam  across  the  river  Lozoya,  in  Spain,  to  impound 
water  for  the  supply  of  Madrid,  has  an  extraordinary 
vertical  drop — 105  feet.  The  back  of  the  dam,  over 
which  the  water  falls,  is  not  vertical,  but  has  a  slight 
batter  given  to  it  by  off-sets.  The  flood-water,  however, 
leaps  clear  over  this  face. 

During  floods,  when  the  reservoir  is  full,  the  whole 
discharge  of  the  river  pours  over  it  in  an  unbroken 


WEIR  OF  HEN  APES  CANAL. 

sheet.     It  has  not  a  water-cushion.     The  dam  was  built 
of  ashlar,  which  is  not  the  best  method  of  construction 


120  IRRIGATION    CANALS    AND 

for  such  a  work.  Uiicoursed  rubble  is  much  better 
suited  for  a  dam,  as  there  is  less  likelihood  of  percolation 
through  its  broken  joints  than  through  the  regular- 
coursed  ashlar. 

The  cross-section  of  the  weir  of  the  Henares  Canal,  on 
the  river  Henares,  in  Spain,  is  given  in  Figure  46.  The 
masonry  of  this  weir  is  first-class  in  every  respect.  Its 
design,  however,  as  to  its  cross-section,  is  one  not  adopt- 
ed in  India.  For  a  masonry  weir,  a  vertical  drop  on  the 
down-stream  side  and  a  water-cushion,  is  preferred  in 
the  latter  country. 

The  action  of  the  water  on  the  Ogee  Falls,  011  the 
Ganges  Canal,  was  found  very  destructive,  whereas  the 
vertical  falls  with  water-cushion  stood  well. 

Where  the  Henares  Canal  is  taken  from  the  river,  the 
river  bed  is  composed  of  compact  clay  rock,  mixed  with 
strata  of  hard  conglomerate,  which  had  to  be  blasted  out 
to  fit  it  for  the  foundation  of  the  weir.  The  weir  itself 
is  390  feet  in  length  of  crest,  formed  on  two  curves  of 
397  and  198.5  feet,  running  obliquely  across  the  river  so 
as  to  be  tangential  to  the  axis  of  the  canal.  It  raises 
the  water  to  a  height  of  twenty  feet.  Its  thickness  at 
crest  is  3.14  feet,  and  on  the  general  level  of  the  river's 
bed,  45.8  feet.  As  this  bed,  however,  was  very  uneven, 
it  was  necessary  to  carry  down  the  thrust  of  the  apron 
by  a  series  of  blocks  of  stones  formed  in  steps,  the  last 
firmly  embedded  three  feet  in  the  rock.  The  body  of 
the  weir  consists  of  hydraulic  concrete;  the  apron  is 
faced  with  cut-stone  blocks,  every  fifth  course  being  a 
bond  three  feet  deep,  and  is  a  beautiful  specimen  of  ma- 
sonry. Much  pains  have  been  bestowed  on  preventing 
the  least  filtration.  For  this  purpose  a  channel  was  cut 
in  the  rock  along  the  central  axis  of  the  weir  for  its 
whole  length,  and  into  this  a  line  of  stones  was  fitted, 
half  bedded  in  the  rock,  half  rising  into  the  concrete. 


OTHER    IRRIGATION    WORKS.  121 

Into  each  vertical  joint  of  these  stones  a  groove  was  cut 
an  inch  deep.  The  stones  were  built  in  cement  into  the 
rock,  and  the  joints  run  with  pure  cement.  The -con- 
crete was  then  rammed  tightly  round  them,  arid  a  water- 
tight joint  thus  formed. 

With  the  same  object  V-shaped  grooves  were  formed 
in  the  sides  of  each  stone  of  the  four  upper  courses  of 
the  weir,  as  shown  in  Figure  46,  and  horizontal  grooves 
cut  to  correspond  with  them  on  the  upper  and  lower 
faces  of  each  stone,  as  shown  in  Figure  47.  When, 
therefore,  the  stones  were  set,  there  was  formed  a  con- 
tinuous channel,  one  inch  square,  running  between  each, 
and  this  was  filled  with  pure  cement,  poured  in  liquid, 
so  as  to  form  a  tight  joint  between  each  stone. 

In  spite  of  all  the  precautions  taken  the  floods  exerted 
an  erosive  action  on  the  bed  of  the  river  below  the  weir, 
and  a  large  hole  was  scooped  out  of  the  rock  at  the  tail, 
where  the  apron  ended.'" 

The  head  of  the  Cavour  Canal  in  Italy  is  on  the  left 
bank  of  the  Po,  about  a  quarter  of  a  mile  below  the 
Chivasso  bridge. 

The  bird's  eye  view,  Figure  48,  shows  the  position  of 
the  weir,  regulator,  uiider-sluices  and  escapes.  In  Indian 
canals  the  escapes  are  usually  channels  from  the  main 
canals  to  carry  away  any  surplus  water.  In  the  bird's 
eye  view  the  channels  marked  "  Escapes"  are  really 
channels  to  carry  away  the  water  that  is  used  for  scour- 
ing purposes.  These  scouring  or  under-sluices  were  in- 
tended to  prevent  the  silting  up  of  the  channel  from  the 
left  bank  of  the  Po  to  the  regulator. 

In  the  bird's  eye  view  is  shown  the  location  of  the 
proposed  weir  (not  yet  built),  placed  obliquely  in  a 
curve,  across  the  river. 

*Irrifjation  in  Southern  Europe,  by  Lieut,  (now  General)  C.  C.  Scott 
Moncrieff,  K.  E.  - 


122 


IRRIGATION    CANALS    AND 


OTHER    IRRIGATION    WORKS. 


123 


Its  length  was  to  be  2,300  feet,  forming  a  curve  of,  for 
the  most  part,  823  feet  radius,  but  less  at  the  ends.  The 
design  was  to  raise  the  water  by  means  of  this  weir~to-a~ 
height  of  about  eight  feet;  and  of  such  excellent  stiff 
soil  is  the  bed  composed,  that  it  was  thought  suffi- 
cient to  build  a  wall  of  concrete  going  down  to  only 
CAVOUR  CANAL-DETAILS  OF  PROPOSED  WEIR  ACROSS  THE  PO. 


THE  FIGURES  IN  BRACKETS  GH 


(579  ^Estimated  surface  of  water  in  a  flood  as  great 

(5S3.52)Inlradosof3ridae  near  Ckivasso.       "s  tluit  o/1839.     The  discharge  being  143000  cubic  feet 
S2A(n_Sitrfarji  H-titcrjLr>jtl,e/lood  of  1839.       Per  sec-  J*»*«i>'0  over  a  weir  1280  feet  long. 

FIG.49 


Cross  section  on  AD. 


6.56  feet  below  the  bed,  enclosed  in  front  and  rear 
by  sheet  piling,  its  upper  portion  cased  in  granite  slabs 
of  five  inches  in  thickness,  and  the  rest  of  blocks  of 
rough  stone  forming  a  protection  in  front  sloping  down 
to  a  horizontal  distance  of  sixteen  feet,  and  in  rear  to 
twenty-six  feet,  with  a  line  of  sheet  piling  at  its  toe,  and 
beyond  it  an  apron  of  similar  blocks,  of  the  same  width 
of  twenty-six  feet, ^  with  another  row  of  piling. 


124  IRRIGATION    CANALS    AND 

The  weir  was  intended  to  rest  on  solid  abutments  at 
the  two  ends,  and  on  the  end  next  the  canal  was  to  be 
supplied  with  a  set  of  scouring  sluices,  or  escapes,  con- 
sisting of  seventeen  openings,  each  4.6  feet  in  width 
and  eight  feet  in  height.  All  the  bed  for  ninety-six  feet 
below,  and  500  feet  above,  is  to  be  paved  \vith  splendid 
blocks  of  cut  granite,  brought  from  the  neighborhood 
of  the  Lago  Maggiore. 

From  the  left  flank  of  this  escape  the  regulating  bridge 
is  retired  for  a  distance  of  about  700  feet,  as  shown  in 
the  bird's-eye  view,  Figure  48,  and  close  to  its  right 
abutment  is  built  a  second  escape  of  nine  openings,  each 
5.54  feet  wide  and  ten  feet  high .  The  floor  of  this  escape 
is  one  foot  lower  than  that  of  the  regulating  bridge,  the 
more  effectually  to  establish  a  scour.* 

Article  29.     Scouring  Sluices — Under  Sluices. 

These  sluices  are  sometimes  called  Weir  Sluices  and 
again  Dam  Sluices. 

The  first  effect  of  the  construction  of  a  weir  across  a 
river  is  that  the  pool  formed  by  it  gradually  silts  up, 
partly  by  deposit,  during  floods,  of  matter  in  suspension 
in  the  water,  and  partly  by  the  gradual  forward  motion 
of  the  bed  of  the  river  which  exists  in  all  streams,  but 
is  only  visible  to  the  eye  in  rivers  with  sandy  beds. 
Islands  begin  to  form,  which  would  in  time  obstruct 
navigation  across  the  river  above  the  weir,  and  would 
prevent  the  water,  in  the  dry  season,  from  finding  ac- 
cess to  the  canals  led  off  from  the  pool. 

In  rivers  in  India  carrying  sand  and  silt,  the  silting 
up  of  the  bed  of  the  river  to  the  level  of  the  crest  of  the 
weir  seems  to  be  inevitable.  This  sand  and  silt  if  not 


Irrigation   in  Southern  Eiirope,   by   Lieut,    (now  General)   C.  C.  Scott 
Moncrieff,  K.  E. 


OTHER    IRRIGATION    WORKS.  125 

removed  choked  the  head  of  the  canal  and  locks,  located 
above  the  weir,  and  stopped  their  supply  of  water.  In. 
order  to  obviate  these  difficulties,  every  weir  has  td~t)(r 
furnished  at  one  extremity,  or  at  both  extremities,  ac- 
cording as  one  canal  or  two  canals  are  taken  off  from 
above  it,  with  a  set  of  scouring  sluices.  In  very  long 
weirs,  such  as  that  across  the  Sone  River  in  Bengal, 
another  scouring  sluice  is  placed  in  the  center,  to  assist 
in  keeping  open  a  navigable  channel  across  the  river. 

The  proper  location  for  a  scouring  sluice,  with  respect 
to  the  regulator  of  a  canal,  is  that  the  crest  of  the  weir 
should  be  at  right  angles  to  the  face  line  of  the  regulator, 
and  also  at  right  angles  to  the  face  line  of  the  lock  when 
the  channel  is  navigable. 

This  is  well  exemplified  in  the  plan,  of  the  Okhla  Weir 
Works,  Figure  40.  It  can  be  seen  there  that  the  cur- 
rent of  the  river  flows  flush  with,  and  parallel  to,  the 
face  line  of  the  canal  and  lock,  and  that  there  is  no 
recess  for  still  water  and  consequent  silting. 

An  instance  of  the  defective  location  of  a  regulator, 
with  respect  to  the  scouring  sluices,  is  seen  at  the  head- 
works  of  the  Upper  Ganges  Canal,  Figures  26  and  28. 
Here,  the  entrance  to  the  canal  is  located  over  two 
hundred  feet  lower  down  the  river  than  the  scouring 
sluices,  in  consequence  of  which,  the  strong  current 
flowing  to  the  scouring  sluices,  is  not  across  the  face 
of  the  regulator,  and  there  is  a  tendency  to  silt  where 
the  marks  *  *  *  are  shown,  on  Figure  28.  In  the 
low  stages  of  the  river  the  silt  prevents  the  free  flow  of 
the  current  towards  the  regulator. 

Another  instance  is  in  the  location  of  the  regulator 
of  the  Cavour  Canal,  Figure  48.  The  regulating  bridge 
is  located  700  feet  below  the  weir,  and  the  course  of  the 
current  through  the  scouring  sluices,  leaves  somewhat 
still  water  in  the  left  corner,  just  above  the  sluices  of 


120 


IRRIGATION    CANALS    AND 


OTHER    IRRIGATION    WORKS. 


127 


the  regulator.  When  these  sluices  are  opened  the  silt 
is  washed  into  the  canal. 

The  flow  through  the  scouring  sluices  is  controHed-  as 
explained  in  Article  31. 

The  regulator  should  be  as  close  as  possible  to  the 
scouring  sluice,  and  the  sill  of  the  latter  should  be  about 
three  feet  lower  than  the  sill  of  the  former.  Under  these 
circumstances,  when  the  scouring  sluices  are  opened,  the 
scour  takes  place  across  the  whole  face  of  the  regulator, 
and  washes  away  any  silt  or  debris  likely  to  obstruct  the 
free  flow  of  the  supply  into  the  canal. 


Article  30.     Regulators. 

The  Regulator  at  the  head  of  a  canal  is  also  called, 
Regulating  Bridge,  Regulating  Gate,  Regulating  Sluice, 
Head  Gate,  Head  Sluice,  Canal  Sluice,  Head  of  Canal, 
etc.  To  be  precise,  the  regulator  is  the  structure  in 
which  are  fixed  the  sluice  gates  to  control  the  water  sup- 
ply to  the  canal. 

Regulating  Gates  Del  Norte  Canal — Cross-Section  and  Elevation. 


U 


Iii  India,  Egypt  and  Italy,  the  regulator  is  sometimes 
part  of  a  highway  bridge,  as  shown  in  Figures  27,  32 
and  48.  In  the  latter  case,  however,  the  use  of  the  cov- 
ered bridge  is  confined  to  the  canal  officials. 

The  Myapore  Regulating  Bridge,  of  the  Upper  Ganges 


128 


IRRIGATION    CANALS    AND 


Canal,  is  shown  in  Figure  54.  The  view  is  taken  from 
the  down-stream  end  of  the  bridge,  so  that  the  sluice- 
gates, which  are  located  on  the  up-stream  side,  are  not 
seen.  The  sluice-gates  of  this  regulator  are  shown  in 
Figures  62  and  63.  These  sluice-gates  are  twenty  feet 
in  width,  but  regulating  sluices  are  seldom  more  than 
six  feet  in  width,  011  account  of  the  difficulty  of  working 
large  sluices  under  a  great  head  of  water. 

Idaho  Canal  Regulator  Head — Cross-Section  and  Elevation. 


The  Reglating  Gates  of  the  Del  Norte  Canal,  in  Colo- 
rado, are  shown  in  Figures  55  and  56,  and  Figures  57 
and  58  show  an  Idaho  Canal  Regulator  Head  for  pipe 
inlets.* 

It  is  usual,  on  Indian  canals,  to  make  the  floor  of  the 
regulator  at  head  of  canal,  the  zero  for  levels  on  the 
canal. 


Article  31 .    Sluices — Gates — Movable  Dams  and  Shutters. 

The  terms  Sluices,  Head  Sluices,  Gates,  Sluice  Gates 
and  Head  Gates,  are  variously  employed  to  mean  the 
sluices  that  are  fixed  in  the  regulator,  and  which  are 
used  to  control  the  supply  of  water  at  the  head  of  a  ca- 
iial.  The  sluice  gates  usually  used  on  Irrigation  Canals 
are  the  sliding  sluice  gate  Figures  55,  56,  57,  58,  59,  60, 

*Figures  55,  56,  57  and  58,  are  taken  from  a  paper  on  American  Irriga- 
tion Engineering,  by  Mr.  H.  M.  Wilson,  M.  Am.  Soc.  C.  E.,  in  Vol.  24  of 
the  Transactions  of  Am.  Soc.  C.  E. 


OTHER    IRRIGATION    WORKS. 


129 


62,  63,  64,  65,  69,  70  and  71,  the  horizontal  plank  gate, 
Figures  20  and  61,  and  the  vertical  piank  or  needle  sluice. 
These,  and  other  methods  not  so  generally  in  use~arc 
explained  below. 

The  gates  of  the  Cavour  Canal  Regulator,  of  which 
there  are  twenty-one,  are  fitted  with  a  double  set  of 
gates,  and  the  cutwaters  of  the  piers,  on  the  up-stream 

SLUICE  GATE— CAVOUR  CANAL. 

El 


SLUICE  GATES— INDIAN  CANALS. 


Old  Method  on  the  Jumna, 


Improved  Method  on  the  Ganges, 


side,  have  grooves  besides,  for  stop-planks.     These  latter 
are  intended  to  be  used  in  case  of  accident  or  repairs  to 
the  gates  or  regulator. 
9 


130  IRRIGATION    CANALS    AND 

The  gates  are  of  wood,  braced  with  iron,  as  shown  in 
Figures  59  and  60.  They  are  raised  by  means  of  an  iron 
bar  four  by  three-quarter  inches,  and  about  eighteen 
feet  long,  firmly  fastened  to  the  center  of  the  upper  edge 
of  the  gate,  and  connected  with  diagonal  bars  to  the 
lower  corners  to  distribute  the  force.  This  bar  passes 
through,  to  the  platform  above  the  highest  flood  level, 
from  which  the  gates  are  worked.  The  bar  is  pierced 
with  holes,  a,  a,  one  and  one-half  inches  in  diameter  at 
every  two  inches  of  its  length,  through  which,  when  it  is 
required  to  raise  it,  the  iron  point,  c,  of  a  crow  bar  is 
put,  and  it  is  raised  up  hole  by  hole,  an  iron  key,  b,  be- 
ing pressed  at  the  same  time  through  another  of  these 
holes,  and  resting  on  two  cross  bars  to  prevent  it  slipping 
down  again.  One  man  works  the  crow-bar  while  another 
holds  the  key.  By  pulling  this  out  the  gate  falls  at  once, 
and  this  is  important,  as  it  is  of  consequence  sometimes 
to  be  able  to  close  the  canal  quickly. 

This  arrangement  has  the  great  merit  of  simplicity 
and  it  is  frequently  adopted  on  American  canals. 

On  some  of  the  regulators  in  Northern  India,  a  drop 
gate  is  used  in  a  simple  groove,  and  sleepers,  with  a  scant- 
ling of  six  inches  square,  are  dropped  upon  the  top  of 
the  gate.  Both  time  and  labor  are  required  to  close  or 
open  the  bays,  although  they  were  only  six  feet  in  width. 
On  the  Ganges  Canal  regulator,  however,  with  ten  bays, 
having  each  a  width  of  twenty  feet,  on  which  the  safety 
of  the  works  depended,  it  was  necessary  to  devise  some 
quicker  method  to  economize  the  labor  required  for  using 
the  apparatus.  Figures  61  and  62,  show  the  old  and  also 
the  improved  method  of  operating  the  sluices.  Figure 
61  represents,  in  section,  the  drop  gate,  a,  and  the  sleep- 
ers, b,  b,  b,  opposed  to  the  up  stream  current;  a,  repre- 
sents a  gate  five  feet  in  depth,  which  is  kept  suspended 
in  dry  seasons,  and  is  dropped  down  on  the  expectation 


OTHER    IRRIGATION    WOKKS. 


131 


of  a  flood;  b,  b}  b}  show  the  sleepers  or  long  bars  of  tim- 
ber, which  when  the  chains  are  removed  from  the  gates, 
are  successively  dropped  upon  them  until  the  bay ~ is 

CANAL  REGULATING  APPARATUS. 


REGULATING  BRIDGE  WITH  LIFT-GATE  &  SLEEPERS 
Elevation. 


III 


Lift-gate. 


FIG.  63 


DROP-GATE  FOR  DAMS. 

Elevation.     .  , 


Plan 


FIG.64 


Plan 


FIG.68 


WINDLASS  FOR  REGULATING  BRIDGE. 


20. 


FIG. 6  5 


PLAN  OF  SLEEPER. 


FIG.GG 


132  IRRIGATION    CANALS    AND 

closed,  Figure  61.  The  time  that  this  takes  is  equal  to 
eighteen  minutes. 

Figures  62,  63,  64  and  65,  show  the  improved  design 
gained  by  the  use  of  the  windlasses.  The  bay  or  sluice 
opening,  it  will  be  observed,  is  divided  into  three  series, 
the  lowest  shutter  having  its  sill  on  the  floor  of  the  reg- 
ulator, which  is  the  zero  level  of  the  canal;  the  centrical 
and  top  shutters  having  their  sills  elevated  in  heights  of 
six  feet,  but'  working  in  separate  grooves  in  the  piers. 
The  shutter  marked  1,  Figure  62,  is  dropped  from  wind- 
lass, 1;  that  marked  2  from  windlass,  2;  and  that 
marked  3  consists  of  sleepers,  which  are  raised  and  low- 
ered without  the  aid  of  a  windlass.  The  three  gates, 
therefore,  are  quite  independent  of  each  other;  each  has 
its  own  sill  to  rest  upon;  and  the  whole  can,  if  necessary, 
be  worked  simultaneously.  The  great  advantage  of  this 
method  will  be  understood,  by  supposing  that  a  supply 
of  water  not  exceeding  six  feet  in  depth  is  required  for 
canal  purposes.  In  this  case,  the  whole  of  the  shutters, 
2,  and  3,  may  remain,  closed;  and  when  floods  come  on, 
the  whole  of  the  water-way  may  be  stopped  by  releasing 
one  gate  only. 

The  machinery  attached  to  these  gates  is  of  the  most 
simple  description,  intelligible  to  the  commonest  laborer 
on  the  works,  and  not  liable  to  disarrangement. 

On  some  canals  in  India  and  also  in  other  countries, 
Needle  Dams,  as  they  are  termed,  are  adopted  to  control 
the  supply.  A  horizontal  bar  of  wood  or  masonry  is 
fixed  011  the  floor  of,  and  across  the  opening,  and  a  beam 
of  timber  is  placed  vertically  over  and  parallel  to  this  and 
fitting  into  sockets  in  the  piers.  Planks,  called  needles, 
about  four  inches  scantling,  are  placed  vertically  in  front 
of  these,  and  are  operated  from  the  flooring  of  the  bridge, 
whether  permanent  or  temporary.  This  plan  has  been 
found  to  work  well  in  some  places.  There  is  always 


OTHER    IRRIGATION    WORKS. 


133 


FIG.70    i 


SLUICE  OF  HEN  ARES  CANAL 


134  IRRIGATION    CANALS    AND 

more  leakage  through  a  plank  sluice  than  through  a 
properly  constructed  framed  sliding  sluice. 

For  the  openings  of  Level  Crossings,  Drop  Gates  are 
sometimes  provided.  They  are  retained  in  their  upright 
position,  Figures  67  and  68,  by  chains  against  the  pres- 
sure of  the  canal  water  from  the  inside,  and  which,  on 
the  occurrence  of  a  flood,  can  be  dropped  down  on  the 
flooring  by  releasing  a  catch,  and  allowing  the  flood 
water  to  pass  through  the  openings.  When  the  flood  is 
over,  the  gates  are  raised  upright  by  a  movable  windlass, 
the  pressure  of  the  water  being  temporarily  taken  off  by 
dropping  planks  into  the  groves. 

The  sluices  of  the  Hen  ares  Canal  are  five  in  number, 
each  four  feet  wide.  The  details  of  these  sluices  are 
shown  in  Figures  69,  70  and  71. 

The  gates  are  made  of  elmwood,  and  rest,  on  their 
down  stream  side,  against  pinewood  frames,  instead  of 
against  the  edges  of  the  stone  grooves,  arid  thus  consid- 
erably reducing  the  friction,  and  at  the  same  time  secur- 
ing a  tight  fit  and  preventing  loss  of  water  by  leakage. 

The  gates  are  raised  by  ratchets.  One  man  can  with 
tolerable  ease  raise  a  gate  at  a  time.  The  ratchets,  pin- 
ions, etc.,  are  enclosed  in  rather  heavy  cast-iron  boxes. 
This  allows  of  no  provision  for  suddenly  dropping  the 
gates  in  case  of  floods;  but  an  overfall  weir  has  been 
built  in  the  left  bank  of  the  canal  just  below,  to  allow  of 
any  flood  water  above  the  full  supply  falling  back  directly 
again  into  the  river. 

What  seems  a  strange  omission  is,  that  the  piers  of 
the  regulator  are  not  provided  with  grooves  for  stop- 
planks  to  be  used  to  dam  out  the  water  in  case  of  acci- 
dent or  repairs.* 


*Lieut.  (now  General)   f.   C.    Scott   Moiicrieff,    Irrujalion    in  Southern 
En  rope . 


OTHER    IRRIGATION    WORKS.  135 

In  the  old  works  such  as  the  Godavery,  the  Kistna, 
the  Cauvery,  and  other  weirs,  it  was  the  custom  to  make 
sluices  with  vents  only  six  feet  wide,  and  raised  to~ordy 
about  half  the  height  of  the  flood.  In  these  works  the 
scouring  sluices  were  closed  in  the  dry  season,  either 
by  balks  of  timber  dropped  one  after  another  into  the 
grooves  in  the  pier,  or  by  gates,  sliding  in  vertical 
grooves,  which  gates  were  raised  and  lowered  from 
above  by  levers  working  into  long  rods  attached  to  the 
gates.  This  system  necessitated  the  construction  of  a 
masonry  superstructure  to  above  the  level  of  the  highest 
flood,  which  opposed  great  resistance  to  the  free  flow  of 
the  floods,  and  stopped  floating  cUbrix  in  the  river,  so 
that  the  sluices  not  uiifrequently  became  choked  with 
trees  and  brushwood. 

As  these  earlier  works  were  inefficient,  in  the  more 
modern  works,  much  larger  openings  have  been  left, 
and  movable  dams  have  been  erected,  with  110  super- 
structure above  the  level  of  the  weir,  so  that  floods  pass 
without  obstruction  over  the  weirs  to  the  depth,  it  may 
be,  of  eighteen  or  twenty  feet. 

That  these  movable  dams  may  thoroughly  perform 
their  duty,  it  is  necessary  that  they  should  be  large  and 
strongly  constructed,  and  that  they  should  be  capable 
of  being  operated  quickly.  It  was,  therefore,  attempted, 
in  Orissa,  India,  to  increase  considerably  the  size  of  the 
sluice  openings  in  the  weir  in  the  Mahanuddy  River, 
and  shutters  on  the  plan  adopted  by  the  French  engi- 
neers in  the  navigation  of  the  Seine  were  constructed. 
The  center  sluices  are  divided  into  ten  bays,  of  fifty 
feet  each,  by  masonry  piers.  Each  bay  is  composed  of 
a  double  row  of  parallel  timber  shutters,  which  are 
fastened  by  wrought-iron  bolts  and  hinges  to  a  heavy 
beam  of  timber  embedded  in  the  masonry  floor  of  the 
sluices.  There  are  seven  upper  shutters  and  seven 


136 


IRRIGATION    CANALS    AND 


lower  in  each  bay.  The  lower  shutters  are  nine  feet  in 
height  above  the  floor,  and  the  upper  seven  and  a-half 
feet.  Each  bay  is  separated  from  the  next  one  by  a 
stone  pier  five  feet  thick,  in  which  the  gearing  for  work- 
ing the  shutters  is  fixed. 


FIG. 7 2 


SHUTTERS  OF  THE  MAHANUDDEE  WEIR. 

The  up-stream  shutter  fell  up-stream,  and  the  down- 
stream shutter  fell  down  stream,  so  that  the  up-stream 
shutter,  unless  intentionally  fastened  down,  would,  in 
times  of  flood,  be  raised  by  the  water  getting  under  it 
and  flowing  against  it,  and  would  thus,  automatically, 
shut  itself,  and  leave  the  shutter  below  quite  dry.  The 
up-stream  shutter  was  supported  up-stream  by  chain 
ties.  When  it  became  necessary  to  open  the  sluice 
again,  of  course  it  would  not  have  been  practicable  to 
lower  the  upper  shutter  against  the  head  of  water  stand- 
ing against  it,  and,  therefore,  the  lower  shutter  was 
raised  and  strutted  up  by  hand,  as  men  could  walkabout 
with  safety  on  the  dry,  down  stream  sluice  channel,  and 
this  left  a  double  row  of  shutters  standing  against  the 
stream.  The  space  between  these  shutters  was  then 
allowed  to  fill  with  water,  and  then  the  upper  shutter, 
being  in  equilibrium,  was  allowed  to  fall  back  into  its 
place  on  the  bottom  of  the  sluice,  while  the  low^r  shutter 
supported  the  head  of  water 


OTHER    IRRIGATION    WORKS.  137 

If,  at  any  time,  it  was  required  to  open  the  sluice,  the 
back  shutter  was  lowered  by  knocking  away  the  feet  of 
the  struts  .which  supported  it,  on  the  down-stream  sid^, 
and  it  then  fell  down-stream,  and  the  sluice  was  open. 

It  has  been  found  that  in  a  dam  constructed  011  this 
principle,  500  lineal  feet  of  shutters  can  be  easily  low- 
ered in  one  hour,  with  a  head  of  six  feet  of  water,  and 
that  with  a  similar  head  an  equal  length  can  be  closed  in 
twenty-five  minutes  arid  that  three  men  (East  Indians) 
standing  on  the  floor  are  sufficient  to  knock  away  the 
back  struts  with  safety  to  themselves.  The  back  shut- 
ters are  not  damaged  as  they  fall  on  the  floor,  because 
water  escapes  as  each  shutter  falls,  sufficient  to  form  a 
a  cushion  for  the  other  shutters  to  fall  into.  Twelve 
men  are  necessary  to  lift  each  of  the  back  shutters  into 
position/''" 

This  kind  of  shutter  has  never  been  raised  against  a 
greater  head  of  water  .than  about  six  feet  nine  inches. 
The  front  shutter  is  only  used  when  the  level  of  the 
river  has  fallen  to  at  least  six  feet  above  the  floor  of  the 
weir,  and  frequently  the  engineers  hesitate  to  use  the 
shutters  until  the  water  has  fallen  lower. 

The  objection  to  this  plan  was,  that  the  upper  shutter 
was  raised  by  the  stream  with  such  velocity  and  force 
that  the  chain  ties  supporting  it  frequently  gave  way, 
and  the  shutter  was  carried  off  its  hinges.  On  one  oc- 
casion ths  front  beam  was  pulled  up  from  the  floor. 

Major  Allan  Cunningham,  R.  E.,  has  given  the  fol- 
lowing formula,  for  finding  the  tension  on  the  chains  <of 
shutters  similar  to  those  used  on  the  Mahaiiuddy  Weir.f 


*Mr.  E.  B.  Buckley,  C.E.,  on  Movable  Dams  in  Indian  Weirs,  in  Trans- 
actions of  the  Institution  of  Civil  Engineers,  Vol.  60. 

t Professional  Papers  on  Indian  Engineering,  Vol.  4,  Second  Series. 


138  IRRIGATION    CANALS    AND 

Let  />  =  breadth  of  shutter  in  feet. 
j  depth  of  shutter  j 
(  stream  } 

r— mid-surface  velocity  (over  shutter  when  down) 

in  feet  per  second. 

w  ==  weight  of  a  cubic  foot  of  water  ===  62.5  Ibs. 
(j  =  acceleration  of  gravity -=  32.2. 
T  ===  total    sudden    tension    of    the    wliole     set  'of 

chains  in  Ibs. 

(/,  =  angle  of  inclination  of  chains  to  shutters 
when  vertical,  that  is,  at  instant  when  strained 
taut. 


Total  tensile  stress  in  Ibs.-—  T=[  rf-H4—  }wb  d  cosec  a. 

v     /// 

Example.  In  the  sluice  shutters  of  the  Midiiapore 
Weir,  given  b .—6'. 25,  d  —  0'.5,  v=12'  per  second,  «=55°. 

Total  tensile  stress   ^G.5-r  4 X,l^r;)  x  62-5  x  r)-25 

X6. 5X1. 221=75, 587  Ibs. 

And  if  there  be  two  chains  equidistant  from  the 
<e  center  of  percussion  "  of  the  shutter,  then 

Tensile  stress  of  each  chain  =  37, 794  Ibs. 

In  order  to  diminish  the  violent  shock  caused  by  the 
rapid  rising  of  the  upper  shutter,  Mr.  Fouracres,  C.  E., 
made  important  improvements  in  the  method  of  work- 
ing them.  Figures  74,  75,  70  and  79,  give  four  views  of 
the  shutters  of  the  Sone  weir  in  different  positions. 
Figure  74  shows  the  sluice  "all  clear/'  with  both  shut- 
ters lying  on  the  floor,  the  flood  being  supposed  to  be 
running  freely  between  the  piers,  which  are  eight  feet 
in  height.  When  it  becomes  necessary  to  close  the  sluice 
mid  shut  off  the  water  flowing  through  it,  a  clutch  worked 
from  a  handle  from  the  top  of  the  pier  is  turned,  which 
frees  the  shutter  from  the  floor,  and  it  then  floats  par- 


OTHER    IRRIGATION    WORKS. 


139 


tially  up  from  its  own  buoyancy,  when  the  stream,  im- 
pinging upon  it,  raises  it  to  an  upright  position  with 
great  force, .shutting  up  the  sluice-wray,  Figure  75. 


Ml  ON  A  PORE  CANAL 
Tumbler  Regulating  Gear  for  Distributaries. 


o_a 
aaaa 

rzoa 

— i  —  \ 


But  if  a  shutter,  twenty  feet  long  and  eight  feet  in 
height,  were  allowed  to  come  up  with  such  velocity,  it 
would  either  carry  away  the  piers  or  be  carried  away 
itself.  To  destroy  this  sudden  shock,  Mr.  Fouracres 
fixed  to  the  down-stream  side  of  the  upper  shutters  six 
hydraulic  buffers  or  rams,  which  also  act  as  struts  for 
the  shutters  when  in  an  upright  position.  These  rams 
are  simply  pipes  with  a  large  plunger  inside,  as  shown 
in  longitudinal  section,  Figure  77,  and  cross-section, 
Figure  78. 

The  pipes  fill  witli   water  when   the  shutter  is  laying 


140 


IRRIGATION    CANALS    AND 


down,  and  when  it  commences  to  rise,  the  water  has  to 
be  forced  out  of  them  by  the  plunger  in  its  descent,  and, 
as  only  a  small  orifice  is  provided  for  the  escape  of  the 

FOURACRES'  SLUICES  AT  THE  WEIR  ON  THE  RIVER  SOME. 


water,  the  ascent  of  the  shutter,  forced  up  by  the  stream, 
is  slow  and  gentle,  instead  of  being  violent.     The  orifices 


OTHER    IRRIGATION    WO11KS. 


141 


in  the  pipes  are  covered  with  india-rubber  discs  to  pre- 
vent them  from  being  filled  with  sand  or  silt. 


The  water  is  now  shut  off  effectually,  as  shown  in  Fig- 
ure 75;  but  without  other  means  being  taken  it  would 
'be  impossible  to  open  the  sluice  again,  as  it  could  not 

^     7? 


SECTION    Of   HYDRAULIC    BRAKE    HEAD.  SONE~WEIR. 

be  forced  up-stream.  The  back  shutter  is  therefore  pro- 
vided below  it,  as  shown  in  this  same  view.  This  lower 
or  back  shutter  is  so  arranged  that  it  can  bo  lifted  up  by 
hand  and  placed  upright,  ties  being  placed  to  support  it, 
as  shown  in  Figure  76.  The  water  is  then  allowed  to  fill 
the  space  between  the  two  shutters,  and  the  upper  one 
can  then  be  thrown  down  on  the  floor  again,  but  the 
lower  one  is  held  up  by  ties  which  are  hinged  to  it  at 
one-third  of  its  height,  and  by  this  means  it  is  "  bal- 


142 


IRRIGATION    CANALS    AND 


OTHER    IRRIGATION    WORKS.  143 

anced,"  and  resists  the  pressure  on  it  until  the  water 
rises  to  its  top  edge,  when  it  loses  its  equilibrium  and 
falls  over,  thus  opening  the  sluice  again. 

The  sluices  can  be  left  to  fall  of  themselves  if  the  river 
rises  in  the  night;  or,  if  it  is  thought  not  expedient, 
they  can  be  made  fast  by  a  clutch  on  the  pier-head,  as 
shown  in  Figures  74,  75  and  76.  By  these  expedients, 
these  large  sluice-ways,  twenty  feet  broad  and  eight  feet 
deep,  can  be  shut  off  or  opened  as  required,  with  the 
greatest  facility  arid  expedition,  and  the  whole  set  of 
twenty-five  sluices  can  be  opened  in  a  few  minutes,  and 
when  opened  they  can  pass  through  them  anything  that 
the  river  brings  down,  without  danger  to  the  wier.* 

Figure  79  shows  the  upper  shutter  as  it  is  being  raised 
by  the  current  through  the  sluice-way. 

During  the  hot  season,  when  it  is  of  importance  to 
utilize  all  the  available  water,  all  leaks  between  the  shut- 
ters and  piers  are  calked  with  hemp  and  straw,  to  pre- 
vent loss  of  water  by  leakage. 

It  has  been  found  in  practice  on  the  Soric  Weir,  that 
the  shutters  can  be  safely  lifted,  without  shock,  against 
a  head  of  ten  feet  of  water,  and  they  haAre  been  fre- 
quently worked  under  these  conditions.  The  great- 
est head  against  which  other  shutters  on  any  other 
weir  have  been  lifted  is  believed  to  be  about  six  feet 
nine  inches  only.  It  is  stated  to  be  a  sight  worth  see- 
ing to  watch  a  stream  of  water  twenty  feet  broad 
and  eight  or  nine  feet  deep,  flowing  with  a  veloc- 
ity of  seventeen  to  twenty  feet  a  second  through  the 
sluices,  with  a  difference  of  ten  feet  between  the  water 
level  above  and  below  the  sluices,  to  be  suddenly  closed 
by  a  single  gate  twenty  feet  long  by  ten  feet  deep.  The 
water,  when  the  shutter  reaches  the  vertical,  rises  in  a 


i(/.  September  10th,  1873. 


144 


IRRIGATION    CANALS    AND 


wave  one  or  two  feet  above  the  top  of  the  shutters  and 
piers,  and  flows  over  for  a  few  seconds  before  it  sinks  to 
the  mean  level  of  the  stream. 

In  the  Transactions  of  the  Institution  of  Civil  En- 
gineers, Vol.  60,  Mr.  F.  M.  G.  Stoney,  C.  E.,  has  given 
a  design  for  a  large  span  lifting  sluice,  shown  in  Figures 
80,  81,  82,  83  and  84.  This  is  inserted  here  to  show  a 
design  that  in  certain  circumstances  it  may  be  very  ad- 
vantageous to  adopt,  where  it  is  necessary  to  have  a 
large  opening. 


The  clear  span  was  forty  feet,  and  the  depth  of  water 
twelve  feet.  The  gates  were  designed  to  be  lifted  twelve 
feet.  The  up-stream  face  was  vertical,  and  the  gate 
simply  fitted  at  its  ends  against  planed  guides  in  the 
pier  faces,  the  contact  being  kept  close  by  self-adjusting 
slips,  and  the  gate  was  free  to  press  down  fairly  on  a 
level  sill.  The  gate  was  simple.  It  was  composed  of  two 
main  girders,  placed  equally  at  each  side  of  the  center 
of  pressure;  cross  vertical  beams  connected  these  gird- 
ers, and  carried  the  sheeting  and  the  top  of  the  gate. 
The  static  pressure  was  eighty-one  tons.  The  weight  of 
the  gate  was  eighteen  and  one-half  tons,  and  the  mov- 
ing load,  including  rollers,  was  roughly,  twenty  tons. 
The  whole  was  arranged  to  be  lifted,  by  a  pair  of  strong 
right  and  left  screws.  These  screws  were  placed  liori- 


OTHER    IRRIGATION    WORKS. 


145 


146 


IRRIGATION    CANALS    AND 


zontally  011  a  foot  bridge,  and  acted  011  large  nuts  travel- 
ing in  guides,  each  nut  pulled  chains  which  passed  over 
large  pulleys  down  to  the  gate,  where  they  were  sym- 


metrically  grouped  round  its  center  of  gravity.  The 
weight  of  this  sluice-gate,  foot  bridge  and  all,  was  only 
twenty-seven  tons. 


AND    OTHER    IRRIGATION    WORKS.  147 

Article  32.     The  Loss  of    Waiter  by  Percolation   Under 

a  Weir. 

While  it  is  not  practicable,  by  direct  experiment,  to 
find  the  quantity  of  water  lost  by  percolation  through 
a  sandy  bed  under  a  weir,  still  an  approximation  can  be 
found  'to  this  loss  by  the  method  given  below: — 

By  D'Arcy's  experiments  the  discharge  of  a  fourteen- 
inch  pipe  filled  at  the  bottom  with  sand,  to  a  depth  of 
from  two  feet  to  six  feet,  was  carefully  ascertained  under 
heads  ranging  from  three  feet  to  forty-six  feet.  Dupuit, 
in  summarizing  these  and  other  experiments,  states  that 
the  discharge  is  directly  proportional  to  the  head,  and 
inversely  proportional  to  the  thickness  of  sand,  and  that 
for  one  meter  head  and  one  meter  thickness  of  filtering 
material,  the  rate  of  percolation  is  twenty-six  cubic 
meters  per  day  for  coarse  sand,  and  4.5  cubic  meters  for 
the  finest  sand.  To  check  percolation,  then,  coarse 
sand  is  required  as  a  matrix  to  give  stability,  and  fine 
sand  to  fill  up  the  interstices.  With  these  materials,  as 
Brunei  found  at  the  Thames  Tunnel,  the  water  will  run 
through  at  first,  but  soon  stop. 

To  give  an  instance  of  the  application  of  D'Arcy's  ex- 
periments, let  us  find  the  loss  by  percolation  under  the 
Godavery  Anicut  or  Weir,  Figure  44.  A  description  of 
this  anicut  has  already  been  given  in  Article  28.  This 
ariicut  rests  upon  a  bed  of  coarse  sand  of  unknown 
depth,  through  which  an  incessant  percolation  takes 
place,  the  water  passing  under  the  anicut,  and  rising  to 
the  surface  of  the  river  again,  below  it.  There  is,  at 
the  same  time,  a  constant  draught,  by  the  three  main 
irrigation  canals,  of  the  greater  part  of  the  available 
supply  entering  the  pool  above  the  anicut.  Yet  the 
water  only  falls  a  foot  or  two  below  the  crest,  in  the  hot- 


148  IRRIGATION    CANALS    AND 

test  weather.  There  is  a  certain  area  of  the  surface  of 
the  bed  of  the  river,  above  the  dam,  through  which 
leakage  takes  place.  The  leakage  is  greatest  near  the 
dam,  and  gets  less  as  the  distance  from  the  dam  in- 
creases up  stream.  We  have  no  means  of  knowing  to 
what  distance  the  appreciable  leakage  extends.  Let  us 
assume  one  hundred  feet  as  a  reasonable  distance,  and, 
as  the  total  length  of  the  anicut  is  11,866  feet,  we  have 
1,186,600  square  feet  of  porous,  sandy  surface  con- 
stantly leaking  under  a  head  of  twelve  feet  to  fourteen 
feet.  Notwithstanding  this  immense  area  of  porous 
surface,  the  water  level  in  the  pool  above  the  anicut 
falls  but  little,  though  the  total  supply  in  the  river  may 
be  less  than  3,000  cubic  feet  per  second.'* 

The  mean  distance  the  water  would  have  to  traverse 
the  sand,  Figure  44,  in  order  to  pass  from  above  to  below 
the  anicut,  upon  the  preceding  hypothesis,  would  be 
about  eighty  meters,  and  since  the  head  of  water  is, 
say,  four  meters,  the  velocity  of  filtration,  by  Dupuit's 
formula,  already  stated,  with  a  constant  of  fifteen  cubic 
meters,  that  is  a  mean  of  the  coarse  and  fine  sand, 
would  be:  — 

=f  meter  per  day  =——  feet  per  second. 


80 
Now  this  velocity  multiplied  by  the  area  is:  — 

_  =338  cubic  feet  per  second  or  about  11  per 

cent,  of  3,000  cubic  feet  per  second,  which  is   the  ordi- 
nary flow  down  the  river  in  the  dry  season. 

We  thus  see  that  the  loss  of  water  is   not  great,  even 
under  the  most  favorable    conditions    for   percolation, 

*  Engineering,  April  28th,  1876. 


OTHER    IRRIGATION    WORKS.  149 

with  a  large  area  and  clean  sand.  Under  ordinary  cir- 
cumstances, however,  the  interstices  of  the  sand,  above 
the  weir,  and  near  the  surface  of  the  bed  of  theTrlver, 
get  filled  up  with  fine  silt,  and  a  layer  of  silt  is  formed 
on  the  bed  and  banks  of  the  river,  thus  materially  pre- 
venting the  percolation. 

Article  33.     Bridges — Culverts. 

Only  a  few  brief  remarks  will  be  made  with  reference 
to  Bridges.  There  are  several  very  good  works  published 
treating  very  fully  on  this  subject. 

Ordinary  highway  bridges  are  required  wherever  roads 
cross  the  canal,  to  accommodate  the  traffic  of  the  court- 
try. 

In  America,  bridges  011  Irrigation  Canals  are  usually 
constructed  of  timber,  but  in  India,  Egypt  and  Italy, 
they  are  as  a  rule  constructed  of  masonry. 

Bridges  are  sometimes  combined  with  and  form  part 
of  Regulators  and  Falls.  There  is  no  difficulty  about 
the  water-way  of  canal  bridges,  as  the  regulators  and 
escapes  enable  the  high  water  in  the  canal  to  be  always 
kept  within  the  limits  of  its  intended  full  supply. 

The  Culverts  for  passing  the  drainage  of  the  country 
under  the  canal,  are,  in  America,  of  the  usual  timber 
box-culvert  type. 

The  culvert  should  be  amply  large  to  pass  away  the 
flood-water,  without  causing  much  heading  up  above  its 
top.  Before  fixing  its  size,  it  is  advisable  to  have  a  rough 
survey  made  of  the  area  draining  into  the  culvert,  and 
then,  assuming  a  heavy  rainfall,  the  number  of  cubic 
feet  of  water  per  second  reaching  the  culvert  can  be 
found.  Having  fixed  the  grade  of  the  culvert,  we  have 
the  grade  and  discharge  from  which  the  required  area 
can  be  found,  as  explained  in  the  Flow  of  Water. 


150  IRRIGATION    CANALS    AND 

Myers  has  given  a  formula  for  finding  approximately 
the  required  area  of  the  culvert.  It  is: — 

<i  ~c\/  Drainage  area  in  acres. 

where  a  —  cross-sectional  area  of  culvert  in  square  feet, 
and  c  is  a  variable  co-efficient  having   the  fol- 
lowing values: — 

c  —  1.0  for  slightly  rolling  prairie; 
c  ==  1.5  for  hilly  ground; 
c  =-  4.0  for  mountainous  and  rocky  ground. 

It  may  appear  that  this  is  going  too  much  into  com- 
putations to  design  a  simple  culvert,  but  surely  the 
results  from  these  are,  as  a  rule,  better  than  mere  guess 
work.  The  computations  would  take  but  a  few  minutes. 
A  defective  culvert,  causing  a  breach  in  a  canal  during 
the  irrigation  season,  would  do  a  great  deal  of  damage. 

Article  34.     Aqueducts — Flumes. 

Aqueducts,  usually  called  Flumes  in  America,  are  used 
to  carry  a  canal  over  a  river  or  other  obstruction.  Before 
adopting  an  aqueduct,  it  is  advisable  to  investigate 
whether,  by  altering  the  course  of  the  river,  the  latter 
can  be  made  to  run  clear  of  the  former.  A  very  in- 
structive example  of  this  was  the  diversion  of  the  Chuk- 
kee  torrent  on  the  Baree  Doab  Canal,  in  India,  for  the 
passage  of  which  costly  works  were  originally  designed. 
The  Chukkee,  at  the  time  of  the  commencement  of  the 
canal  works,  had  two  outlets.  Just  above  the  crossing 
point  of  the  canal,  the  main  channel  divided;  one,  the 
larger  branch,  running  into  the  river  Beas,  the  other 
into  the  river  Eavee.  This  latter  was  embanked  across 
at  the  bifurcation  by  bowlder  dams,  and  spurs  of  the 
same  material,  protected  at  the  extremity  by  masonry 


OTHER    IRRIGATION    WORKS.  151 

revetments.  By  these  means  the  whole  of  the  water  was 
forced  to  flow  into  the  Beas,  and  the  expense  of  the 
works  for  the  canal  crossing  saved. 

When,  however,  a  canal  meets  a  river  that  cannot  be 
diverted,  there  are  three  cases  under  one  of  which  it 
may  have  to  be  crossed: 

First.  When  the  river  is  OH  a  lower  level  than  the 
canal. 

Second.  When  the  river  is  on  the  same  level  as  the 
canal. 

Third.  When  the  river  is  on  a  higher  level  than  the 
canal. 

Ill  the  first  case  the  canal  is  carried  over  the  river  by 
an  Aqueduct  or  Flume. 

In  the  construction  of  an  aqueduct  there  are  two 
things  to  attend  to  of  vital  importance.  The  first  is  that 
the  waterway,  under  the  aqueduct,  should  be  amply 
large,  in  order  to  pass  the  greatest  floods  with  safety, 
and  the  second  is  that  the  junction  of  the  aqueduct  and 
the  earthen  embankment  at  its  ends,  should  be  made 
water-tight. 

For  want  of  ample  provision  for  flood  water  the  Kali 
Xuddee  Aqueduct  on  the  Low^er  Ganges  Canal  in  India, 
was  destroyed  on  January  17th,  1885,  causing  a  loss,  not 
only  for  its  reconstruction,  but  also  on  account  of  the 
stoppage  of  irrigation. 

Every  practical  method  should  be  employed  to  find 
the  flood  discharge  of  the  river,  in  order  to  have  several 
checks  on  the  results,  and  sufficient  waterway  should  be 
provided  to  pass  this  flood  wrater  through  the  aqueduct, 
without  endangering  its  stability  in  any  way.  For  in- 
formation on  this  subject  see  the  articles  entitled  Flow  of 
Water. 

The  embankments  at  the  cuds   of  the   masonry   aque- 


152 


IRRIGATION    CANALS    AND 


duct  over  the  river  Dora  Baltea,  on  the  line  of  the  Ca- 
vour  Canal,  in  Italy,  leaked  very  much  at  first.  To 
remedy  this  the  embankment  was  dammed  up  at  the 
lower  end  and  filled  with  water  to  a  depth  of  about  three 
feet.  Several  boats  were  then  employed,  throwing  in. 
clay  all  over  the  bed.  After  a  time  the  water  was  turned 
off,  and  cattle  driven  into  the  muddy  channel,  which 
was  turned  over  and  worked  into  puddle.  Again  it  was 
filled  with  water,  and  where  filtration  was  observed,  more 
clay  was  thrown  in,  and  the  puddling  process  repeated; 
and  so  on,  till  after  nearly  a  year  the  filtration  had  en- 
tirely ceased. 


For  purposes  of  economy  a  high  velocity  is  usually 
given  to  an  aqueduct. 

An  aqueduct  differs  from  a  bridge  in  having  to  carry 
a  water  channel  over  it,  instead  of  a  road  or  railway, 
but,  unlike  the  latter,  it  is  not  constantly  subjected  to 
the  jars  of  a  suddenly  applied  load. 


OTIIKR     IRRIGATION    WORKS.  153 

Aqueducts  are  usually  constructed  of  masonry,  iron 
or  wood,  or  a  combination  of  them.  The  Solani  Aque- 
duct in  India,  and  the  Dora  Baltea  Aqueduct  in  Itahr, 
are  two  very  fine  specimens  of  masonry  aqueducts. 

A  great  deal  of  water  is  lost  through  the  use  of  wooden 
troughs  in.  flumes.  When  they  are  dry,  the  action  of  the 
sun  causes  numerous  cracks  which  it  is  afterwards  im- 
possible to  keep  water-tight. 

Figures  85  and  86  show  an  elevation  and  section  of  a 
flume  on  the  Uiicompahgre  Canal  in  Colorado.  Figures 
87  and  88  show  plan  and  section  of  the  Big  Drop  on  tha 
Grand  Eiver  Canal  in  Colorado.  This  drop  shows  anr 
other  peculiarity  of  American  engineering.  Before 
reaching  the  drop  the  section  of  the  channel  is  thirty 
feet  wide  by  four  feet  deep.  At  the  drop  it  descends 
thirty-five  feet  in  135  feet,  and  at  the  bottom  the  water 
is  discharged  against  a  boom  of  solid  timbers  and  thrown 
backward  in  a  penstock,  whence  it  escapes  over  a  riffled 
floor. 


Figure  89  is  a  view  on  the  Platte  Canal  (High  Line),, 
showing  the  flume  issuing  from  tunnel,  and  Figure  90 
is  a  view  of  flume  of  Platte  Canal  (High  Line,  Colo- 
rado), crossing  Plum  Creek  at  Acequia.  Mr.  P.  O'Meara, 
C.  E.,  in  Transactions  of  the  Institution  of  Civil  Engin- 
eers, volume  73,  describes  flumes  constructed  in  Colo- 
rado. The  North  Poudre  Canal  is  carried  from  the  dam 


154 


IRKIGATIOX    CANALS    AND 


to  the  mouth  of  the  canon,  through  a  series  of  tunnels 
and  flumes,  these  latter  supported  on  shelves  and  gulch 
bridges. 


Platte  River,  with  Platte  Canal,  Colorado, 

The  shelves  are  cut,  for  the  most  part,  in  the  solid 
rock,  and  are  nine  feet  wide  at  the  base.  The  flume 
which  rests  on  them,  as  on  the  bridges,  is  eight  feet 


OTHER    IRRIGATION    WORKS 


155 


156 


IRRIGATION    CANALS    AND 


wide  by  six  feet  deep  in  the  clear,  and  projects  a  little 
over  the  edge,  a  few  running  beams  and  upright  props 
being  occasionally  used  to  support  it  where  fissures  occur. 
Lower  down,  where  the  canal  crosses  some  creeks  or  riv- 
ulets, the  flumes  are  twelve  feet  wide  by  four  feet  three 
inches  deep  in  the  clear,  to  accord  better  with  the  section 
of  the  canal  in  the  open  plain,  which  is  twenty  feet  wide 
at  the  bottom  and  four  feet  three  inches  deep.  Precau- 
tions are  taken  to  secure  the  sides  of  the  canal  for  a 
short  distance  from  the  ends  of  the  flume  against  the 
effects  of  increased  speed  in  the  water,  and  a  slight  al- 
lowance is  made  at  these  points  in.  the  general  gradient. 


Fig.  91.     High  Flume  over  Malad   River,  West  Branch,  Utah. 

The  whole  of  the  flume  work  is  carefully  calked  with 
oakum.  In.  earthwork  the  ends  of  the  flumes  are  raked 
off  to  a  slope  one  and  one-half  to  one,  and  the  spaces  be- 
tween the  ties  and  posts,  for  about  twelve  feet  back,  are 
filled  with  retentive  clay.  Where  the  flume  terminates 
in  a  rock  cutting  or  tunnel,  the  side  of  the  flume  near  the 
end  and  the  rock  is  built  up  with  cement  masonry,  for 


OTHER    IRRIGATION    WORKS.  1O< 

three  or  four  feet  in  length,  or  with  two  faces  of  masonry 
filled  between  with  clay. 

Mr.  O'Meara  further  stated  that  the  soil  was  very  stony 
and  pervious  to  water,  and  therefore,  it  was  found 
necessary  to  use  wooden  flumes  instead  of  embankments 
to  carry  the  water.  In  one  case  about  a  quarter  of  a 
mile  of  the  North  Poudre  Canal  was  embanked,  and 
water  let  into  it,  and  the  consequence  was  that  nearly  all 
of  it  was  carried  away,  and  a  flume  of  wood  had  to  be 
inserted,  and  calked  well  to  prevent  the  water  from  es- 
caping. » 


Fig.  92.     Iron  Flume  over  Malad  River,  Corlnne  Branch,  Utah. 

Figure  91  shows  the  high  iron  flume  over  the  Ma- 
lad  river  at  the  ninth  mile  of  the  Bear  River  Canal 
in  Utah.  This  flume  is  378  feet  in  length  and  eighty 
feet  in  maximum  height,  supported  on  iron  trestles,  the 
river  span  of  which  is  seventy  feet.  The  trough  of  this 
flume  is  constructed  of  wood.  It  is  twenty  feet  wide  in 
the  clear  and  is  intended  to  carry  seven  foot  in  depth  of 


158 


IRRIGATION    CANALS    AND 


OTHER    IRRIGATION    WORKS. 

water,,  and  the  approaches  to  the  iron  trestle  are  also 
wooden  flumes  of  similar  dimensions,  and  500  feet  in 
length. 

Figure  92  shows  the  iron  flume  over  the  Malacl  river 
on  the  Corhme  Branch  of  the  Bear  River  Canal.  This 
(lume  is  founded  on  piles  and  iron  cylinders  filled  with 
concrete."  This  flume  consists  of  three  principal  bents 
from  twenty-five  to  sixty  feet  in  length,  the  peculiarity 
of  its  construction  being  that  the  superstructure  form- 
ing the  bridge  itself  is  of  iron  plate  girders  and  consti- 
tutes the  flume  which  carries  the  water.* 

Probably  the  most  celebrated  aqueduct  in  existence  is 
the  Solani  Aqueduct,  near  lloorkee  Civil  Engineering 
College,  on  the  line  of  the  Ganges  Canal.  A  brief  de- 
scription of  this  work  is  herewith  given. 

The  work  by  which  the  canal  is  carried  across  the 
valley  of  the  Solani  river,  consists  of  three  parts. 

Fi-wt.  The  embankment  of  earth  and  brickwork, 
10,713  feet  in  length,  from  the  high  land  on  the  up- 
stream side  of  the  canal  to  the  Solani1  river.  This  is 
shown  in  cross-section  in  Figure  94. 

Second.  The  maxoiii't/  aqueduct  over  the  Solani  river, 
9-20  feet  in  length. 

Third.  An  embankment  2,723  feet  in  length,  similar 
to  Figure  94. 

The  earthen  embankment  or  platform  is  raised  to  an 
average  height  of  sixteen  and  a  half  feet  above  the  coun- 
try, having  a  base  of  350  feet  in  width,  and  a  breadth  at 
top  of  290  feet.  On  this  platform  the  banks  of  the  canal 
are  formed,  thirty  feet  in  width  at  top,  and  twelve  feet 
in  depth.  These  banks  are  protected  from  the  action  of 
the  water  by  lines  of  masonry  retaining  walls,  formed  in 


*The    views    and   descriptions    of  the    two   flumes   on    the  Bear   lliver 
Canals  are  taken  from  the  Irrigation  Age  of  July  ],•  1891. 


160  IRRIGATION    CANALS    AND 

steps,  extending  along  their  entire  length,  or  for  nearly 
two  and  three-quarter  miles. 

The  river  itself  is  crossed  by  a  masonry  aqueduct, 
which  is  not  merely  the  largest  work  of  the  kind  in  In- 
dia, but  one  of  the  most  remarkable  for  its  dimensions 
in  the  world.  The  total  length  of  the  Solani  Aqueduct  is 
920  feet.  Its  clear  waterway  is  750  feet,  in  fifteen  arches 
of  fifty  feet  span  each.  The  breadth  of  each  arch  is  192 
feet.  Its  thickness  is  five  feet;  its  form  is  that  of  a  seg- 
ment of  a  circle,  with  a  rise  of  eight  feet.  The  piers 
rest  upon  blocks  of  masonry,  sunk  twenty  feet  deep  in 
the  bed  of  the  river,  being  cubes  of  twenty  feet  side, 
pierced  with  four  wells  each,  and  under-sunk  in  the 
usual  manner.  These  foundations,  throughout  the  whole 
structure,  are  secured  by  every  device  that  knowledge  or 
experience  could  suggest;  and  the  quantity  of  masonry 
.sunk  beneath  the  surface  is  scarcely  less  than  that  visible 
above  it.  The  piers  are  ten  feet  thick  at  the  springing 
of  the  arches,  and  twelve  and  a  half  feet  in  height.  The 
total  height  of  the  structure  above  the  valley  of  the  river 
is  thirty-eight  feet.  It  is  not,  therefore,  an  imposing 
work  when  viewed  from  below,  in  consequence  of  this 
deficiency  of  elevation;  but  when  viewed  from  above, 
and  when  its  immense  breadth  is  observed,  with  its  line 
of  masonry  channel,  nearly  three  miles  in  length,  the 
effect  is  most  striking. 

The  water-way  of  the  masonry  channel  is  formed  in 
two  separate  channels,  each  eighty-five  feet  in  width; 
the  side  walls  are  eight  feet  thick  and  twelve  feet  deep, 
the  depth  of  water  at  full  supply  being  ten  feet.  A  con- 
tinuation of  the  earthen  aqueduct,  about  three-quarters 
of  a  mile  in  length,  connects  the  masonry  work  with  the 
high  bank  at  Roorkee,  and  brings  the  canal  to  the  ter- 
mination of  the  difficult  portion  of  its  course. 

The   aqueduct   has   carried   over   7,000    cubic    feet  of 


OTHP:R  IRRIGATION  WORKS. 


161 


water  per  second,  but  usually  carries  between  5,000  and 
6,000  cubic  feet  per  second. 


Fig.  94.     Cross-Section  of  Solan!  Aqueduct  Embankment. 

Captain  J.  Crofton,  R.  E.,  in  his  Report  on  the  Ganges 
Canal,  states  that:  "  The  aqueduct  over  the  Solani  tor- 
rent has  stood  well.  The  state  of  the  bed  of  the  torrent 
above  and  below  shows  that  the  waterway  under  the 
aqueduct  is  just  sufficient  and  no  more;  there  is  no  hole 
or  retrogression  of  levels  down  stream,  and  little  or  no 
silt  has  been  deposited  except  under  the  side  arches, 
where  a  certain  quantity  would  naturally  be  left  on  the 
subsidence  of  floods.  The  flooring  of  the  canal  channel 
above  requires  some  waterproof  covering;  dripping  still 
continues  through  the  arches,  though  less  than  at  first, 
the  effect  of  which  has  been  to  loosen  a  considerable 
surface  of  the  outside  plaster,  and  here  and  there  bricks 
of  an  inferior  description  (of  which  it  is  next  to  impos- 
sible to  prevent  a  few  finding  their  way  into  so  great  a 
mass  of  brickwork)  may  be  seen  slowly  decomposing 
from  the  same  cause.  It  was  at  one  time  supposed  that 
the  pores  of  the  brickwork  would  gradually  fill  up  and  so 
stop  the  percolation,  but  the  fact  is,  that  even  the  very 
best  of  brickwork  is  of  too  absorbent  a  nature  to  be 
proof  by  itself  against  the  constant  pressure  of  a  head 
of  water  even  much  less  than  that  passing  over  this  aque- 
duct. 

."A  breach  occurred  some  years  since  along  a  short 
portion  of  the  right  bank  revetment,  Figure  94,  from  the 
heeling  over  inwards,  towards  the  channel  of  the  wall, 
A,  from  a  point  some  four  or  five  feet  below  the  level  of 

the    bed.       The    channel    here    had  been    considerably 
11 


162 


IRRIGATION    CANALS    AND 


deepened,  and  the  accident  occurred  just  after  the  canal 
had  been  laid  dry.  The  outer  wall,  B,  was  very  little,  if 
at  all  affected. 


Solan!  Aqueduct,  Ganges  Canal. 

"  From  the  investigation  made  immediately   after   its 
occurrence,  it  appears  to  have  been  caused  by   the  pres- 


OTHER    IRRIGATION    WORKS.  163 

sure  of  the  earth  filling,  between  the  waits,  which  had 
become  saturated  by  the  percolation  through  the_ brick- 
work. When  the  counteracting  pressure  of  the  water  in 
the  canal  was  removed,  the  thin  wall  gave  way,  there 
being  no  weep  holes  through  it  by  which  the  drainage 
from  the  backing  could  find  an  exit.  The  bed  all  along 
between  these  revetments  was  to  have  been  protected  by 
a  layer  of  bowlders;  this,  however,  has  been  deferred 
from  economical  motives,  the  actual  protecting  work 
now  being  confined  to  a  sloping  talus  of  bowlders  and 
brick  kiln,  rubbish,  thrown  down  from  time  to  time, 
along  the  foot  of  the  revetments." 

11  The  Henares  Canal*  is  carried  over  the  Majanar 
Arroyo  or  torrent,  in  an  iron  aqueduct  which  is  worthy  of 
admiration  on  account  of  its  perfect  fitness,  both  in  de- 
sign and  construction,  for  the  work  it  has  to  perform. 
The  discharge  of  the  canal  at  full  supply  is  177  feet  per 
second. " 

Full  details  are  given  in  Figures  98,  99,  100,  101,  102, 
103. 

The  iron  trough  is  seventy  feet  long,  with  a  clear  bear- 
ing of  sixty-two  feet.  Its  waterway  is  10.17  feet  wide, 
the  sides  being  composed  of  iron  box-girders  6.2  feet 
deep.  The  total  weight  of  iron  in  the  trough  is  27.3 
tons,  and  the  weight  of  water  when  full  is  ninety  tons. 
Each  girder  is  calculated  to  bear  200  tons,  equally  dis- 
tributed, or  the  whole  trough  400  tons.  The  aqueduct 
is  absolutely  free  from  leakage,  which  was  most  inge- 
niously prevented.  The  ends  of  the  trough  rest  on 
stone  templates.  Four  inches  from  each  end  a  pillow, 
composed  of  long  strips  of  felt  carpet,  about  nine  inches 
wide,  soaked  in  tallow,  is  let  into  the  stone  right  across, 
below  the  breadth  of  the  trough,  which  pressing  fully 


*  Lieut,  (now  General)  C.  C.  Scott  Moncrieff,  R.  E.,  Irrigation  in  South- 
ern Europe. 


164 


IRRIGATION    CANALS    AND 


on  it,  makes  a  water-tight  joint  without  taking  the  bear- 
ing off  the  stonework.  Still  further  to  make  things  se- 
cure, a  recess  about  one  foot  deep  and  four  inches  wide, 
is  cut  in  the  stone  all  around  the  bottom  and  sides.  In 
this  rests  a  lead  flushing,  riveted  to  the  trough  like  a 


fringe.  Round  this  lead  is  poured  in,  a  hot  mixture  of 
pitch,  gas  tar,  and  fine  sand,  forming  a  water-tight  joint, 
and  yet  flexible  enough  to  allow  a  slight  play,  as  re- 
quired by  the  expansion  and  contraction  of  the  iron 
trough.  The  result  produced  is  perfect  in  preventing 
the  loss  of  water  by  leakage. 

Article  35.      Level  Crossings. 

The  second  case,  mentioned  at  page  151,  where  a 
canal  crosses  a  river  on  the  same  level,  is  called  a  Level 
Crossing.  Small  drainage  channels  carrying  small  quan- 
tities of  silt,  may  be  passed  into  the  canal  without  doing 


OTHER    IRRIGATION    WORKS.  165 

any  material  damage.  If  the  river,  or  torrent,  is  of  large 
dimensions,  and  brings  down  a  great  volume  of  water  at 
a  high  velocity,  the  above  method  will  not  answer;  as 


Level  Crossing,  Ganges  Canal. 

the  water  loaded  with  silt  would  in  some  places  choke 
up  the  canal  bed  and  cause  the  water  to  overflow  its 
bank,  and  in  other  places  it  would  erode  the  banks  and 
cause  breaches  in  them.  Arrangements  have,  therefore, 
to  be  made  to  pass  the  flood  water  across  the  canal, 
which  will  be  briefly  explained,  and  will  be  understood 
from  the  following  description  of  a  level  crossing  shown 
in  plan,  in  Figure  104: — 

B  is  a  regulating  bridge  across  the  canal,  provided 
with  the  usual  sluice-gates.  A  is  a  dam  across  the  chan- 
nel of  the  torrent,  provided  with  flood-gates.  Under 
ordinary  circumstances,  A  is  closed  and  B  is  open,  so 
that  the  canal  water  flows  along  its  own  channel  as  usual. 
But  when  the  torrent  is  in  flood,  then  A  must  be  open, 
and  B  closed,  so  that  the  flood  water  may  cross  the  canal 
and  run  down  its  own  channel.  The  quantity  of  water 
flowing  past  the  dam  is  likely  to  be,  on  some  occasions, 
equal  to  the  flood  discharge  of  the  torrent,  in  addition  to 
the  full  supply  of  the  canal. 

The  bed  and  banks  of  the  canal  and  torrent,  as  far  as 
they  are  exposed  to  the  erosive  action  of  the  water,  must 
be  paved  or  otherwise  protected,  to  prevent  them  from 
being  injured  by  the  action  of  the  water. 


166 


IRRIGATION    CANALS    AND 


OTHER    IRRIGATION    WORKS. 


167 


A  very  good  example  of  a  level  crossing  is  at  Dhuno- 
wree,  on  the  Upper  Ganges  Canal,  where  the  Rutmoo 
torrent  is  passed.  Figure  105  shows  a  view  of  tTielDrrdge 
and  dam  at  this  crossing. 


Fig.   106.     Rutmoo  Crossing,  Ganges  Canal. 

Figure  106  shows  the  plan  of  the  level  crossing. 

The  dam  itself  consists  of  forty-seven  sluices  of  ten 
feet  in  width,  some  of  which  are  shown  in  Figure  108, 
with  their  sills  flush  with  the  canal  bed,  separated  by 
piers  of  three  and  a  half  feet  in  width.  The  above  are 
flanked  on  each  side  by  five  overfalls  of  the  same  width, 
having  the  sills  raised  to  a  height  of  six  feet,  with  inter- 
mediate piers  of  the  same  dimensions  as  those  in  the 
center  sluices.  On  the  extreme  flanks  are  platforms 
raised  to  a  height  of  ten  feet  above  the  canal  bed,  and 
corresponding  in  height  with  the  rest  of  the  piers. 
These  elevated  platforms,  which  are  seventeen  feet  in 


168 


IRRIGATION    CANALS    AND 


length,  are  connected  with  the  revetment  esplanade  by 
inclined  planes  of  masonry,  carried  through  the  flanks 
of  the  dam. 


_Lr~  W 

H^l^b!ifialBH!tea*iU=A»aJ 


The 


Dhunowree  Level  Crossing,  Ganges  Canal, 

amount    of    waterway,    therefore,    through   the 


sluices,  up  to  a  height  of  six  feet,  is  equal  to  470  feet  in 
width;  to  a  height  of  from  six  to  ten  feet  it  is  increased 
to  570  feet,  and  when  flood  water  passes  over  the  full 
expanse  of  the  masonry,  which  is  equal  in  width  to  800 
feet. 

For  the  ten  sluices  in  the  flanks,  the  closing  and  open- 


OTHER    IRRIGATION    WORKS.  169 

ing  is  effected  by  sleeper  planks,  for  which  grooves  are 
fitted  to  the  piers. 

For  the  center  openings  drop  gates  are  provide^,— a& 
explained  in  Article  31,  and  Figures  67  and  68. 

On  the  down-stream  side  of  the  dam  a  platform  of  box- 
work,  filled  with  river  stone,  extends  to  a  width  of  forty- 
three  and  a  half  feet  from  the  masonry  flooring.  This 
is  held  in  position  by  double  lines  of  twenty-feet  piling, 
strongly  clamped  together  by  sleepers  fastened  on  to  the 
upper  surface,  the  slope  of  which  is  two  and  a  quarter 
feet  on  an  incline  down-stream. 

The  regulating  bridge  has  ten  waterways  each  twenty 
feet  broad,  and  provided  with  gates  to  prevent  any  flood- 
water  passing  down  the  canal.  In  addition  to  this,  there 
is  a  roadway  bridge,  and  about  a  mile  of  revetment  walls, 
all  resting  on  blocks  of  brick  masonry,  sunk  to  a  depth 
of  twenty  feet  below  the  canal  bed.  The  whole  of  this 
work  is  protected  by  a  forest  of  piles,  and  an  enormous 
number  of  bottomless  boxes  filled  with  bowlders. 

The  river,  when  not  in  flood,  flows  under  the  canal 
by  a  double  tunnel  upwards  of  500  feet  long. 

The  great  objection  to  this  kind  of  work  is,  that  it  re- 
quires a  permanent  establishment  of  men  on  the  spot  to 
work  it,  and  that,  if  they  are  careless  or  neglectful,  a 
sudden  flood  may  do  serious  damage.  On  this  account 
level  crossings  are  to  be  avoided  whenever  it  is  possible 
to  do  so.* 

Article  36.     Superpassages. 

The  third  case  mentioned  at  page  151,  where  the  tor- 
rent crosses  at  a  higher  level  than  the  canal,  and,  in  this 
case,  the  structure  is  called  a  superpassage ,  to  distinguish 
it  from  the  first  case,  where  the  canal  flows  over  a  river 
and  is  carried  by  an  aqueduct.  In  America  a  superpas- 
sage is  usually  called  a  flume. 


'Roorkee  Treatise  on  Civil  Engineering. 


170  IRRIGATION    CANALS    AND 

Carrying  a  large  body  of  water  across  and  over  a  canal 
is  a  very  expensive  and  troublesome  work,  as  a  large 
water  channel  has  to  be  provided  to  carry  any  extraor- 
dinary flood  over  the  canal  in  safety,  and,  in  navigable 
canals,  sufficient  headway  must  be  allowed  under  the 
superpassage  so  as  not  to  interrupt  the  navigation. 
AVhen  the  grade  of  the  country  admits  of  it,  as  is  almost 
always  the  case,  the  canal  can  be  dropped  to  the  required 
level  by  a  masonry  fall,  a  lock  being  provided  for  navi- 
gation purposes,  if  required.  The  torrent  will  probably 
require  constant  watching  to  prevent  its  shifting  its 
course  and  attacking  the  canal  bank. 

When  not  in  flood  a  superpassage  can  be  used  as  a 
highway  bridge. 

The  superpassage  possesses  the  great  advantage  of 
keeping  the  canal  completely  free  from  any  influx  of 
flood-water  from  the  torrent,  which  is  always  more  or 
less  heavily  charged  with  silt.  It  has  the  additional 
recommendation  of  not  requiring  the  maintenance  of  a 
large  establishment  every  rainy  season,  as  in  the  case  of 
a  level  crossing,  where  the  regulating  apparatus  must  be 
worked  by  manual  labor.  And  lastly,  the  canal  supply 
can  thus  be  kept  up  without  interruption,  there  being- 
no  necessity  to  shut  it  off  at  the  crossing  to  keep  the  silt- 
laden  flood-water  out  of  the  canal.  The  recommenda- 
tions apply  equally  to  a  passage  by  aqueduct,  and  render 
them  both  generally  preferable  to  a  level  crossing,  such 
as  that  at  Dhuiiowree,  given  in  Article  35,  when  the 
levels  will  admit  of  the  substitution. 

There  are  two  fine  examples  of  superpassages  a  few 
miles  below  the  headworks  of  the  Upper  Ganges  Canal, 
by  which  the  Puttri  and  Ranipore  torrents  are  carried 
across  the  canal.  These  have  a  clear  waterway  between 
the  parapets  of  200  and  300  feet,  respectively,  and  when 


OTHER    IRRIGATION    WORKS. 


171 


172  IRRIGATION    CANALS    AND 

the  torrents  are  not  in  flood,  they  are  used  as  bridges  of 
communication.*" 

Figure  110  gives  a  view  of  the  Ranipore  Superpassage. 
It  is  taken  from  Irrigation  in  India,  by  Mr.  H.  M.  Wil- 
son, M.  Am.  Sec.,  C.  E.,  in  Transactions  American  So- 
ciety of  Civil  Engineers,  Volume  23. 

The  Seesooan  Superpassage  on  the  Sutlej  Canalf  is 
shown  in  Figures  111,  112,  113  and  114. 

Taking  the  catchment  basin  of  the  Seesooan  to  be 
eight  miles  in  length  by  three  miles  in  Avidth,  we  obtain 
an  area  of  twenty-four  square  miles,  which  would  give  a 
maximum  rainfall,  at  the  rate  of  half  an  inch  per  hour, 
of  7,  752  cubic  feet  per  second,  agreeing  very  closely  with 
the  discharge  calculated  from  the  area  of  the  section  at 
the  canal  crossing,  with  the  velocity  due  to  a  declivity  of 
1  in  791.  To  pass  off  this  discharge,  a  water-way  of  150 
feet  wide  by  six  and  a  half  feet  in  depth  was  given  to 
the  masonry  channel  of  the  Superpassage.  This  would 
require  a  mean  velocity  of  about  eight  feet  per  second. 
The  dimensions  given  are  more  than  ample  for  the  re- 
quired discharge,  even  with  the  worst  description  of 
masonry  surface.  Major  Croftoii,  the  designer  of  this 
work,  computed  the  velocity  by  one  of  the  old  formulae, 
having  a  constant  value  of  c,  that  is: 


Computing  the  mean  velocity  through  the  masonry 
channel,  by  Kutter's  formula,  and  with  different  values 
of  n,  suitable  to  masonry  surfaces,  we  obtain  the  results 
given  in  Table  16.  The  water  channel  is  150  feet  wide, 
with  vertical  sides  six  and  a  half  feet  deep,  as  shown  in 
Figure  114.  The  slope  is  1  in  794.  In  round  numbers, 

*Koorkee  Treatise  on  Civil  Engineering. 

t  Report  on  the  Sutlej  Canal,  by  Major  J.  Crofton,  E.  E. 


OTHER    IRRIGATION    WORKS. 


173 


is  equal  to  2.4  feet.     For  further  information  011  this 
subject,  see  Flow  of  Water. 


174  IRRIGATION    CANALS    AND 

TABLE  16.     Giving  velocities  and  discharges  of  channels  with  different 
values  of  n. 


Value  of                     ]  r 
n                      in  feet. 

Slope  1  in  794 
1« 

1 
i  Mean  velocity 

j      in  feet  per 
second. 

V 

Discharpe  in 
cubic  feet  per 
second. 
Q 

.013                  2.4 

.035489 

12.6 

12,285 

.015                  2.4 

.  035489 

11.0 

10,725 

.017                  2.4 

.035489 

9.8 

9,555 

.020                  2.4 

.  035489 

8.4 

8,190 

The  difference  of  level  between  the  beds  of  the  canal 
and  the  torrent  is  21.93  feet,  which  is  thus  disposed  of: 

Feet. 

Depth  of  water  in  canal 7.00 

Head  up  to  soffit  of  arch  (for  navigation) 10.00 

Thickness  of  arch ,    3  00 

Brick-on-edge  flooring 1.93 

Total 21.93 

The  canal  channel  will  be  spanned  by  three  central 
arches  of  forty-five  feet  span  each,  and  two  at  the  sides 
of  thirty-two  feet  each;  tow-paths,  of  seven  and  a  half 
feet  wide  in  the  clear,  will  be  carried  under  each  side 
arch,  leaving  an  aggregate  water-way  of  184  feet.  The 
mean  water-way  of  the  earthen  channel  of  the  canal  is 
only  177  feet.  The  addition  is  made  to  this  work,  in 
consideration  of  the  expense  of  increasing  its  dimensions 
should  the  canal  be  required  to  carry  a  larger  supply 
hereafter.  The  water-way  for  the  torrent  above  the  canal 
(Figure  114  shows  one-half  of  this  channel),  is  projected 
in  one  channel  150  feet  wide  at  the  bottom,  with  side 
walls  (head  walls  of  the  work)  ten  feet  in  height,  five 
feet  thick  at  the  base,  four  feet  at  top;  the  flooring  over 
the  arches  to  be  formed  of  asphalt  or  some  substance 


OTHER    IRRIGATION    WORKS.  175 

impervious  to  water,  the  upper  surface  being  covered 
with  some  hard  material,  probably  a  layer  of  kunkur 
(nodular  limestone)  slabs.  The  backing  of  the  abut- 
ments will  be  of  puddled  clay,  covered  with  a  flooring  of 
kunkur,  slag,  or  bowlders  packed  in  cribs. 

Article  37.     Inverted  Syphons. 

An  inverted  syphon,  sometimes  called  a  syphon,  is,  in 
some  cases,  used  instead  of  an  aqueduct  or  super-pas- 
sage. The  levels  of  the  channels  which  cross  each 
other  determine  the  work  best  suited  for  the  locality. 
The  syphon  is  under  pressure,  and  it  is  usual  to  give  it 
such  a  head,  or  fall  of  water  surface,  from  its  inlet  to  its 
outlet,  that  it  has  a  high  velocity,  and,  therefore,  its 
current  has  sufficient  scouring  force  to  prevent  the  de- 
position of  silt  and  debris. 

If  the  syphon  has  not  sufficient  velocity  to  keep  itself 
clear,  not  only  of  the  silt  held  in  suspension,  but  also  of 
the  material  rolled  along  its  bed,  it  will  in  time,  get 
partly  or  entirely  choked,  and  its  waters,  being  thus 
dammed,  will  cause  floods,  and  very  likely  break  the 
canal  banks  and  do  material  damage. 

Probably  the  most  interesting  inverted  syphon  in  ex- 
istence is  that  under  Stony  Greek,  on  the  line  of  the 
Central  Irrigation  Canal,  in  Colusa  County,  California. 
It  serves  four  purposes,  namely: — 

1.  As   an   inverted    syphon  or   conduit  under  Stony 
Creek. 

2.  As  an  escape-way  for  surplus  canal  water  into  the 
creek. 

3.  As  a   secondary  gate    for   checking    the  flow   of 
water  in  the  canal  above  Stony  Creek. 

4.  As  an  inlet  from  the  creek  in  the  lower  portion  of 
the  canal. 


176  IRRIGATION    CANALS    AND 

The  following  description  of  the  work  is  given  by  the 
designer,  Mr.  C.  E.  Grunsky,  Chief  Engineer  of  the 
Central  Irrigation  District,  and  the  drawings,  descriptive 
of  the  work,  are  reduced  from  drawings  supplied  by 
him: — 

"  Central  Irrigation  District  Canal  has  been  planned 
for  the  irrigation  of  156,000  acres  of  land  in  the  cen- 
tral portion  of  the  west  side  Sacramento  Valley  plain. 

"  The  canal  is  cut  out  from  Sacramento  River  on  a 
gradient  of  one  in  ten  thousand  (6|  inches  per  mile). 
It  has  a  bottom  width  of  60  feet,  and  has  been  planned 
to  carry  a  maximum  depth  of  six  feet  of  water.  Its 
capacity  is  730  cubic  feet  per  second. 

"In  its  southerly  course,  this  canal  crosses  the  creeks 
which  drain  the  eastern  slope  of  the  Coast  Range.  The 
largest  of  the  creeks  thus  crossed,  is  Stony  Creek,  which 
has  a  drainage  area  of  760  square  miles,  and  a  maximum 
flow  of  about  30,000  cubic  feet  per  second. 

"The  grade  of  the  bottom  of  the  canal  and  the  lowest 
point  of  the  creek  bed  at  the  point  of  crossing  have  the 
same  height.  The  width  of  the  creek  between  firm 
banks  is  about  600  feet.  Its  bed  is  clean  gravel.  Its 
flow  at  the  canal  crossing  generally  ceases  in  June  or 
July. 

"  The  conduit  under  the  creek,  shown  in  Figs.  115  to 
119,  consists  of  seven  semi-circular  wooden  tubes,  con- 
structed of  long  staves  and  covered  by  a  common  hori- 
zontal platform  top.  The  wooden  tubes  are  to  be  hung 
under  the  platform  by  means  of  iron  bands,  whose  ends 
will  project  above  longitudinal  timbers  on  top  of  the 
platform,  serving  to  secure  the  same  against  upward 
movement.  The  structure  will  be  weighted  with  gravel 
and  anchored  to  the  creek  bed  to  prevent  its  floating  out 
of  place. 

"  The  conduit  ends  will  rest  on  concrete  in  masonry 
inlet  and  outlet  chambers.  Each  of  these  will  be  so 


OTHER    IRRIGATION    WORKS.  177 

constructed  that  the  space  between  masonry  walls  can  be 
opened  or  closed  to  the  creek.  The  gates  to  accomplish 
this  will  be  arranged  on  the  flash  board  principle,  i.  e., 
grooves  along  vertical  posts  will  be  provided  to  receive 
and  support  the  ends  of  loose  horizontal  boards  ~ 

"  The  structure  thus  becomes  an  escape-way  for  canal 
water  to  Stony  Creek. 

"  It  serves  as  a  check- weir  to  the  main  canal  and  can 
be  used  to  regulate  the  volume  of  flow  in  the  canal. 

"  It  serves  as  an  inlet  for  waters  of  Stony  Creek, 
thus  enabling  the  creek  to  be  used  as  a  secondary  source 
of  supply." 

Figures  115,  116,  117,  118  and  119  show  part  plan 
and  sections  of  this  work. 

The  line  of  the  Agra  Canal,  India,  crosses  the  Buriya 
Torrent.  The  volume  of  the  latter  is  2,000  cubic  feet  per 
second,  and  it  flows  over  a  steep  and  rocky  channel.  Its 
passage  under  the  canal  is  provided  for  by  a  partial  sy- 
phon having  seven  culverts,  6  feet  wide  and  4  feet  deep, 
the  velocity  of  which,  in  high  floods,  will  be  12  feet  per 
second.  This  velocity  is  sufficient  to  move  ordinary 
sized  bowlders,  and,  therefore,  sufficient  to  keep  the 
channel  clear  of  any  deposit  that  can  reach  it. 

The  culverts  are  covered  by  large  stones  bolted  down 
to  the  piers,  and,  for  this  purpose,  bolts  are  built  into  the 
latter.  A  strong  breast  wall  on  each  side  supports  the 
canal  banks,  and  the  ordinary  earthen  section  of  the 
canal  is  carried  over  the  syphon,  culverts.  The  canal 
flows  over  the  syphon  without  any  change  in  its  wetted 
cross-section  or  in  its  velocity.  The  syphon  is  provided 
with  a  floor  of  massive  rough  ashlar,  the  entrance  and 
egress  for  the  torrent  being  also  built  with  large  stone. 

Figures  120,  121,  122  and  123  show  the  syphon  carry- 
ing the  Hurroii  Creek  (Nullah)  under  the  Sirhind  or  Sut- 
lej  Canal.     This  work  is  constructed  of  brick  masonry. 
12 


178 


IRRIGATION    CANALS    AND 


OTHER    IRRIGATION    WORKS.  179 

The  Inverted  Syphon  carrying  the  Cavour  Canal,  Italy, 
under  the  Sesia  torrent,  is  one  of  the  finest  works  of  the 
kind  in  existence.  During  extreme  floods  the  Sesia  car- 
ries about  160,000  cubic  feet  per  second. 

The  syphon  is  863  feet  in  length.  It  consists  of  five 
elliptically  shaped  conduits,  or  culverts,  the  horizontal 
diameter  at  the  entrance  of  each  being  16  feet  5  inches, 
and  the  vertical  diameter  of  7  feet  10  inches  at  the  en- 
trance, and  7  feet  6  inches  at  the  exit.  The  area  of  the 
five  culverts  at  the  entrance  is  about  483  square  feet,  and 
the  canal  was  designed  to  carry  3,883  cubic  feet  per  sec- 
ond. This  would  give  a  mean  velocity,  at  the  entrance, 
of  about  8  feet  per  second,  and  with  a  supply  of  3,000 
feet  per  second,  it  would  give  a  mean  velocity  of  about  6 
feet  per  second,  and,  with  these  velocities,  it  is  found 
that  no  silting  of  the  culverts  takes  place. 

The  arch  is  of  brickwork  1  foot  9  inches  in  thickness. 
On  this  is  laid  a  thin  layer  of  concrete  and,  again  on 
this,  phmkiiig,  the  upper  surface  of  which  coincides  with 
the  bed  of  the  river. 

The  planks  are  laid  in  the  direction  of  the  general 
flow  of  the  current  of  the  river.  The  total  thickness  of 
brickwork,  concrete  and  planking  from  the  soffit  of  the 
arch  to  the  bed  of  the  torrent  is  only  3  feet  2  inches. 
The  surface  of  the  water  in  the  canal,  after  passing 
through  the  syphon,  is  2  feet  3  inches  above  the  bed  of 
the  Sesia. 

On  the  Verdoii  Canal  in  France,  there  are  several 
wrought  iron  syphons;  four  of  which  are  across  deep 
valleys.  The  most  important  is  that  at  St.  Paul,  890 
feet  long,  constructed  of  two  parallel  wrought-iroii  tubes, 
each  5  feet  9  inches  in  internal  diameter,  with  a  max- 
imum pressure  equal  to  116J  feet  head  of  water.  The 
capacity  of  this  canal  is  equal  to  212  cubic  feet  per  sec- 
ond, so  that  at  full  supply  the  mean  velocity  through 
this  syphon  is  equal  to  8  feet  per  second. 


180 


IRRIGATION    CANALS    AND 


OTHER    IRRIGATION    WORKS.  181 

The  horizontal  portion  of  the  syphon,  laid  at  the  bot- 
tom of  the  valley,  is  321.6  feet  in  length.  The  re- 
mainder of  its  length,  consisting  of  the  two  inclines,  is 
laid  at  a  slope  of  about  2|  to  1.  The  pipes  are  of 
wrought-iron,  and  respectively  0.353  inch  andTTT.315  inch 
thick  for  the  horizontal  and  inclined  portions.  They 
are  supported  on,  and  fixed  in,  masonry  at  the  junctions 
of  the  horizontal  and  inclined  portions.  The  remainder 
of  the  lengths  bear  on.  cast-iron  rollers,  resting  on  stone 
blocks,  placed  about  31  feet  apart.  The  arrangements 
for  the  expansion  and  contraction  consist  in  construct- 
ing a  short  length  of  the  tubes,  in  each  of  the  horizon- 
tal and  inclined  portions,  of  a  gradually  increasing  di- 
ameter from,  and  then  increasing  back  to,  the  normal 
diameter  of  the  tube.  The  metal  of  the  tubes  at  these 
swellings  is  reduced  to  about  J  inch  in  thickness;  in 
order  to  obtain  greater  elasticity,  and  it  is  contended 
that  the  bulging  in  and  drawing  out  of  the  tube,  at  these 
swellings,  will  respectively  allow  for  expansion  and  con- 
traction of  the  metals. 

At  the  beginning  of  the  works  on  this  canal,  the  long 
syphons,  including  that  of  St.  Paul,  above  described, 
were  constructed  through  the  natural  rock,  and  lined 
with  masonry  to  prevent  leakage,  at  a  depth  of  50  to  82 
feet  below  the  bottom  of  the  valleys,  the  rock  being  in- 
tended to  resist  the  hydraulic  pressure.  After  comple- 
tion, not  one  of  these  tunnel  syphons  acted  satisfactorily 
when  the  water  was  let  into  them.  Repairs  were  then 
commenced,  experimenting  at  first  with  those  under  the 
least,  and  ending  with  those  under  the  greatest  head  of 
pressure.  After  much  trouble  and  expense  all  were  at 
length  caused  to  act  satisfactorily,  with  the  exception  of 
that  of  St.  Paul,  which  had  to  be  abandoned,  and  wrought 
iron  pipes  substituted  as  above  described. 


182  IRRIGATION    CANALS    AND 

On  one  of  the  branches  of  this  canal,  there  is  a  syphon 
443  feet  long,  under  a  head  of  pressure  equal  to  71J  feet. 

The  Lozoya  Canal,  in  Spain,  with  a  discharge  of  89 
cubic  feet  per  second,  has  six  syphons,  one  of  which 
consists  of  four  cast  iron  pipes,  each  2.8  feet  in  diame- 
ter, three  of  which  carry  the  canal,  the  fourth  being 
used  in  case  of  accidents  to  any  of  the  other  three. 

There  are  two- most  interesting  syphons  on  the  Jucar 
Canal,  in  Spain,  under  the  barrancos  or  torrents  of  Carlet 
and  Alginet,  the  former  455  and  the  latter  524  feet  long. 
The  Carlet  syphon,  situated  about  14J  miles  below  An- 
tella,  is  a  very  old  construction.  Its  discharge  is  350 
cubic  feet  per  second.  The  canal  is  19  feet  wide  just 
above,  but  diminishes  to  7.5  at  the  entrance  of  the 
syphon,  which  is  barred,  first  by  an  iron  grating,  and 
again  by  a  wooden  one,  the  bars  being  about  six  inches 
apart.  Directly  over  the  entrance  stands  the  guard's 
house.  There  are  two  masonry  shafts  built  in  the  bed 
of  the  torrent  .down  to  the  syphon.  They,  too,  are  pro- 
tected by  gratings.  The  mouth  is  closed  in  masonry 
revetments,  supported  by  arches,  and  the  water-section 
just  below  is  6.75  feet  wide  and  8  feet  deep.  The  fall 
through  the  syphon  is  4.9  feet.  M.  Aymard  questioned 
some  workmen  who  had  once  been  in  it,  and  they  told 
him  the  gallery  was  5.9  feet  wide  and  6.5  feet  high.  He 
hence  calculated  the  velocity  through  it  to  be  10  feet  per 
second. 

General  Scott  Moiicrieff*  says  that  the  Moors  of  Spain 
have  left  many  proofs  of  their  skill  in  making  tunnels 
and  syphons  on  their  irrigation  canals.  The  Mijares 
Canal,  which  irrigates  9,800  acres  of  land,  and  close  to 
its  prise,  or  headworks,  enters  a  tunnel  1,300  feet  long; 
after  which  it  is  carried  by  a  syphon  327  feet  in  length 
under  the  Viuda  ravine.  The  lowest  point  of  this 


*  Irrigation  in  Southern  Europe. 


OTHER    IRRIGATION    WORKS.  183 

syphon  is  about  180  feet  below  the  mouth,  and  90  feet 
below  the  present  bed  of  the  torrent  which  crosses  it. 
There  is  a  fall  through  it  of  13  feet. 


Article  38.     Retrogression  of  Levels. 

Retrogression  of  levels,  or  the  lowering  of  the  bed  of 
a  channel  by  erosion,  on  long  lines,  is  a  serious  evil  in. 
any  irrigation  channel,  especially  in  a  canal  carrying  a 
large  volume  of  water,  say  over  1,000  cubic  feet  per 
second.  Scour  or  erosion  is  usually  referred  to  local 
action  of  the  water,  while  Retrogression  of  Levels  is 
usually  applied  to  long  reaches  of  a  channel.  It  is 
caused  by  giving  too  great  a  slope,  and,  therefore,  too 
great  a  velocity  to  the  canal.  For  example,  a  canal  is 
constructed  with  a  slope  of  two  feet  per  mile,  the  bed  of 
which  is  shown  by  the  line  A  B,  Figure  124.  The  canal 


Retrogression   of  Levels  in  Canals. 

has  a  high  mean  velocity,  over  three  feet  per  second.  The 
material  through  which  the  canal  runs  is  sandy  loam, 
which  cannot  bear  a  higher  mean  velocity  than  2.25 
feet  per  second  without  erosion.  In  the  course  of  a  few 
years  the  current  in  the  canal  scours  the  bed  to  such  an 
extent  that  retrogression  of  bed  levels  has  taken  place 
from  A  B,  with  a  grade  of  two  feet  per  mile,  and  a  mean 
velocity  of  over  three  feet  per  second,  to  C B,  with  a  grade 
of  one  foot  per  mile,  and  a  velocity  of  about  2.25  feet 
per  second.  Retrogression  of  levels  ceases  at  the  line 


184  IRRIGATION    CANALS    AND 

C  B,  and  on  this  grade  line  the  canal  has  established  its 
regimen. 

In  another  case,  through  the  same  material,  the  bed  of 
the  canal,  from  A  to  E,  Figure  125,  was  given  a  fall  of 
two  feet  per  mile.  At  E  was  a  vertical  drop  of  four  feet 
to  F,  and  then  a  grade  of  two  feet  per  mile  from  F  to  R. 
The  fall  E  F  was  so  badly  constructed  that  it  was 
washed  away  and  not  rebuilt,  thus  practically  adding 
four  feet  to  the  fall  of  the  bed  from  A  to  B.  Retrogres- 
sion of  levels  took  place  until  all  scour  stopped  at  the 
line  C  B  at  a  ruling  grade  of  one  foot  per  mile. 

Bad  results  generally  follow  the  lowering  of  the  bed, 
of  which  a  few  are  here  mentioned. 

The  beds  of  the  distributing  channels  taken  from  the 
main  channel  between  A  and  B  were  fixed  with  refer- 
ence to  the  bed  of  the  canal,  A  B,  Figure  124,  and  any 
lowering  of  this  bed  would  diminish  the  depth  of  water 
at,  and,  therefore,  the  supply  entering  their  heads.  For 
example,  midway  between  A  and  B,  at  E}  a  small  chan- 
nel is  taken  out  with  its  bed  three  feet  above  the  bed  of 
the  main  channel,  but  after  some  time,  retrogression  of 
levels  has  lowered  the  bed  of  the  main  canal  four  feet 
from  E  to  F.  The  surface  of  water  in  the  main  chan- 
nel, at  full  supply  of  six  feet  in  depth,  is,  therefore,  one 
foot  below  the  bed  of  the  distributing  channel  at  E.  In. 
order,  therefore,  to  get  water  through  the  distributary, 
a  regulating  gate  would  have  to  be  constructed  on  the 
main  channel  below  E,  so  that,  by  closing  this  gate 
as  required,  the  level  of  the  water  could  be  raised. 
Another  plan  would  be  to  deepen  the  distributing  chan- 
nel for  some  distance  from  its  head.  This  deepening  of 
the  distributing  channel  would  flatten  its  grade  and 
cause  a  diminution  of  its  velocity  and  discharge.  Fur- 
thermore, the  land  on  each  side  of  the  distributary,  for 
some  distance  from  its  head,  would  be  too  high  above  it 
for  irrigation  by  gravity. 


OTHER    IRRIGATION    WORKS.  185 

Another  evil  caused  by  lowering  the  canal  bed  would 
be  the  lowering  of  the  sub-surface  water  in  the  land  on 
each  side  of  the  canal,  where  in  some  cases  such  lower- 
ing is  not  required. 

Any  one  who  has  inspected  the  old  Irrigation  Chan- 
nels in  parts  of  California  will  have  seen  that  retrogres- 
sion of  levels  has  taken  place  with  bad  results  in 
numerous  cases.  As  a  rule,  too  much  grade  has  been 
given  to  the  old  canals. 

In  the  early  days  of  the  construction  of  large  irriga- 
tion canals,  by  the  British  Government,  in  India,  this 
mistake  was  made.  The  greatest  canal  engineer  that 
ever  existed,  General  Sir  Proby  Cautley,  the  designer 
and  constructor  of  that  magnificent  work,  the  original 
or  Upper  Ganges  Canal,  decided,  after  careful  thought 
and  due  regard  to  the  experience  gained  on  canals  pre- 
viously opened,  that  15  inches  per  mile  was  required  as 
the  grade  of  this  canal.  This  slope  was  too  great,  and 
probably  six  inches  per  mile  would  have  been  ample. 
After  the  canal  was  in  use  for  some  years,  retrogression 
of  levels  took  place  to  an  alarming  extent;  deep  holes 
were  scoured  out  below  many  of  the  falls  and  bridges, 
thereby  endangering  their  stability,  and  the  bed  of  the 
canal  was  in  some  places  deepened,  and  in  others 
widened  beyond  the  original  cross-section. 

When  Cautley  fixed  the  slope  of  the  Ganges  Canal, 
nothing  was  then  known  of  the  experiments  and  inves- 
tigations of  Humphreys  and  Abbot,  D'Arcy,  Baziii, 
Gordon,  Kutter  and  Ganguillet  and  others.  Cautley 
fixed  his  slope  in  accordance  with  the  formula  of  Du- 
buat,  a  formula  that  was  used  for  many  years  in  India, 
both  before  and  after  the  opening  of  the  Ganges  Canal. 
Neville's  Hydraulics  was  then  a  standard  work,  in  use 
by  the  canal  engineers  of  Northern  India,  and  in  the  last 
edition  of  this  work,  1875,  a  table  based  on  Dubuat's 


186  IRRIGATION    CANALS    AND 

formula  is  given  for  finding  the  Mean  Velocity  of  Water 
jioiuing  in  Pipes,  Drains,  Streams  and  Rivers. 

No  blame  whatever  can  be  attached  to  Cautley  for  de- 
termining the  slope  of  the  Ganges  Canal  by  this  for- 
mula, for  it  was  generally  used  in  India  at  the  time,  and 
A\ras  believed  to  be  correct.  It  is  now  known  to  be  very 
inaccurate. 

This  mistake  of  the  slope  was  the  only  radical  defect 
in  the  design  of  the  Ganges  Canal;  and,  with  this  excep- 
tion, there  has  never  been  constructed  a  work  of  equal 
magnitude,  that  showed  so  few  mistakes,  or  that  dis- 
played more  originality  and  boldness  in  design  and 
execution. 

Notwithstanding  all  this,  a  set  of  carping  critics  made 
the  last  years  of  the  life  of  General  Cautley  miserable, 
by  direct  and  indirect,  unjust  attacks  on  his  great  work. 

In  1864  a  committee  of  five  Royal  Engineers — not  a 
single  Civil  Engineer  was  on  it— recommended  that  Cap- 
tain J.  Crofton,  another  Royal  Engineer,  should  report 
on  the  remodelling  of  the  Ganges  Canal.  Captain  Crof- 
ton did  so  report  in  1866,  and  he  estimated  the  cost  of  re- 
modelling at  $12,500,000. 

One  able  Civil  Engineer,  Mr.  Thomas  Login,  proved 
conclusively  that  protective  works,  at  a  comparatively 
small  expense,  would  ensure  the  safety  of  the  Canal.  He 
raised  the  crests  of  the  falls  in  some  places  by  planking, 
and  crib-work  filled  with  bowlders  was  placed  below 
them  in  the  bed  of  the  canal.  By  these  means  water- 
cushions  were  formed  below  the  falls,  which  materially 
reduced  the  destructive  effect  of  the  falling  water.  For 
a  detailed  description  of  this  work  see  the  account  given 
by  Mr.  Thomas  Login,  C.  E.*~  His  only  thanks  was  re- 
moval to  another  work,  and  he  was  never  again  appointed 

''Transactions  of  the  Institution  of  Civil  Engineers.  Vol.  XXVII. 
1867-68. 


OTHER    IRRIGATION    WORKS.  187 

to  the  Ganges  Canal.  Mr.  Login  and  the  writer  of  this 
work  were  intimate  friends,  and  in  justice  to  the  former 
this  brief  reference  is  made  to  his  work  on  the  Ganges 
Canal,  for  which  he  did  not  get  the  credit  that  he  de- 
served. 

In  1868  Mr.  Login  stated:*  "  Six  years  ago  the  Author 
stood  almost  alone  in  maintaining  the  opinion  that  the 
Ganges  Canal  needed  only  some  protective  work,  and  did 
not  require  the  radical  alterations  then  proposed.  The 
Author  will  only  add  the  expression  of  his  firm  convic- 
tion, that  the  works  may  be  placed  out  of  danger  by  the 
judicious  use  of  wood  and  iron,  at  a  less  cost  than  if 
stone  be  employed,  without  depriving  the  country  of  the 
benefits  of  irrigation  beyond  a  short  time." 

Time  has  fully  justified  Mr.  Login's  opinion,  and  a 
few  years  since  General  C.  E.  Moncrieff,  R.  E.,  testified 
to  his  sound  judgment.!  He  states: 

"Did  they  not  remember  how  a  committee  of  engi- 
neers had  pronounced  Cautley's  great  Ganges  Canal  un- 
sound, and  how  they  would  have  spent  fabulous  sums 
on  it,  had  not  Bro willow's  common  sense  and  attention 
to  details  shown  that  the  work  was  all  right,  as  it  has 
triumphantly  proved  to  be." 

Had  General  Moncrieff  given  the  credit  of  this  success 
to  Login  instead  of  Browiilow,  his  statement  would  be 
more  in  accordance  with  the  facts.  It  was  mainly  due 
to  Login's  sound  judgment,  sturdy  independence,  and 
having  practically  proved  what  could  be  done  at  com- 
paratively small  expense,  that  overtaxed  India  was  saved 
from  the  great  expense  that  was  proposed  to  be  incurred 
in  remodelling  the  canal,  and  another  serious  matter, 
the  closing  of  the  canal  for  one  or  two  years. 


*  Transaction  of  the  Institution  of  Civil  Engineers,  Vol.  XXVII,  1867- 
68. 

t  Irrigation  in  Egypt  in  Nineteenth  Century.     February,  1885. 


188  IKKIGATION    CANALS    AND 

Figures  126  and  127  are  plan  and  profile  of  the  orig- 
inal Ganges  Canal,  through  the  Toghulpoor  sand  hill  in 
mile  37.*  There  was  here  more  erosion  in  the  width 
than  in  the  depth.  The  plan,  Figure  126,  shows  the 
widening,  and  the  profile,  Figure  127,  shows  that  the 
bed  of  the  canal  through  this  wide  section  is  higher 
than  the  narrow  channel  above  and  below  that  place. 


..._---—  —  -—  -- 


! 


. 

[      ^  y  ^     j.    •     _L^T^V^»  .  »t.  ^  •"*  .  ••^r"l»»*  *^  *  *•  *  >*T'r*W""*'i  *i  •  •  vX-^^s^-K^^ 

*'*  •''  v   *   "    "  ~'  *""  v  "v  *•'•'•'  "''1 


Figs.  126,  127.    Widening  of  Ganges  Canal  at  Toghulpoor. 

The  Eastern  Jumna  Canal, f  having  a  discharge  of 
1,068  cubic  feet  per  second,  had,  when  originally  con- 
structed, a  grade  of  372  feet  in  130  miles,  or  at  the 
average  rate  of  2.86  feet  per  mile.  In  some  reaches  the 
grade  was  considerably  more  than  this. 

Immediately  after  the  water  was  admitted  into  the 
canal  the  effect  of  a  rapid  current  was  apparent.  Ketro- 
gression  of  levels  on  an  extensive  and  dangerous  scale 
took  place.  From  the  Nowgong  Dam  to  the  Muskurra 
River,  where  the  fall  was  eight  feet  per  mile,  deep 

*  Report  on  the  Ganges  Canal  by  Captain  J.  Crofton,  E.  E. 
t  Notes  and  Memoranda  on  the  Eastern  Jumna  Canal,  by  Colonel  S:r 
P.  T.  Cantley,  K.  C.  B. 


OTHER    IRRIGATION    WORKS. 


189 


erosion  took  place.  A  specimen  cross-section  011  this 
reach  is  given  in  Figure  128,  where  the  shaded  portion 
shows  the  part  scoured  out.  The  silt  resulting  from  the 
erosion  was  carried  down  the  canal  until  it  got  to  a  level 
reach,  where  it  was  deposited,  causing  the  TaeclT^and 
banks  to  silt  up,  as  shown  in  Figure  129.  The  shaded 
part  shows  the  silting  up;  the  top  of  the  bank  and 
outside  slope  are  shown,  dressed  up. 


Fig.  128.    Erosion  on  Eastern  Jumna  Canal. 

To  prevent  the  canal  from  being  destroyed  it  had  to 
be  reconstructed  at  great  expense. 


Fig.  129.    Silting  up  on  Eastern  Jumna  Canal. 

Twenty-three  falls  were  constructed,  being  at  the  rate 
of  about  one  fall  to  six  miles  of  canal,  and  the  grade  was 
reduced,  varying  from  17  to  22  inches  per  mile. 

Article  39.     Falls — Drops — Checks. 

In  designing  an  artificial  channel  for  the  passage  of 
a  large  volume  of  water,  the  first  thing  that  presents 
itself  for  decision  is  the  rate  of  slope  that  is  to  be  given 
to  the  bed,  to  insure  that  velocity  of  current  which 
prevents  the  deposition  of  silt,  keeps  the  channel  clear 
of  weeds  and  other  impediments,  and,  at  the  same  time, 
shall  not  erode  the  bottom  and  sides  of  the  channel. 


190  IRRIGATION    CANALS    AND 

"When,  the  slope  or  grade  of  the  canal  is  the  same  as 
the  natural  fall  of  the  country  through  which  the  canal 
is  excavated,  and  when  the  current  is  adjusted,  as  ahove 
explained,  to  prevent  silting  up  and  erosion,  then  the 
level  of  its  bed  will,  of  course,  remain  at  a  uniform 
depth  below  the  surface  of  the  ground. 

Bed  of  Canal  in  Embankment. 


Fig.  ISO.    Longitudinal  Section,  Canal  in  Embankment. 

Usually  the  slope  of  the  country  is  greater  than  that 
of  the  canal,  and,  with  canals  having  a  large  discharge, 
that  is,  from  1,000  to  6,000  cubic  feet  per  second,  this  is 
invariably  the  case,  and  the  excess  of  slope  of  the 
country  has  to  be  disposed  of,  either  by  embankments 
or  by  works  variously  called  falls,  drops,  and  sometimes 
in  America,  checks. 


Fig.  131.    Longitudinal  Section,  Falls  in  Canal. 

In  brief,  then,  the  object  of  falls  is  to  get  rid  of  a 
greater  declivity  of  bed  than  it  is  advisable  to  allow  in 
mere  earthen  channels,  and  it  is  sought  to  be  attained 
by  giving  at  intervals  sudden  falls  protected  by  masonry, 
between  which  the  simple  earthen  bed  may  preserve  its 
proper  slope. 

Figure  130,  not  drawn  to  scale,  shows  a  reach  of  a 
canal  in  embankment,  five  miles  in  length.  In  this 
five  miles  the  grade  of  the  country  has  gained  25  feet 
on  that  of  the  canal,  and,  it  is  obvious,  that  an  em- 


OTHER    IRRIGATION    WORKS.  .1.91 

bankment  is  out  of  the  question  on  account  of  its  great 
cost,  the  danger  of  breaches  in  its  banks  and  several 
other  good  reasons.  To  compensate,  therefore,  for  the 
difference  of  slope,  falls  are  constructed  on  irrigation 
canals,  as  they  are  safer  arid  cheaper  than^enrbank- 
ments. 

Figure  131,  not  drawn  to  scale,  shows  how  the  falls 
are  arranged  so  that  the  canal  is,  either  in  whole  or  in 
part,  in  soil.  The  canal  is  laid  out  in  a  series  of  steps  t 
so  as  to  keep  it  at  a  tolerably  uniform,  level  below  the 
surface  of  the  country,  until  the  flat  country  is  reached. 
By  this  time,  the  supply  of  the  canal  is  diminished,  and 
it,  therefore,  requires  a  greater  slope  to  keep  up  the 
original  velocity,  and  usually  a  point  will  be  reached 
where  the  slope  of  the  country  is  the  same  as  that  fixed 
for  the  canal. 

When  designing  an  irrigation  canal,  a  minimum 
depth  of  excavation  is  determined,  and  then,  when  the 
depth  of  cutting  becomes  less  than  this,  it  is  time  to 
locate  a  fall. 

The  shape  and  construction  of  falls  are  questions  re- 
quiring much  thought  and  consideration.  Their  loca- 
tion should  evidently,  from  the  diagrams,  Figures  130 
and  131,  be  near  the  places  where  the  canal  bed,  if  con- 
tinued without  a  break,  would  have  to  be  carried  in  em- 
baiikmeiit  above  the  surface  of  the  country.  Their 
exact  location  is  generally  made  to  coincide  with  the 
requirements  of  a  highway  bridge,  regulator,  or  some 
other  masonry  work,  such  as  are  herein  described,  for 
the  sake  of  economy,  or  for  some  other  good  reason. 

In  America,  falls  are  usually  constructed  of  timber, 
and  they  have  not  only  the  disadvantage  of  being  built 
of  perishable  material,  but  they  have  also  other  defects, 
the  chief  of  which  is  the  great  velocity  of  the  water  at 
and  near  them,  which  often  causes  their  destruction. 


192 


IRRIGATION    CANALS    AND 


Outside  of  America,  in  India,  Italy  and  other  irrigat- 
ing countries,  the  falls  are  permanent  works,  constructed 
of  brick  or  stone  masonry.  On  the  best  works  the 
banks  of  the  canal,  both  above  and  below  the  fall,  are 
protected  from  the  erosive  action  of  the  water. 

Six  descriptions  of  falls  are  in  use: — 

1.  The  Ogee  Fall. 

2.  The  Vertical  Fall,  with  water  cushion. 

3.  The  Vertical  Fall,  with  gratings  attached. 

4.  The  Vertical  Fall,  with  sliding  gates. 

5.  The  Vertical  or  Sloping  Fall,  with  plank  panels 
or  flash  boards. 

6.  Rapids. 

Rapids  are  described  in  Article  40. 

Ogee  Falls. 

There  has  been  much  difference  of  opinion  with  re- 
ference to  the  exact  shape  of  the  fall.  Ogee  falls,  similar 
to  that  shown  in  Figure  132,  were  adopted  by  Sir  Proby 
Cautley,  on  the  Ganges  Canal,  with  the  view  of  deliver- 
ing the  water  at  the  foot  of  the  fall  as  quietly  as  pos- 
sible. 


Fig.  132.    Section  of  Ogee  Falls. 

The  following  is  a  description  of  one  of  the  Ogee  falls 
•on  the  Ganges  Canal:  Figure  133  shows  a  plan,  and  Fig- 
ure 134  a  view  of  the  Asufnuggur  Fall  on  the  Upper 


OTHER    IRRIGATION    WORKS. 


193 


Ganges  Canal.  This  fall  is  shown  attached  to  a  bridge. 
The  bridge  consists  of  eight  spans  of  25  feet  in  width 
each,  which  crosses  the  canal  on  the  upper  levels.  To 
the  tail  or  apron  of  this  bridge  the  ogees  are  attached, 
delivering  the  water  into  four  chambers  of  54|  feet  in 
width,  every  alternate  bridge-pier  being  prolonged  on 
its  down-stream  face,  so  as  to  divide  the  space,  which  is 
occupied  by  the  lower  floorings,  into  four  compartments. 
In  advance  of  the  three  dividing  walls,  which  are  car- 
ried to  a  distance  of  84  feet  from  the  down-stream  face 
of  the  bridge,  there  is  an  open  space  of  masonry  floor- 
ing, which  is  protected  by  an  advanced  area  of  box- 
work,  or  heavy  material  filled  into  boxes  or  crates,  and 
covered  with  sleepers,  so  as  to  retain  the  material  in  po- 
sition. 

IL 


Plan  of  Asufnuggur  Falls. 

Additional  defenses  are  given  these  floorings  by  lines 
of  sheet  piling.  The  flanks  of  the  chambers  below  the 
descent  are  protected  by  revetments,  equal  in  height  to 
the  dividing  walls.  Between  and  on  the  flanks  of  these 
two  jetties,  lines  of  piles  and  other  protective  arrange- 
ments are  distributed,  so  as  to  secure  the  safe  passage  of 
the  water  over  the  floorings,  and  to  admit  of  the  cur- 
rents escaping  from  the  works  with  as  little  tendency 
to  danger  as  possible.  The  Ogee  .Falls  have  proved  fail- 
ures, both  on  the  Upper  Ganges  and  Baree  Doab  Canals. 
Col.  Crofton,  in  his  Report  on  the  Ganges  Canal,  states 
13 


194 


IRRIGATION    CANALS    AND 


OTHER    IRRIGATION    WORKS. 


195 


that  the  greater  number  of  the  Ogee  Falls  on  this  canal 
suffered  injury  more  or  less  severe,  in  their  lower  floor- 
ings from  the  action  of  the  water,  and  in  one  or  two 
cases  the  brick,  on  edge  covering  to  the  J3geej*  was 
stripped  off,  but  timely  repairs  and  protection  saved  the 
evil  from  spreading. 

Vertical  Falls  with  Water  Cushions. 

Vertical   Falls   with  water  cushions  are  illustrated  in 
Figures  135  to  140  inclusive. 


Fig.  135.    Section  of  Vertical  Fall. 

These  falls  have  been  found  much  safer  than  the  Ogee 
Falls.  On  the  Baree  Doab  Canal,  and  generally  011  the 
new  canals  in  India,  Vertical  Falls  are  used.  These 
falls  have  a  cistern  on  the  lower  side,  and  this  cistern 
acts  as  a  water  cushion,  and  opposes  a  dead  resistance  to 
the  falling  water.  The  velocity  of  the  falling  water  in 
a  forward  direction  is  also  checked. 

To  lessen  the  destructive  action  of  the  falling  water 
Mr.  T.  Login,  M.  I.  G.  E.*  secured  a  framework  of  tim- 
ber about  five  feet  in  height,  above  the  crown  of  the 
Ogee  Falls,  instead  of  trusting  to  sleepers  which  were 
constantly  giving  way.  By  this  arrangement  the  water 
was  held  up,  so  that  erosive  action  on  the  bed  and  banks 


*On  the  Benefits  of  Irrigation  in  India,  and  011  the  proper  Construction 
of  Irrigation  Canals  by  Thomas  Login,  M.  Inst.  C.  E.,  in  Proceedings  of  the 
Institution  of  Civil  Engineers,  Volume  XXVII. 


I'JG 


IRRIGATION    CANALS    AND 


was  prevented  on  the  up-stream  side  of  the  canal,  and  it 
is  a  remarkable  fact,  that  though  there  was  a  perpendic- 
ular fall  of  five  feet  or  more  on  the  crown  of  the  Ogee, 


Section  of  Vertical  Fall  on  Baree  Doab  Canal. 

no  injury  was  done  to  the  brickwork  at  the  point  where 
the   water  impinged.     Probably   this   was  owing  to  the 


water,  which  passed  through  the  open  spaces  of  the  tim- 
ber framework,  forming  a  cushion  for  the  descending 
water . 


OTHER    IRRIGATION    WORKS. 


197 


Mr.  Login  also  constructed  a  rough  sort  of  submerged 
weir  3J  feet  high  across  the  chambers  of  the  falls,  by 
which  a  cistern  was  formed  to  receive  the  descending 
mass,  and  in  this  manner  diminished  the  destructive 
effect  of  the  falling  water. 

Figure  136  shows  a  vertical  fall  with  water  cushion  on 
the  Baree  Doab  Canal,  India.  It  will  be  seen  that  the 
bed  is  protected  for  some  distance,  011  the  lower  side, 
with  masonry  and  paved  flooring. 

Figure  137  shows  a  longitudinal  section,  Figure  138 
a  cross-section,  and  Figure  139  a  plan  of  a  vertical  fall 
with  water  cushion,  constructed  of  timber  and  bowlders, 
on  a  small  irrigation  canal  on  the  Canterbury  Plains, 
New  Zealand.* 

The  maximum  discharge  of  this  canal  is  about  50 
cubic  feet  per  second.  A  water  gauge,  for  delivering 
the  required  quantity  of  water  to  one  of  the  distributing 
channels,  is  shown  by  the  dotted  lines. 


Section  of  Timber  Fall    with  Water  Cushion. 

Figure  140  shows  a  vertical  fall  with  water-cushion  on 
the  Turlock  Canal,  California.  This  diagram  is  taken 
from  a  paper  by  Mr.  H.  M.  Wilson,  C.  E.,  in  Transac- 
tions of  Am.  Soc.  C.  E.,  Vol.  XXV. 


*  Water  Supply  and  Irrigation  of  the  Canterbury  Plains,  New  Zealand, 
"by  George  Frederick  Ritso,  Assoc.  M.  Inst.  C.  E.,  in  Proceedings  of  the 
Institution  of  Civil  Engineers.  Volume  LXXIV,  1883. 


198 


IRRIGATION    CANALS    AND 


The  following  formula  lias  been  used  in  India  to  find 
the  depth  of  the  cistern  below  the  lower  bed  of  the  canal. 
It  is:  — 

x  ==    /**  X    d* 


in  which  x  =  the  required  depth  of  cistern  below  the 
lower  bed  of  the  canal. 

h  =  the  height  or  fall,  that  is,  the  difference  of  level 
between  the  surface  of  water  above  the  fall  and  the  sur- 
face of  water  below  it. 

d  =  full  supply  depth  of  water  in  the  channel. 


Section  of  Vertical  Fall  with  Water  Cushion. 

It  has  been  stated  that  all  the  cisterns  constructed 
with  depths  thus  obtained,  have  answered  admirably, 
having  required  but  slight  repairs  since  they  were  built. 

The  very  dangerous  scouring  and  cutting  action  of  a 
large  body  of  water  falling  over  a  height  of  even  a  few 
feet  can  be  readily  understood.  The  greater  the  height 
of  the  fall  and  the  depth  of  water,  the  more  violent,  of 
course,  will  be  the  action.  Those  on  the  original 
Ganges  Canal  are  not  higher  than  eight  feet,  but  the 
destructive  action  of  over  6,000  cubic  feet  of  water  per 
second,  and  having  a  depth  on  the  crest  of  the  fall  of 
six  feet  or  more,  is  very  great,  and  nothing  but  the  best 
masonry  is  capable  of  resisting  it. 


OTHER    IRRIGATION    WORKS.  199 

If  stone  of  good  quality  can  be  obtained  it  should 
always  be  employed,  laid  011  an  unyielding  foundation, 
with  fine  mortar  joints.  The  banks  must  be  protected 
with  masonry  for  a  considerable  distance  down  stream, 
and  the  bed  of  the  canal  protected  by  a  solid  masonry 
flooring,  the  down  stream  end  of  which  is  protected  by 
a  row  of  sheet  piling. 

The  depth  of  water  over  the  crest  of  a  fall  is  less  than 
that  in  the  canal  above  the  fall,  and  it  follows  that  the 
effect  of  a  fall  occurring  at  the  end  of  a  canal  reach  is  to 
increase  the  grade,  and,  therefore,  the  velocity,  and  to 
diminish  the  depth  of  water  for  a  considerable  distance 
above  the  fall.  The  increase  of  velocity  and  diminu- 
tion of  depth  are  gradual  from  the  point  where  the 
action  commences  down  to  the  fall  itself,  where,  of 
course,  they  attain  a  maximum,  so  that  the  depth  of 
water  passing  over  the  fall  is  very  much  less,  as  the 
velocity  is  very  much  greater,  than  the  normal  depth 
and  velocity  above.  This  increase  of  velocity,  before 
the  water  reaches  the  fall,  produces  a  dangerous  scour  on 
the  bed  and  banks  of  the  canal,  and  in  order  to  guard 
against  this,  it  has  been  found  necessary  to  head  up  the 
water  at  the  falls  on  the  Ganges  Canal  by  means  of 
sleepers  dropped  in  the  grooves  of  the  piers,  which  has 
virtually  increased  the  height  of  the  fall,  and  has  been 
one  cause  of  the  flooring,  on  the  lower  side  of  the  fall, 
suffering  in  places  from  the  violent  action  of  the  water. 
It  has  also  been  proposed  to  narrow  the  falls  to  produce 
the  same  effect. 

The  method  most  commonly  adopted  in  India  is  to 
raise  the  crest  of  the  falls  by  a  masonry  weir,  as  shown 
in  Figure  132.  At  first  the  crest  of  the  fall  was  on  the 
level  of  the  bed  of  the  canal  on  the  upper  reach.  The 
height  to  which  it  is  necessary  to  raise  the  crest  of  the 
weir  may  be  found  from  the  following  investigation,  as 


IRRIGATION    CANALS    AND 

given  by  Colonel  Dyas,  modified,  however,  bv  the 
writer  to  suit  the  symbols  used,  and  also  Kutter's 
formula,  as  simplified  in  this  work. 

v  =  mean  velocity  in  feet  in  open  channel. 

a  =  sectional  area  of  open  channel  in  square  feet. 

r  =  hydraulic  mean  depth  of  same  in  feet. 

s  ==  sine  of  slope. 

h  =  height   in   feet  of   surface  of  water  in  channel, 
above  crest  of  fall. 

I  =  length  of  crest  of  fall  in  feet. 

rn  —  co-efficient  of   discharge  over  weir  varying  from 
2.5  to  3.5. 

c  —  co-efficient  of  discharge  of  open  channel. 

Allowing  for  velocity  of  approach,  we  have  discharge 
over  fall  complete,  that  is,  a  free  fall: — 


but  v  =  c  X  (  r  s)1  .'.   v2  =  c2  X  rs 
substituting  value  of  v2  we  have:  — 

(C2  T  H  V- 
h  -f-  ----  '  -  i* 
2(/  / 

The  discharge  in  channel  above  weir:  — 
Q  =  a  c  (•/•«)* 

.-.       m  I  (h  -f    c*r8  V  ==  a  c  (•/•«)* 
dh  -f  c2rs 


^ 
X 


m  2gh+  <?rs  2g  h 


X 


OTHER    IRRIGATION    WORKS.  201 

1 


/N  £/  '          \    C\        1  •)  /\      Cl         7          I  9 

m  V2(/  A  -j-  <r  r  -sy  5w «  -T  c  r  8 


..... 
(2  1;  /i  +  cr  ra)* 

Now,   to    find  //,  we    have    from    equation    above    by- 
squaring, 


m 


T* 


Z2    ^  -f  ^=  a2  c2  r* 


extract  cube  root 

/    2  72  v  \x  /  2gr/i  +  c?r  s  \        /   2   2      \ 
(ma  r  )3  X  I-   --  -  j  =  (a2  c2  rs) 

2g  h  +  c2  r  .s       /  ^c2j?-.s  U 
~~  ~  \    m1  P  / 


.  =  Ar 
-  \ 


m 

rs  . 

" 


Having  thus  got  the  value  of  h,  deduct  it  from  the  depth 
of  water  in  the  channel,  and  we  have  the  height  to 
which  the  weir  should  be  raised  above  the  bed  of  the 
canal,  Figure  132,  in  order  that  the  water  in  its  ap- 
proach to  the  weir  may  not  have  any  increase  of  ve- 
locity. 

Example:  —  Let  the  bed  width  of  the  channel  above 
the  weir  be  60  feet,  depth  9  feet,  side  slopes  1  to  1, 
grade  6  inches  per  mile  and  n  =  .025.  Also,  let  the 
length  of  the  crest  of  weir  be  55  feet.  Now,  let  us  com- 
pute to  what  depth  the  crest  of  the  weir  must  be  raised, 
in  order  that  the  water  approaching  the  weir  may  not 
have  a  greater  velocity  than  the  mean  velocity  in  the 
open  channel. 

In  the  open  channel  we  have:  (see  Flow  of    Water) 


IRRIGATION    CANALS    AND 
621 


==  7,3295  and  ,/r  =  2.7  m  =  3, 


, 
p         84.  /  2b 

and  c  ==  86.4 

,s  ==  6  inches  per  mile  =  .000094697; 
substituting  values  of  a,  c,  r,  s,  m,  /,  and  </,  in  above 
formula  (A)  we  have 

'621'2        S6.42  4-  7.3295  X  .000094697 


/62T_   -  86.42  -|-  7.3295  X  . 000094697 \ 
=  \  ~  32  X  552  J 

/86.42  X  7.3295  X  .000094697x      .        y 

\  2  X32.2  ; 


Now,  as   a   check,  let  us    compute   the  discharge  over 
\veir:  — 

Q  =  3  X  55  X  4.1808  v/ 


=  1409  nearly,  which  is  also  the  discharge  in  the 
open  channel,  computed  by  Kutter's  formula,  with  the 
dimensions  above  given.  Now  9  —  4.1808=4.8192  feet 
is  the  height  above  crest  of  fall  to  which  the  weir  must 
be  built.  This  raising  of  crest,  however,  is  suited  to  only 
one  depth  of  water  in  the  open  channel.  A  much  better 
plan  by  which  the  crest  of  the  weir  can  be  adjusted  to 
any  depth  of  water  in  the  channel,  is  shown  in  Figures 
152,  153  and  154. 

Vertical  Falls,  with  Grating*. 

The  result  of  experience  seems  to  show  that  Vertical 
Falls  with  Gratings,  as  used  on  the  Baree  Doab  Canal, 
and  illustrated  in  Figures  142  to  151  inclusive,  are  the 
best  that  have  yet  been  adopted. 

By  referring  to  the  drawings,  it  will  be  seen  that,  the 
water  is  made  to  fall  vertically  through  a  grating  laid  at 
aslope  of  about  one  in  three,  and  that  its  action  on  the 
surface  below  is  thus  spread  over  as  large  an  area  as  may 
be  wished.  Owing  to  the  several  filaments  of  water 


OTHER    IRRIGATION    WORKS. 


203 


being  separated  by  the  bars,  much  air   is   carried   down 
with  the   water,  and   the   action   below  is  reduced   to  a 


VERTICAL     FALL     WITH     GRATING. 

BAREfc    DOA8    CANAL. 


ElevaUon,  8cc,up  Stream 


^91  Th*  tftton^of tht.  Ji>usi«ta£lon  is  suppose*,  to  rest  on,  a,    \\tcycr  *f  Ctau,  , 


204 


IRRIGATION    CANALS    AND 


minimum.     The  bars   are  laid  longitudinally  with  the 
stream,  and  at  their  lower  ends,  which  rest  on  the  crest 


of  the  fall,  they  are  close  together,  and  at  the  upper  end 
they  are  farther  apart.  The  teeth  of  a  comb  give  a  good 
idea  of  the  arrangement. 


OTHER    IRRIGATION    WORKS.  205 

The  grating  consists  of  a  number  of  wooden  bars 
resting  on  an  iron  shoe  built  into  the  crest  of  the  fall, 
and  one  or  more  cross-beams,  according  to  the  length 
of  the  bars.  They  are  laid  at'  a  slope  of  one  in  three, 
and  are  of  such  length,  that  the  full  supply  leveFoT^tlie 
water  in  the  canal,  tops  their  upper  ends  by  half  a  foot.* 

The  grating  divides  the  water  into  a  number  of  fila- 
ments or  threads,  and  spreads  the  falling  volume  over  a 
greater  area,  thus  lessening  very  much  its  destructive 
action  on  the  floor  of  the  cistern. 

The  scantling  of  the  bars  as  well  as  of  the  beams 
should,  of  course,  be  proportioned  to  the  weight  they 
have  to  bear,  plus  the  extra  accidental  strains  to  which 
they  are  liable,  from  floating  timber  for  instance,  which 
may  possibly  pass  between  the  piers  and  so  come  in  con- 
tact with  the  grating.  In  consideration  of  strains  and 
shocks  of  this  nature,  the  supporting  beams  are  set  with 
their  line  of  depth  at  right  angles  to  the  bars  instead  of 
vertically. 

The  dimensions  of  the  bars  used  on  the  falls  of  the 
Baree  Doab  Canal,  where  the  depth  of  water  is  6.6  feet, 
are  as  follows: — 

Deodar  Wood. 

Lower  end  of  bars,  0'.50  broad  X  0'.75  deep, 
Upper  end  of  bars  0.25  broad  X  0.75  deep, 
and  they  are   supported    on    two    deodar   beams,   each 
measuring  one  foot  in  breadth  X  1.5  feet  in  depth;  the 
first  beam  being  placed  at   a  distance  of  7.5  feet  (hori- 
zontal measurement)  from  the  crest  of  the  fall,  and  the 
second  7.5  feet  beyond  the  first  beam. 

The  bars  of  the  grating  on  these  falls  were  originally 
placed  touching  each  other,  side  by  side,  at  their  lower 

*Captain  J.  H.  Dyas   in   Professional  Papers  on  Indian  Engineering, 
Volume  3.     First  Series. 


206  IRRIGATION    CANALS    AND 

ends,  as  there  was  not  then  a  full  supply  of  water  in  the 
canal.  There  were  thus  20  bars  in  each  10-feet  bay. 
Since  then  the  number  of  bars  has  been  necessarily  re- 
duced to  19  and  to  18,  the  latter  being  the  present  num- 
ber. The  reduction  of  the  number  of  bars  and  the 
equal  spacing  of  the  remaining  bars  is  done  with  ease, 
as  they  can  be  pushed  sideways  in  the  iron  shoo  and 
along  the  beams,  to  which  latter  they  are  held  with  spiko 
nails.  Once  the  correct  spacing  is  arrived  at,  cleats  and 
blocks  are  preferable  to  spike  nails. 

The  bars  are  undercut  from  the  point  where  they 
leave  the  shoe,  i.  e.,  from  the  crest  of  tho  fall,  so  as  to 
make  each  space,  as  it  were,  "an  orifice  in  a  thin  plate," 
and  it  facilitates  the  escape  of  small  matters  which  may 
be  brought  down  with  the  current.  Large  rubbish, 
which  accumulates  on  the  grating,  is  daily  raked  off  and 
piled  011  one  side  of  the  fall.  This  is  done  by  the  es- 
tablishment kept  up  for  the  neighboring  lock.  There 
is  considerable  advantage  in  thus  clearing  the  canal  of 
rubbish,  which  would  otherwise  stick  in  rajbuha  (dis- 
tributary) heads,  on  piers  of  bridges,  etc.,  or  eventually 
ground  on  the  bed  of  the  canal,  and  become  nuclei  of 
large  lumps  and  silt  banks.  But  supposing  that  there 
were  no  one  at  hand  to  rake  the  debris  off,  and  that  the 
grating  became  choked,  the  water  would  merely  rise 
until  it  could  pour  over  the  top  of  the  grating,  and  the 
rubbish  would  be  swept  over  with  it. 

Where  gratings  are  used  they  act  instead  of  a  weir  in 
checking  the  velocity  of  the  water  above  the  fulls,  and 
the  principle  to  be  adopted  in  spacing  the  bars,  is  to  ar- 
range them  so  that  the  velocity  of  no  one  thread  of  the 
stream  shall  be  either  accelerated  or  retarded  by  the 
proximity  of  the  fall.  This  effected,  it  is  evident  that 
the  surface  of  the  water  must  remain  at  its  normal 
slope,  parallel  to  the  bed  of  the  canal,  until  it  arrives 
at  the  grating. 


OTHP:R  IRRIGATION  WORKS. 


207 


To  take  an  example,  let  us  assume  that:— - 

mean  vel.     v  =  0.81  vmax 

vb  =  0.62  rM,~  (in  every  vertical  line  of  the 

current  flowing  naturally  *-)____ 
where  v  —  mean  velocity  in  foet  per  cecond, 
t>max  ==  surface  velocity  in  feet  per  second, 
vb  ==  bottom  velocity  in  feet  per  second. 

'Then  if  we  make  v  ==  2.5  foot  per  second,  we  shall 
have  the  following  velocities  at  the  given  depths  below 
the  surface  in  a  stream  G  foot  deop: — 


Depths 

below  surface 
in  feet. 

Velocities  in 
feet  per  second 

REMARKS. 

Surface 

0 

3  .  0864 

1 

2  .  8909 

«      .< 

2 

2.6955 

Center 

3 

2.5 

Common  difference  0.1955  nearly. 

n        « 

4 

2  .  3046 

<c      if 

- 

2.1091 

Bottom 

'j 

1  .9136 

What  is  required,  then,  is  to  shape  the  sides  of  a  given 
number  of  bars,  placed  in  a  given  width  of  bay,  so  that 
the  above  velocities  may  be  maintained  till  the  water 
touches  the  grating,  when,  in  consequence  of  the  clear 
fall,  the  velocity  becomes  considerably  accelerated.  This 
accelerated  velocity  multiplied  by  the  reduced  area,  of 
space  between  the  bars,  should  give  the  same  discharge, 
\vith  the  canal  running  full,  as  the  product  of  the  orig- 
inal normal  velocity  and  the  original  undiminished 
space,  the  width  of  which  is,  of  course,  the  distance  be- 
tween the  centers  of  two  contiguous  burs. 


208  IRRIGATION    CANALS    AND 

Thus,  taking  the  lowest  film,  along  the  bed  of  the 
canal,  whose  normal  velocity  is  1.9136  feet  per  second, 
and  supposing  20  to  be  the  number  of  bars  in  each  bay, 
then  the  uiidimmished  space  for  each  portion  of  the 
stream  will  be  half  a  foot,  which  multiplied  by  the  above 
velocity  gives  a  product  of  0.9568.  Again,  taking,  the 
same  lowest  film  as  it  passes  through  the  grating,  with  a 
clear  fall,  and  under  a  head  of  pressure  of  six  feet,  we  find 
its  velocity  to  be  19.654  feet  per  second.  Now,  if  we 
called  the  required  width  of  space  between  the  bars  at 
this  point  xa,  and  assume  the  co-efficient  of  contraction 
to  be  0.6,  we  shall  have: 

0.9568 

a;-=          —   =0.08  foot. 

19.654  X  0.6 

Similarly,  taking  the  film  on  the  level  of  the  tops  of 
the  bars,  or  0.5  foot  below  the  surface  of  the  water,  the 
normal  velocity  of  which  is  2.9887,  the  uridiminished 
space  being,  as  before,  0.5  foot,  we  get  a  product  of 
1.4944;  and  as  the  velocity  of  the  film  falling  through 
the  bars  is  5.673  feet  per  second,  we  get: — 

xs  = L4944 =-  0.44  foot. 

5.673  X  0.6 

And  lastly,  taking  the  center  film,  the  normal  veloc- 
ity of  which  is  2.5  feet  per  second,  we  have  a  product  of 
1.25,  and  as  the  velocity  of  the  same  film  passing  through 
the  grating  is  13.89  feet  per  second,  we  get: — • 

1    9Pi 

ajt  =-  -0.15  foot. 

13.89  X  0.6 

Hence,  it  is  seen  that  the  sides  of  the  bars  should  be 
cut  to  a  curve,  as  shown  in  Figure  149,  convex  towards 
the  open  space;  but  in  practice  this  nicety  is  scarcely  re- 
quisite, and  they  may  be  made  as  shown  in  Figure  150. 

The  above  remarks  have  been  limited  to  a  consider- 
ation of  the  effect  caused  by  the  grating  on  the  channel 


OTHER    IRRIGATION    WORKS. 


209 


above  the  fall.  Its  effect  on  the  channel  below  the  fall  is 
equally  important.  The  velocity,  eddies  and  consequent 
erosion  below  the  fall  are  much  diminished  by  the  grat- 
ings. Fig.  ,49. 


Fig.  150.     Plans  of  Bars  of  Grating. 

Colonel  Dyas,  an  engineer  of  great  experience,  when 
in  charge  of  the  Baree  Doab  Canal  wrote  011  this  sub- 
ject* :- 

"  In  my  opinion  the  Grating  Fall  is  the  best  fall  yet 
known,  and  the  next  best  is  the  Vertical  Fall  without 
grating.  We  have  but  one  Ogee  Fall  on  the  Baree  Doab 
Canal,  and  that  one  has  given  us  more  trouble  in  repair- 
ing it  than  all  the  rest  together.  Indeed  we  have  not 
had  to  touch  the  others  although  we  have  had  a  flood 
down  the  canal  that  submerged  them.  You  can  have  110 
idea  without  seeing  them  how  completely  under  control 
the  water  is  by  their  means.  Divide  and  conquer  is  their 
motto,  and  I  think  it  is  the  true  principle." 


'Professional  Papers  on  Indian  Engineering,  Volume  1. 

14 


First  Series. 


210 


IRRIGATION    CANALS    AND 


Figure  151  is  a  cross-section  of  a  grating  having  hori- 
zontal bars  at  right  angles  to  the  axis  of  the  canal. 


Section  of  Grating  having  Horizontal   Bars. 

Fall  with  Sliding  Gate. 

A  Fall  with  a  sliding  gate,  on  the  Sukkur  Canal,  in 
India,  is  shown  in  Figures  152,  153  and  154.* 

Above  the  fall  the  canal  has  a  bottom  width  of  60  feet, 
depth  9  feet,  side  slopes  1  to  1,  and  a  fall  of  6  inches 
per  mile.  The  mean  velocity  is  2.27  feet  per  second, 
and  the  discharge  1,410  cubic  feet  per  second.  Kutter's 
formula,  with  a  value  of  n  =  .025,  applied  to  this  chan- 
nel, will  give  the  mean  velocity  mentioned  of  2.27  feet 
per  second.  See  the  Flow  of  Water. 

The  fall  is  divided  into  five  bays  of  11  feet  each  in 
wTidth,  by  piers  4  feet  thick.  The  plan  of  one  of  these 
bays  is  shown  in  Figure  152.  The  difference  of  level 
between  the  beds  of  the  canal  above  and  below  the  fall 
is  7.55  feet,  and  of  the  high  water  lines  3.55  feet.  The 
crest  of  the  masonry  portion  of  the  weir  is  nine  inches 
above  the  bed,  Figure  153. 


*  Col.  J.  Le  Mesm-ier,  K.  E.,  in  Professional  Papers  on  Indian  Engineer- 
ing, Vol.  o,  Second  Series 


OTHER    IRRIGATION    WORKri. 


211 


The  thickness  of  the  weir  is  two  feet  six  inches.  It 
is  in  fact  nothing  more  than  a  brickwork  facing  to  the 
rock,  forming  an  even  surface,  on  which  the  timbers  are 
fixed,  against  which  the  gates  can  slide. 


Fall  on  the  Sukkur  Canal,  India. 

There  is  no  cistern  or  basin  to  form  a  water-cushion 
under  the  falling  water,  as  the  bed  at  this  place  is  com- 


212  IRRIGATION    CANALS    AND 

posed  of  sound  rock.  The  bed  and  banks,  for  a  dis- 
tance of  400  feet  below  the  falls,  are  protected  with 
rough  stone  pitching,  laid  dry,  about  one  foot  six  inches 
or  two  feet  thick. 

The  plan  of  using  sliding  gates  to  form  the  weir,  in- 
stead of  building  up  a  mass  of  masonry  above  the  bed, 
is  believed  to  have  been  introduced  for  the  first  time 
on  the  Sukkur  Canal,  to  regulate  the  depth  of  fall  to 
actual  discharge  on  a  canal  with  a  maximum  capacity  of 
over  1,400  cubic  feet  per  second. 

The  gate,  Figures  153  and  154,  is  constructed  of  four- 
inch  teak  plank,  with  a  strip  of  3J-inch  angle-iron 
along  the  top  and  bottom  of  the  down-stream  face. 
The  gate  is  strengthened,  at  front  and  back,  by  four 
strips  of  three-eighths  inch  plate  iron  four  inches  wide, 
and  by  two  cross-pieces  of  Si-inch  angle-iron  at  the 
back.  The  gate,  when  lowered  to  the  full  extent,  rests 
on  a  piece  of  teak  11'  84"  X  5"  X  4-1",  fastened  to  the 
brickwork  by  bolts,  and  its  top  is  then  level  with  the 
crest  of  the  masonry,  or  nine  inches  above  the  bed  of 
the  canal.  It  slides  up  and  down  against  two  vertical 
straining  pieces  of  teak  scantling  5"  X  4i",  fastened  by 
lewis  bolts  to  the  piers,  which  are  recessed  for  the  pur- 
pose; the  thickness  of  the  pier  being  four  feet,  and  of 
the  upper  cutwater  three  feet  three  and  one-half  inches. 

When  the  full  supply  is  going  over  the  gate  its  top  is 
five  feet  above  the  level  of  the  bed,  or  its  bottom  nine 
inches  below  the  crest  of  the  masonry.  The  man  in 
charge  of  the  falls  has  orders  to  keep  the  gauges  at  the 
head  regulator  and  at  the  falls,  reading  the  same,  and 
when  this  is  the  case,  the  surface  slope  of  the  water  is 
six  inches  per  mile.  If  less  than  nine  feet  is  admitted 
at  the  head,  the  gates  at  the  falls  are  lowered  until  the 
two  gauges  read  the  same.  If  at  any  time  it  is  neces- 
sary to  admit  a  greater  depth  than  nine  feet,  the  gates 
are  raised. 


OTHER    IRRIGATION    WORKS.  213 

The  apparatus  for  raising  or  lowering  the  gates  is  very 
simple.  Across  the  cutwaters,  a  teak  beam  nine  inches 
wide  by  twelve  inches  deep,  is  laid  and  bolted  down  to 
the  piers  by  a  two-inch  bolt.  The  screws  which  are 
attached  to  the  gates  are  of  two-inch  rod,  cut  to  one- 
quarter  inch  pitch;  they  pass  through  holes  cut  in  the 
teak  beams,  and  are  wound  up  and  down  by  a  brass  nut, 
turned  by  an  iron  handle.  In  the  cold  weather,  when 
the  canal  is  dry,  the  wood  and  iron  work  of  the  gates  are 
well  dressed  with  common  fish  oil,  procured  from  the 
fishermen  on  the  river. 

The  gates  are  eleven  feet  eight  inches  long,  and  as  the 
opening  in  which  they  slide  is  eleven  feet  eight  and  one- 
half  inches,  they  have  a  play  one-quarter  inch  at  each 
end.  There  is  also  a  small  play  between  the  front  of 
the  gate  and  the  back  of  the  masonry  of  the  weir  wall; 
one-quarter  inch  is  shown  in  Figure  153,  but  it  is  in 
reality  less  than  this.  The  four-inch  strips  of  plate  iron 
are  countersunk  into  the  front  of  the  gate,  but  not  into 
the  back,  and  all  the  rivets  and  bolts  as  well,  so  that  the 
face  of  the  gate  is  perfectly  level  and  flush;  and  there  is 
no  reason  why  more  than  one-sixteenth  of  an  inch  play 
should  be  given.  It  was  considered  advisable,  how- 
ever, as  the  gates  had  to  be  made  in  Karachi,  and  sent 
up  to  Sukkur  ready  to  be  put  up,  to  allow  for  one-quarter 
inch  play  when  building  the  masonry. 

One  advantage  of  this  kind  of  fall,  and  a  very  great 
one,  is  that  it  suits  a  variable  depth  in  the  canal,  as  the 
gate  can  be  raised  or  lowered,  according  to  the  depth  of 
water  admitted.  Another  advantage  appears  to  be  that, 
the  action  of  the  water  upon  the  bed  and  banks  below 
the  fall  is  reduced  to  a  minimum.  The  canal  is  merely 
protected  by  a  comparatively  thin  layer  of  rough  stones, 
procured  from  the  excavation,  and  laid  dry,  and  up  to 
the  present  time  no  repairs  of  any  sort  have  been  re- 


214 


IRRIGATION    CANALS    AND 


quired.  The  bed  and  banks  of  the  canal  above  the  falls 
are  almost  as  clean  as  the  day  they  were  cut,  as,  what- 
ever the  depth  of  water  is,  the  surface  slope  is  kept  fixed 
at  six  inches  a  mile,  and  the  mean  velocity  never  exceeds 
two  and  one-quarter  feet  per  second,  which  is  the  velocity 
with  maximum  supply. 

Fall  ^vith  Plank  Panels  or  Flash  Boards, 

Figure  155  shows  a  timber  fall  on  the  Galloway  Canal, 
California.  Flash  boards  can  be  placed  on  the  framing 
of  this  fall  to  regulate  the  height  of  the  water  in  the 
upper  reach  of  the  canal.  This  is  a  very  light  structure, 
and  it  is  built  on  a  somewhat  similar  plan  to  that  of  the 
Kern  River  Weir,  Figure  20. 


Fig.  155.    Timber  Fall  with  Plank  Panels  or  Flash  Boards. 

A  good  floor  for  the  lower  part  of  drops  is  sometimes 
made  in  the  following  manner:  A  wooden  box  is  con- 
structed as  large  as  the  intended  floor,  and  from  one  to 
three  feet  in  depth.  If  the  material  is  sand  or  loam, 
the  joints  of  the  boards  are  covered  inside  with  thick 
tarred  brown  paper,  after  which  the  box  is  filled  with 


sand  or  loam  and  the  cover  nailed  on. 
the  box  weight  and  stability. 


The  filling  gives 


OTHER    IRRIGATION    WORKS.  215 

At  the  lower  edge  of  the  box  a  row  of  sheet  piling  is 
sometimes  fixed.  The  sheet  piling  should  not  be  driven. 
The  best  way  to  fix  it  is  to  excavate  a  trench  and,  if  not 
too  large,  to  frame  the  sheet  piling  together  and  put  it 
into  the  trench  framed  in  one  piece,  then  fill  in  the  ma- 
terial on  each  side  and  tamp  it  in  layers.  A  piece  of  tim- 
ber can  then  be  fixed  and  spiked  to  the  top  of  the  sheet 
piling  and  the  box. 

On  the  Uncompahgre  Canal  in  Colorado,  carrying 
725  cubic  feet  per  second,  the  water  drops  230  feet  over 
a  precipitous  rocky  cliff  into  the  bed  of  a  dry  wash. 

Article  40.      Rapids. 

Instead  of  falls,  and  to  accomplish  the  necessary 
change  of  level,  Rapids  have  been  employed  with  suc- 
cess 011  the  Baree  Doab  Canal ,*  that  is,  the  fall  is  laid 
out  on  a  long  slope  of  about  15  to  1,  instead  of  by  a  sin- 
gle drop.  The  slope  is  paved  with  bowlders,  laid  with 
or  without  cement,  and  confined  by  walls  of  masonry  in 
cement,  at  intervals  of  40  feet,  both  longitudinally  and 
across  stream.  The  longer  and  flatter  the  slope,  the 
more  gentle  is,  of  course,  ,the  action  of  the  water;  but 
the  greater,  also,  is  the  quantity  of  masonry  employed. 
In  general  the  choice  between  the  two  is  a  mere  question 
of  expense  and  material  available.  On  the  Baree  Doab 
Canal,  rapids  were  adopted  wherever  bowlders  were  pro- 
curable at  moderate  cost.  Figures  156,  157  and  158 
show  a  rapid  on  the  Baree  Doab  Canal. 

Bowlders  or  quarry  stone  are  the  proper  material  for 
the  flooring  of  a  rapid,  and  soft  stone  or  ordinary  brick 
work  should  not  be  used  in  contact  with  currents  of  such 
high  velocities.  Even  the  very  best  brick  work  cannot 

^Professional   Papers    on    Indian  Engineering,  Vol.  1,  First  Series,  and 
Hoorkee  Treatise  on  Civil  Engineering. 


216 


IRRIGATION    CANALS    AND 


OTHER    IRRIGATION    WORKS.  217 

stand  the  wear  and  tear,  for  any  length  of  time,  of  water 
at  a  high  velocity  and  carrying  sand  and  silt.  Hard 
stone  should  be  used  with  all  surfaces  in  contact  with 
velocities  exceeding,  say,  ten  feet  per  second. 

The  bowlders  should  generally  be  grouted  in^witlrjroed 
hydraulic  mortar  and  small  pebbles  or  shingle.  Port- 
land cement  mortar,  if  available  at  moderate  cost,  would 
be  the  best  cementing  material.  Dry  bowlder  work  is  not 
to  be  depended  on  for  velocities  higher  than  15  feet  per 
second,  even  when  they  weigh  as  much 
as  80  pounds  each,  and  are  laid  at  a 
slope  of  1  in  15.  There  should  be  no 
F«g.  '69.  attempt  made  to  bring  the  surface  of 

the  bowlder  work  up  smooth,  by  filling  in  the  spaces 
a,  a,  a,  Figure  159. 

All  that  is  necessary  is  to  lay  the  bowlders,  and  to  pack 
them,  so  that  their  tops  are  pretty  well  in  line  as  b,  c; 
any  further  filling  in  would  stand  a  good  chance  of  being 
washed  out  very  soon,  and  if  it  remained,  its  effect 
would  be  to  increase  the  velocity  of  the  current  on  the 
rapid  by  diminishing  the  resistance  presented  to  the 
water  by  the  rough  bowlder  work. 

The  Baree  Doab  Canal  Rapids  have  tail  walls  of  pe- 
culiar construction,  Figure  156,  for  the  purpose  of 
destroying  back  eddies,  and  of  protecting  the  canal 
banks  below  the  rapid  from  the  direct  action  of  the  cur- 
rent. These  tail  w^alls  are  intended  to  be  so  arranged 
that  the  heaviest  action  of  water  at  the  foot  of  the  rapid 
shall  take  place  in  the  widest  part  A  A,  the  normal  width 
of  the  rapid  being  represented  by  B  B,  and  they  incline  to- 
wards each  other  from  this  point  so  as  to  direct  the  set  of 
the  stream  well  to  the  center  of  the  canal,  thus  protecting 
the  banks  from  the  direct  action  of  the  current  for  a  con- 
siderable distance.  At  the  same  time,  as  may  be  seen  from 
the  longitudinal  section,  Figure  158,  the  tail  walls  are  not 


218  IRRIGATION    CANALS    AND 

kept  at  their  full  height  throughout,  hut  beginning  a 
little  helow  where  the  curve  ends,  at  the  level  of  full 
supply  only,  they  gradually  become  lower  and  lower, 
slope  1  in  20,  till  they  vanish  altogether,  where  they  are 
on  the  same  level  as  the  bed  of  the  canal.  The  trian- 
gular spaces.  A  C  1),  behind  the  walls  in  plan,  are  filled 
in  with  dry  bowlders,  to  the  level  of  the  top  of  the  slop- 
ing tail  wall.  When  the  full  supply  is  running,  these 
tail  walls  are  submerged  and  invisible,  the  rapid  appear- 
ing to  end  just  below  A  A.  These  tail  walls  do  not 
check  the  "lap-lap"  or  ceaseless  wave-like  undulation 
of  the  water  below  the  rapid.  That  is  not  their  office, 
and  indeed  it  would  be  difficult  to  check  that  movement, 
but  they  effectually  do  away  with  back  eddies  by  keep- 
ing the  current  always  in  onward  motion,  exposing  110 
abruptly  terminating  projection  behind  which  an  eddy 
can  form,  and  at  the  same  time  they  protect  the  banks 
by  making  that  motion  moderate  in  the  neighborhood 
of  the  banks. 

In  case  110  such  tail  walls  are  given,  experience  has 
shown  that  the  banks  of  the  canal  when  constructed  of 
ordinary  loam,  should  be  faced  with  bowlders  or  some 
other  protection  for  a  length  of  300  feet  below  the  rapid 
and  on  each  side  of  the  canal. 

The  maximum  velocity  of  current  which  a  bowlder 
rapid  will  stand  without  injury  cannot  be  exactly  deter- 
mined, but  experience  has  proved  that  a  rapid,  such  as 
is  shown  in  Figures  156,  157  and  158,  with  a  flooring 
composed  of  bowlders,  weighing  not  less  than  eighty 
pounds  each,  well  packed  on  end,  somewhat  similar  to 
Figure  159,  and  at  a  slope  of  1  in  15,  will  not  stand  a 
mean  velocity  of  17.4  feet  per  second. 

A  good  example  of  a  wooden  flume  rapid  has  already 
been  illustrated  in  Figures  87  and  88,  page  153. 


OTHER    1  Rill  NATION    WO11KS, 


210 


Article  41.     Inlets. 

When  a  canal  crosses  a  small  drainage  channel  that 
is    filled  only  occasionally,    in   very  heavy   rains,   and 


whose  duration  of  flood  lasts  but  a  short  time,  an  Inlet 
is  provided  in  the  canal  embankment  to  allow  the  flood 


220 


IRRIGATION    CANALS    AND 


water  to  pass  into  the  canal.  On  the  Indian  and  Italian 
canals,  this  inlet  is  usually  also  a  bridge  to  keep  com- 
munication open  along  the  canal  embankment. 

Figures  160  to  164  show  details  of  an  inlet  on  a  level,* 
that  is,  the  level  of  the  bed  of  the  drainage  channel  is 
at,  or  nearly  on,  the  same  level  as  the  bed  of  the  canal. 
There  are  usually  no  gates  to  an  inlet.  Sometimes  per- 
ennial streams,  when  they  carry  no  debris  or  silt,  are 
admitted  into  the  canal  by  an  inlet. 

An  inlet  differs  from  a  level  crossing,  shown  at  page 
167,  in  so  far  as  that  it  has  not  an  outlet  on  the  opposite 
side  of  the  canal. 

Figure  165  shows  an  inlet  with  10  feet  fall,  from  the 


Section  of  Inlet. 

bed  of  the  torrent  to  the  bed  of  the  canal.  To  pass  the 
torrent  over  the  canal  by  a  Superpassage,  Article  36,  or 
by  an  Inverted  Syphon,  Article  37,  would  be  a  very  ex- 
pensive work,  therefore,  an  inlet  was  adopted  as  being 
by  far  the  least  expensive. 

For  small  streams,  cement  pipe  or  vitrified  stoneware 
pipe  are  very  suitable  as  inlets. 


Sone  Canal  Project,  by  Col.  C.  H.  Dickens. 


OTHER    IRRIGATION    WORKS. 


221 


Article  42.     Heads  of  Branch  Canals. 

On  the  first-class  Indian  Canals  it  is  usual  to  place  a 
Regulator,  both  on  the  main  line  and  at  the  head  of  a 

&A0rr-tJrz.g  «%<?  *?eZa£iese  js>c*&i 'fiori 


11 


^m 


Up-stream  Elevation  of  one  span  of  a  bridge  showing  the  slop-boards  partially  applied. 


Section  of  Bridge,  half  roadway,  with  slop-boards  fixed. 


222  IRRIGATION    CANALS    AND 

branch  canal,  as  shown  in  Figures  166  and  169.  These 
regulators  are  usually  combined  with  highway  bridges 
constructed  of  masonry. 

On  the  Sone  Canals,  India,  the  original  plan  pro- 
vided for  branch  regulators,  on  the  French  Needle 
Dam  plan,  Figures  167  and  168,  and  an  escape  above 
each  bifurcation,  of  sufficient  capacity  to  lay  both  the 
lower  channels  dry,  as  shown  in  Figure  166.  Where 
the  object  is  to  diminish  the  supply  of  water  in  both,  it 
will  be  unnecessary  to  do  more  than  open  the  requisite 
number  of  bays  of  the  escape  bridge.  But  when  it  is 
desired  to  keep  up  the  whole  supply  in  one  channel, 
and  reduce  it,  or  altogether  cut  it  off,  in  the  other,  it 
will  be  necessary  to  drop  the  sill  beam  in  by  the  grooves, 
Figures  167  and  168,  using  the  blocks  and  tackle,  in  the 
deep  channels,  for  the  ends  near  the  pier,  and  after- 
wards to  fix  the  beam  in  its  seat  by  the  same  means. 
After  this,  using  the  upper  beam  as  a  bridge,  the 
needles  will  be  applied  by  hand,  to  such  an  extent  as 
may  be  desired. 

The  plan  will  not  be  so  expeditious  as  that  of  the  drop- 
gates  and  windlasses  shown  in  Figure  62.  It  will,  how- 
ever, provide  in  a  simple  way  for  all  that  is  wanted  for 
small  regulators.  By  the  use  of  a  few  long  drop  boards, 
let  down  from  the  parapet  of  the  bridge,  the  openings 
could  be  partially  closed  without  stopping  navigation. 

In  Figure  167  a  tow-path  for  convenience  of  naviga- 
tion is  shown  under  the  bridge,  and  seven  wooden 
needles  in  position  to  partly  close  the  opening,  and  in 
Figure  168  the  needies  are  shown  in  section,  and 
masonry  steps  are  shown  leading  from  the  bridge  road- 
way to  the  canal. 

The  following  details  of  the  working  of  a  needle  dam 
oil  the  Sidhiiai  Canal,  India,  are  given  here: — * 

*  The  Sidhiiai  Canal  System,  by  Loudon  Francis  MacLeaii,  in  Proceed- 
ings of  the  Institution  of  Civil  Engineers,  Volume  CIII,  1891. 


OTHER    IRRIGATION    WORKS.  223 

"  The  needles  are  made  of  deodar  wood,  and  are  seven 
feet  six  inches  long,  by  five  inches  by  three  and  one-half 
inches,  with  a  stout  handle  18  inches  long,  ending  in  a 
knob;  they  weigh  36  pounds  dry  and  40  pounds  wet, 
and  can  be  manipulated  by  one  man.  After  placmg~lhe 
needles  in  position  at  first,  they  are  forced  up  close  to- 
gether by  a  man  standing  on  the  pitching  below  the 
dam,  who  inserts  a  crowbar  with  a  wedge-shaped  end 
into  the  opening,  causing  the  needles  to  slide  along  the 
face  of  the  crest  wall,  any  leakage  between  them  being 
stopped  in  the  following  way:  A  basket  fixed  to  a 
bamboo  about  10  feet  long,  and  filled  with  shavings  or 
chopped  straw,  or  some  similar  substance,  is  slipped 
down  in  front  of  the  leak,  so  that  the  light  material 
may  be  sucked  by  the  current  into  the  opening,  which 
it  effectually  closes.  It  was  not  found  that  the  shock  of 
closing  on  the  crest  wall,  when  first  placing  the  needles 
in  position,  ever  caused  them  to  break  when  the  wood 
was  sound. 

"When  there  is  a  great  difference  of  level  between 
the  water  above  and  below  the  dam,  a  rush  of  water 
through  the  interstices  makes  it  very  difficult  for  a  man 
to  stand  on  the  pitching  below  and  use  a  crowbar.  The 
difficulty  is  overcome  in  the  following  way:  A  piece  of 
tarpaulin  or  oiled  canvas,  eight  feet  long  and  six  broad, 
is  fastened  at  one  end  to  a  wooden  bar  six  feet  four 
inches  long,  Avith  handles  at  each  extremity,  and  at  the 
other  end  to  a  bar  of  round  iron  six  feet  four  inches 
long  and  one  inch  in  diameter.  It  is  then  rolled  upon 
the  iron  bar,  and  placed  horizontally  against  the  needles, 
above  where  the  excessive  leakage  occurs,  and  the 
wooden  bar,  which  remains  on  the  outside  of  the  roll,  is 
either  tied  or  held  in  position  by  the  handles;  the  roll 
is  then  let  go,  and  the  weight  of  the  iron  bar  causes  it 
to  unroll  itself  down  the  face  of  the  needles,  at  once 


224  IRRIGATION    CANALS    AND 

closing  all  the  leaks.  In  order  that  the  screen  may  be 
more  easily  recovered,  a  cord  is  attached  to  a  loose  collar 
at  each  end  of  the  iron  bar,  and  when  the  needles  have 
been  closed  up,  the  screen  is  pulled  up  from  the  bottom 
by  these  cords. 

'  For  the  purpose  of  regulating  the  height  of  water 
above  the  dam,  it  is  sufficient  in  most  cases  to  push 
some  of  the  needles  forward  at  the  top,  the  water  escap- 
ing through  the  open  spaces  left  in  this  way;  but  should 
it  be  necessary  to  provide  for  a  greater  flow,  a  sufficient 
number  of  them  are  removed  altogether.  This  can 
generally  be  done  by  hand,  but  if  they  have  "jammed" 
from  any  cause,  or  if  the  pressure  of  the  water  against 
them  is  too  great,  they  are  lifted  by  means  of  a  bent 
lever. 

"An  eye  bolt  is  attached  to  each  needle  just  below 
the  handle;  this  serves  as  a  fulcrum  for  the  extracting 
lever,  and  also  to  fasten  tackle  to  when  the  pressure  is 
too  great  for  the  needles  to  be  drawn  forward  by  hand. 
It  was  found  dangerous  to  work  them  from  the  beams, 
which  are  only  18  inches  wide,  and  after  one  life  had 
been  lost,  and  the  Author  himself  had  a  narrow  escape, 
a  foot  bridge  was  added  to  the  dam.  *  *  *  * 

"  Arrangements  have  been  made  to  send  warnings  by 
telegraph  of  any  rise  of  one  foot  in  the  Ravi  at  Mad- 
hopur  and  Lahore  during  twenty-four  hours.  As  floods 
take  a  minimum  of  five  days  from  the  former,  and  two 
days  from  the  latter  place  to  reach  Sidhnai,  these  warn- 
ings have  been  of  the  greatest  service." 

Figure  169  is  a  plan  of  the  regulator  at  the  head  of 
the  Kotluh  branch  of  the  Sutlej  Canal,  designed  by 
Major  J.  Crofton.*  With  reference  to  this  work  he 
states: — 


*  Report  on  the  Sutlej  Canal. 


OTHER    IRRIGATION    WORKS. 


225 


"  The  Kotluh  branch  will  take  off  at  an  angle  of  45° 
from  the  main  channel,  the  direction  of  the  central  line 
remaining  unaltered.  A  water-way  of  64  feet  is  given 
to  the  central  line,  and  50  feet  to  the  Kotluh  branch, 


Kotluh  Branch  Head  at  Suranah,  Sutlej  Canal. 

the  mean  waterway  of  the  channels  below  being  57.5 
and  41.5  feet  respectively,  divided  on  the  central  into 
four  bays,  two  of  14  feet  each  and  two  at  the  sides  of  18 
feet  each;  on  the  Kotluh  branch,  two  at  the  sides  of  18 
feet  each,  with  one  central  bay  of  14  feet;  the  piers 
nearest  the  sides  three  feet  thick,  the  central  one  two 
feet  thick,  built  up  to  the  same  level  as  the  tow-path. 
*  *  *  *  *  -x-  •&  * 

"  One  main  object  of  the  arrangement  of  the  works, 
as  shown  on  the  plan,  was  to  bring  the  bridges  as  close 
together  as  possible,  so  as  partially  to  obviate  the  silting 
15 


226  IRRIGATION    CANALS    AND 

up,  which  invariably  takes  place  in  the  upper  channel 
below  the  point  of  divergence. 

"  A  drop  of  half  a  foot  is  given  to  the  flooring  of  the 
Kotluh  branch,  for  greater  facility  in  adjusting  the 
supply,  as  it  is  advantageous  to  regulate  altogether,  if 
possible,  by  one  bridge,  leaving  the  passage  through 
the  central  line  quite  free.  The  regulation  at  both 
heads  will  be  effected  by  vertical  sleepers,  the  needles 
already  described,  their  lower  ends  resting  in  a  groove 
in  the  flooring,  confined  above  between  two  beams  rest- 
ing on  the  piers  or  side,  retaining  walls.  This  is  an 
economical  expedient,  though,  in  some  respects,  not  so 
efficient  as  the  method  with  drop-gate,  shown  in  Figure 
62,  still  it  will  answer  all  the  purposes  of  adjusting  the 
supply.  It  has  the  advantage  of  dividing  the  entering 
stream  into  vertical  films,  by  which  the  impact  on  the 
flooring  will  be  diminished,  and  it  can  be  worked  by  a 
couple  of  men." 

Article  43.     Escapes — Relief  Gates — Waste  Gates. 

In  order  to  provide  for  the  control  of  the  water  in  the 
canal,  Escapes,  also  called  Relief  Gates  and  Waste  Gates, 
should  be  made  at  certain  intervals  along  the  line  of  the 
canal.  An  excess  of  water  in  the  canal,  and  for  which 
an  escape  should  be  available,  may  arise  from  a  breach 
in  the  canal,  either  at  the  headworks  or  at  one  of  the 
numerous  drainage  channels  crossing  the  line.  Extra- 
ordinary floods  also  cause  breaches  in  the  banks,  and  at 
times  the  water  is  not  required  for  irrigation,  and  there 
are  various  other  causes,  that  point  to  the  necessity  of 
making  ample  provision,  for  emptying  the  canal,  above 
the  point  in  danger,  in  a  short  time. 

The  escapes  should  be  made  of  the  shortest  possible 
length,  from  the  canal  to  some  natural  water-course, 
into  which  the  water  can  be  discharged  without  inun- 


OTHER    IRRIGATION    WORKS. 


227 


dating  or  damaging  the  country  through  which  it  flows. 
The  dimensions  of  the  escape  channel  should  be  fixed 
so  as  to  be  large  enough  to  discharge  the  maximum  sup- 
ply in  the  canal. 

The  location  of  an  escape  channel  will  be  determined 
by  the  topography  of  the  country,  but,  as  a  rule,  con- 
nection from  the  canal  can  be  made  at  intervals  with 
some  natural  water-course. 

An  escape  should  be  located  above  a  heavy  embank- 
ment, and  above  any  part  of  the  canal  likely  to  be 
breached  by  floods. 

Where  possible  to  do  so,  they  are,  in  India,  provided  at 
regular  intervals  along  the  line  of  the  canal.  Where 
they  are  taken  off  from  the  canal,  a  double  regulating- 
head  should  be  built,  as  shown  in  Figure  170,  one  across 
the  canal  AB  to  prevent  the  water  flowing  down  that 


iiimin 


Fig.  17O.    Plan  of  Escape  Head  and  Regulator. 

way  when  the  escape  is  in  use,  and  the  other  across  the 
escape  head  BO  to  prevent  the  water  flowing  down  that 
way  when  the  canal  is  in  use. 

Figure  166,  page  221,  shows   the  relative  position  of 


228  IRRIGATION    CANALS    AND 

an  escape  to  a  regulating  "bridge  at  an  off-take  of  a 
branch  canal  011  the  Soiie  Canals,  India. 

To  prevent  artificial  escape  channels  from  being  choked 
by  brush,  they  should  be  occasionally  cleared,  other- 
wise, when  required  for  use,  they  may  be  found  choked 
and  prevent  the  discharge  of  the  water,  thus  causing  an 
inundation  and  the  destruction  of  life  and  property. 

On  the  Ganges  Canal,  India,  escapes  were  provided 
every  forty  miles. 

An  escape  near  the  head  of  a  canal  is  sometimes  used 
as  a  scouring  escape.  An  instance  of  this  is  on  the  Agra 
Canal,  India,  where  a  scouring  escape  is  placed  one  and 
a-half  miles  below  the  canal  head.  Its  waterway  is 
somewhat  in  excess  of  that  of  the  canal  head,  and  the 
object  of  this  is  to  generate  velocity  enough  in  the  first 
one  and  a-half  miles  of  the  canal,  to  stir  up  and  carry 
away  the  silt  deposited  between  the  escape  and  the  canal 
head. 

In  America,  in  order  to  save  expense,  waste  gates  are 
sometimes  made  in  the  sides  of  flumes,  but  this  plan  is 
liable  to  the  objection  that  the  falling  water  is  likely  to 
wash  out  the  foundations  and  destroy  the  structure.  A 
channel  taken  out  in  cutting,  and  connected  with  the 
water-course,  would  be  the  safer  plan;  the  bed  and  banks 
of  the  channel  being  protected  from  scour,  by  paving 
or  some  other  method. 

A  few  years  since,  the  Naviglio  Grande,  the  Muzzaaiid 
Martesana  Canals,  in  Italy,  had  no  sort  of  regulating 
bridge  across  their  heads,  and  the  flood  waters  were  al- 
lowed to  enter  the  canal  with  their  full  force,  finding 
an  exit  in  a  series  of  escape-sluices  and  weirs.  The 
Naviglio  Grande  has  a  number  of  these  sluices  in  the 
first  few  miles  of  its  course,  and  two  weirs  running 
along  its  side  of  300  feet  and  65  feetiii  length,  with  their 
crests  about  three  ieet  lower  than  the  surface  of  the 


OTHER    IRRIGATION    WORKS.  229 

canal  full-water  supply.  These  are  blocked  up  by  strong 
wooden  fences,  closed  up  tightly  with  bundles  of  fas- 
cines. The  Martesana  and  Muzza  Canals  are  also  fur- 
nished with  long  over-fall  weirs  near  their  heads.  That 
the  syteni  has  gone  on  so  long,  among  an  intelligent 
people  deeply  interested  in  their  irrigation,  is  sufficient 
proof  that,  no  very  great  harm  can  arise  from  it.  The 
soil  is  so  stiff  and  firm,  that  it  is  capable  of  resisting  a 
heavy  flood,  and  there  are  few  masonry  works  near  at 
hand  to  be  damaged  by  it.  There  must,  however,  after 
a  flood,  be  heavy  deposits  of  gravel  and  silt  in  the  canal 
channels. 

Article  44.     Depositing  Basins — Silt  Traps — Sand  Boxes. 

Depositing  basins  for  large  canals  are  fully  described 
in  Article  18,  page  52,  entitled  On  Keeping  Irrigation 
Canals  Clear  of  Silt . 

Small  channels  taken  from  rivers  carrying  large  quan- 
tities of  sand  or  silt,  sometimes  have  Silt  Traps  or  Sand 
Boxes  located  at  convenient  points  for  clearing  them  out. 
These  traps  intercept  the  sand  and  silt  carried  by  the 
water,  and  prevent  the  rapid  silting  up  of  the  channel. 
These  silt  traps  are  flushed  out,  when  required,  with 
canal  water.  Care  should  be  taken  to  locate  them  in 
such  a  position  that  the  debris  does  not  choke  the  out- 
lets from  the  traps.  In  order  to  accomplish  this  the 
debris  should  be  run  into  a  channel  that  has  a  living- 
stream,  or  that  is  scoured  out  occasionally  by  flood  water. 
In  consequence  of  neglecting  this  precaution  in  locating 
some  of  the  silt  traps  on  the  Deyrah  Dhoon  Irrigation 
channels  in  India,  their  outlets  got  choked  and,  after 
some  time,  they  .became  useless. 

Mr.  A.  D.  Foote,  M.  Am.  Soc.  C.  E.,  fixed  a  trap  and 
small  gate  for  the  purpose  of  intercepting  and  scouring 
out  debris  in  a  canal  from  the  Boise  River,  Idaho.  This 


230  IRRIGATION    CANALS    AND 

trap  is  a  trench  cut  in  the  bottom  of  the  canal,  and  run- 
ning diagonally  upward  across  it  from  the  gate.  In  this 
trench  all  small  stones  and  sediment  that  may  be 
loosened  from  the  high  banks  by  spring  thaws,  will  be 
caught,  and  on  opening  the  gate  they  will  be  carried 
out  of  the  canal  by  the  rapid  current  through  the  open- 
ing. 

On  the  Marseilles  Canal,  in  the  south  of  France,  with 
a  maximum  capacity  of  424  cubic  feet  per  second,  the 
water  of  which  is  used,  not  only  for  irrigation,  but  also 
for  domestic  use,  settling  basins  were  provided  to  rid 
the  water  of  the  sediment  mechanically  suspended,  in 
order  to  render  the  water  fit  for  domestic  purposes. 
After  several  settling  basins  were  silted  up  and  rendered 
useless,  one  of  them  having  a  capacity  of  about  159,- 
000,000  cubic  feet,  another  large  basin  was  constructed 
with  the  necessary  works  for  flushing  it  out  periodically. 
This  basin  has  an  area  of  fifty-seven  acres,  and  its  ca- 
pacity is  about  81,000,000  cubic  feet.  It  is  formed  by 
constructing  a  masonry  dam  across  a  valley  654  feet  in 
length,  72  feet  in  height,  and  55|  feet  in  width  at  the 
base.  At  the  end  of  each  year,  when  a  deposit  of  about 
five  feet  of  sediment  has  accumulated  at  the  bottom,  it 
will  be  flushed  out  into  the  river  Durance  at  a  low  level. 

Where  the  line  of  a  canal  passes  through  rolling 
ground,  or  skirts  the  bottom  of  low  hills,  a  hollow  in 
the  ground,  within  a  few  miles  of  the  head  of  the  canal, 
is  sometimes  available  and  can  be  utilized  for  the  depo- 
sition of  silt.  Sometimes  a  few  low  and  cheap  dams 
have  to  be  built  in  the  lower  depressions. 

The  silt-laden  water  enters  the  reservoir  at  its  upper 
end.  Its  velocity  is  then  checked,  and  it  deposits  its 
load  of  gravel,  sand  and  slime,  and  after  passing  through 
the  reservoir,  it  again  enters  the  canal  at  its  lower  end, 
comparatively  clear  water. 


OTHER    IRRIGATION    WORKS.  231 

No  doubt  it  is  only  a  matter  of  time  for  such  a  basin 
to  fill  up  and  become  useless  for  its  intended  purpose, 
but,  as  the  following  instance  will  prove,  a  useful  de- 
positing reservoir  can,  with  due  forethought,  be  made 
at  a  small  expense. 

The  Wutchumna  Canal,  in  Tulare  County,  California, 
is  taken  from  the  right  bank  of  the  Kaweah  River,  at  a 
point  where  this  river  sometimes,  when  the  water  is 
most  required,  carries  large  quantities  of  sand  and  silt. 
The  clearance  of  this  sand  and  silt  at  the  close  of  the 
irrigation  season,  from  other  canals  in  the  same  district, 
entails  heavy  annual  expense. 

When  locating  the  Wutchumna  Canal,  Mr.  Stephen 
Barton,  C.  E.,  with  happy  forethought,  carried  it  through 
a  hollow  in  the  ground  with  the  intention  of  converting 
the  hollow  into  a  depositing  basin.  This  he  accom- 
plished successfully,  and  the  writer  is  not  aware  of  any 
depositing  basin  in  existence,  of  the  same  capacity  as 
the  Wutchumna  reservoir,  that  is  so  well  adapted  to  the 
duty  it  has  to  perform. 

This  reservoir  is  situated  about  seven  miles  from  the 
headworks  of  the  canal,  and  the  velocity  of  the  canal, 
through  this  seven  miles,  is  sufficient  to  prevent  the  de- 
position of  sand  and  gravel  until  it  enters  the  reservoir. 

Mr.  W.  H.  Davenport,  C.  E.,  the  present  Superintend- 
ent of  the  Wutchumna  Canal,  has  lately  sent  the  writer 
the  following  additional  information  on  this  subject: 

"  When  the  reservoir  is  at  what  we  call  low  water,  just 
now,  its  area  is  61  acres,  with  an  average  depth  of  3  feet. 
What  we  call  a  full  reservoir  is  154  acres  in  area,  and 
has  a  depth  of  7  feet  above  low  water.  The  discharge  of 
the  Wutchumna  Canal  is  208  cubic  feet  per  second. 

"  There  is  at  present  an  average  depth  of  1.25  feet  of 
deposit  over  the  lower  water  area  of  61  acres.  Where 
the  ditch  enters  the  reservoir  I  find  a  bar  of  sand  and 


232  IRRIGATION    CANALS    AND 

gravel,  which  the  high  grade  of  the  canal  has  carried. 
This  bar  I  estimate  to  have  an  area  of  20  acres,  and  a 
depth  of  3  feet. 

"  The  Wutchumna  Canal  has  been  in  continual  use 
for  10  years,  drawing  its  supply  every  day  without  in- 
terruption. I  think  I  can  safely  say  that,  the  reservoir 
will  be  useful  for  a  silt  deposit  for  the  next  100  years. 
The  conditions  are  such  that  the  reservoir  can  be  made 
6  feet  deeper." 

Article  45.     Tunnels. 

There  are  occasions,  as  explained  further  on,  when  a 
tunnel  can  be  adopted  with  advantage,  but  they  are 
seldom  used  when  the  supply  required  is  over  2,000 
cubic  feet  per  second.  There  are  no  tunnels  on  any  of 
the  large  irrigation  canals  in  India  that  discharge  over 
2,000  cubic  feet  per  second. 

The  High  Level  Canal  in  Colorado,  with  a  discharge 
of  1,184  cubic  feet  per  second,  has  a  tunnel  at  its  head 
600  feet  in  length.  It  is  20  feet  wide  and  12  feet  high, 
with  a  grade  of  1  in  1,000. 

The  Merced  Canal  in  California,  with  a  discharge  of 
3,400  cubic  feet  per  second,  has  a  tunnel  1,600  feet  in 
length,  through  solid  rock,  and  another  tunnel  2,000 
feet  in  length,  through  ground  so  unstable,  that  it  was 
necessary  to  timber  its  whole  length,  a  work  which  re- 
quired over  1,000,000  feet,  board  measure,  of  redwood. 
In  India,  timber  in  a  similar  position,  would,  in  a  few 
years,  be  destroyed  by  the  white  ants. 

The  Henares  Canal  in  Spain,  with  a  discharge  of  177 
cubic  feet  per  second,  has  a  tunnel  9,513  feet  in  length. 
The  tunnel  is  lined  throughout  with  brick.  It  has  a 
semi-circular  arch  on  top,  and  an  inverted  arch  on  the 
bottom.  Its  height  at  the  center  is  11.2  feet,  its  width 
at  springing  of  invert  7.2  and  its  grade  1  in  3,067. 


OTHER    IRRIGATION    WORKS.  233 

111  Madras,  India,  a  tunnel  is  to  be  constructed  to 
convey  the  waters  of  the  Periar  River  into  the  Viga  Val- 
ley for  irrigation.  This  tunnel  is  in  rock  6,650  feet  in 
length.  Its  cross-sectional  area  is  80  square  feet  and  it 
has  a  slope  or  grade  of  1  in  75. 

Under  certain  conditions  a  tunnel,*  when  in  sound 
rock,  is  preferable  to  an  open  channel  for  conveying 
water.  The  conditions  are,  that  no  water  is  required  to 
be  drawn  off  this  part  of  the  line,  and  that  a  heavy 
grade  can  be  given.  By  sound  rock  is  meant  rock  not 
subject  to  percolation,  to  any  appreciable  extent,  that 
will  stand  the  high  velocity  without  injury  by  erosion, 
and  also  that  will  not  require  lining  for  its  sides  or  arch- 
ing for  its  roof.  When,  in  addition,  a  steep  grade  can 
be  obtained,  a  high  velocity  can  be  given  to  the  water, 
and  the  cross-sectional  area  and  consequent  expense 
reduced. 

In  such  a  tunnel,  the  loss  of  water  by  evaporation  and 
percolation,  and  the  expense  of  maintenance  are  at  a 
minimum.  It  has  several  advantages  over  the  open 
channel  in  steep,  side-hill  ground.  Its  sides  and  bed 
are  impervious  to  water,  and  it  is  covered  from  the  sun- 
light. It  shortens  the  line,  there  is  no  compensation  to 
be  paid  for  land,  and  it  does  not  interfere  with  or  cross 
the  drainage  of  the  country  on  the  surface.  Should  it 
be  required,  at  any  future  time  to  increase  the  carrying 
capacity  of  the  canal,  the  discharge  of  the  tunnel  can 
be  increased  without,  however,-  increasing  its  dimen- 
sions. See  Flow  of  Water. 

All  that  will  be  necessary  is  to  fill  all  the  hollows  be- 
tween the  projecting  ends  of  the  rocky  bed  and  sides  with 
good  cement  concrete,  and  after  this  to  give  a  coat  of 
good  plaster  to  the  surfaces  in  contact  with  the  water 
and  make  them  smooth.  Although  the  section  will  be 

*Keport  on  the  proposed  Works  of  the  Tulare  Irrigation  District  by  P. 
J.  Flynn,  C.  E- 


234  IRRIGATION    CANALS    AND 

diminished,  still,  the  velocity  and  consequent  discharge 
will  be  doubled. 

Let  us  assume  the  loss  of  water  in  a  certain  length  of 
open  channel  at  six  per  cent,  of  the  total  flow.  If  by 
adopting  a  tunnel  line,  the  loss  of  water  is  only  one  per 
cent.,  it  is  evident  that  it  would  pay  to  expend  the  value 
of  five  per  cent,  of  the  water  on  the  tunnel  line  above 
that  on  the  open  channel. 

Another  argument  in  favor  of  the  tunnel  is  that  the 
amount  saved  yearly  in  maintenance  capitalized  could 
be  expended  on  the  tunnel  over  that  upon  the  open 
channel,  in  order  to  give  a  fair  comparison  with  the 
latter.  See  Flow  of  Watery  page  52. 

On  the  Marseilles  Canal,  in  France,  there  are,  in  all, 
ten  miles  of  tunnelling,  the  mean  velocity  through 
them  being  nearly  5  feet  per  second.  The  maximum 
discharge  of  this  canal  is  424  cubic  feet  per  second.  . 

On  the  Verdon  Canal,  in  France,  the  number  of  the 
tunnels  is  seventy-nine,  of  a  total  length  of  twelve  and 
a-half  miles,  the  three  most  important  of  which  are 
respectively  about  three  and  one-fourth,  two  and  five- 
eighths  and  one  and  seven-eighths  miles  in  length .  The 
capacity  of  the  main  canal  is  212  cubic  feet  per  second, 
and  it  has  a  sectional  area  of  113  square  feet. 

Tunnels  are  employed  in  several  instances  in  South- 
ern California,  to  develop  water.  Where  there  is  a  water- 
bearing strata  a  tunnel  is  driven,  and  in  several  in- 
stances, sufficient  water  has  been  developed  to  make  the 
money  expended  a  good  paying  investment,  and  by  the 
use  of  this  water  for  irrigation,  land  has  been  raised  in 
value  from  $5  to  $500  per  acre. 

A  good  example  of  this  kind  of  work  is  the  San  Aii- 
tohio  Tunnel,  which  is  being  constructed  at  Ontario, 
Southern  California,  by  F.  E.  Trask,  Chief  Engineer  of 
the  Ontario  Land  Improvement  Co.,  who  has  supplied 
the  following  account  of  the  work: 


OTHER    IRRIGATION    WORKS.  235 

SAN    ANTONIO    TUNNEL. 

At  an  early  date  the  founders  of  Ontario  concluded 
they  would  need  a  larger  supply  of  water  than  the  one- 
half  flow  of  San  Antonio  Creek— which  gave  tkeinJ365 
miner's  inches — and  it  was  decided  to  tunnel  for  the 
underflow  of  this  creek,  at  the  point  where  it  enters  the 
San  Bernardino  Valley.  Land  controlling  the  mouth  of 
the  canon  having  been  secured,  the  work  of  driving  the 
tunnel  began  in  the  early  part  of  1883.  The  objective 
point  of  the  tunnel  was  the  lowest  point  of  bed  rock  in 
the  cation  about  one-half  mile  from  its  mouth.  Here  it 
was  estimated  that  from  eighty  to  one  hundred  feet  of 
gravel,  bowlders,  etc.,  laid  above  bed  rock.  It  was  de- 
cided to  start  the  tunnel  about  3,000  feet  south  of  the 
objective  point  and  run  on  a  grade  of  one-half  inch  per 
rod — with  a  cross-section  of  twenty-eight  square  feet. 
The  alignment  and  grade  have  not  been  strictly  adhered 
to,  although  no  serious  changes  have  been  introduced. 
The  first  two  thousand  seven  hundred  feet  were  driven 
through  the  rock  and  gravel  formation  of  the  canon,  and 
required  lining,  which  wras  as  follows:  the  bents  were  of 
8"x8"  redwood  and  spaced  4  feet  center  to  center — the 
bed  pieces  were  2"x8"  and  the  lagging  2".  The  clear 
dimensions  were,  height  5'  6" — top  width  2' — bottom 
width  3'  6". 

The  above  portion  of  the  tunnel  has  been  lined  in  the 
following  manner:  slabs  of  concrete,  four  inches  thick, 
were  laid  in  hydraulic  cement  over  the  entire  bottom. 
Between  the  bents  and  on  these  concrete  slabs  for  a 
foundation,  the  side  walls  eight  inches  thick  were  car- 
ried up  of  concrete  blocks  (rock  was  used  in  some  por- 
tions of  this  section),  to  a  height  of  4'  2"  on  which  the 
arch  was  turned.  The  arch  was  composed  of  two  seg- 
ments, with  a  tongue  and  groove  joint  at  the  center. 
These  walls  and  arches  were  laid  in  cement,  care  being 


236 


IRRIGATION    CANALS    AND 


taken  to  make  water-tight  joints.  The  only  deviation 
from  this  was  at  points  where  veins  of  water  were  inter- 
cepted, there,  rectangular  openings,  of  sufficient  size  and 
number,  were  left  to  admit  the  water  at  a  height  of  two 
feet  above  the  bottom  of  the  tunnel.  The  accompany- 
ing section  shows  both  the  method  of  timbering  and 
lining. 


Fig.  171.    Cross-Section  of  San  Antonio  Tunnel. 

Bed-rock  was  reached  at  two  thousand  seven  hundred 
feet,  and  up  to  January,  1891,  the  tunnel  had  penetrated 
six  hundred  feet  into  bed  rock,  making  a  total  length  of 
tunnel  of  3,300  feet.  At  this  time  the  heading  was  con- 


OTHER    IRRIGATION    WORKS.  237 

sidered  to  be  beyond  the  lowest  point  in  bed  rock,  and  it 
became  necessary  to  investigate  the  material  above  the 
roof  of  the  tunnel.  For  this  purpose  a  diamond  drill 
plant  was  procured,  and  about  four  months  work  was^ re- 
quired for  denning  the  surface  of  bed  rock.  From  the 
data  thus  obtained,  it  was  found  that  three  low  points  in 
bed  rock  existed — one  about  fifty  feet  from  the  point 
where  bed  rock  was  first  struck;  another  340  feet;  while 
a  third  was  found  to  be  about  200  feet  beyond  the  head- 
ing of  the  tunnel.  Up  to  the  time  bed  rock  was  struck, 
the  minimum  flow  of  the  tunnel  has  been  about  fifty 
miner's  inches.  On  September  15,  1891,  there  were  137 
inches;  and  at  the  present  writing  (October,  1891), 
about  300  inches  have  been  developed.  As  yet  the  work 
of  development  above  bed  rock  has  hardly  begun,  and 
from  one  to  two  years  work  will  be  required  to  complete 
the  proposed  plans,  when  it  is  believed  1,000  inches 
will  have  been  developed. 

In  general  terms  the  proposed  method  of  development 
consists  of  a  complete  network  of  supplementary  tun- 
nels and  drifts  above  bed  rock,  and  on  the  up  stream  side 
of  the  main  tunnel,  which  will  be  connected  by  means 
of  shafts  to  the  main  tunnel  some  twenty  feet  below. 
On  bed  rock  on  the  doivn  stream  side  of  the  main  tun- 
nel will  be  built  a  submerged  dam  of  sufficient  height  to 
intercept  the  summer  underflow. 

Seven  shafts  have  been  used  in  the  entire  length  of 
tunnel,  and  increase  in  depth  from  No.  1,  20  feet,  to  No. 
7,  104  feet.  They  are  unevenly  spaced,  the  greatest 
run  being  600  feet. 

Quicksand  was  encountered  at  several  places  and  gave 
much  trouble.  Cost:  The  cost  of  driving  the  first 
twenty-seven  hundred  feet,  including  temporary  wooden 
lining,  varies  from  $2.50  to  $20  per  lineal  foot.  The 
contract  for  concrete  lining  was  $2.50  per  lineal  foot. 


238  IRRIGATION    CANALS    AND 

The -total  cost  for  completed  tunnel  (2,700  feet),  as 
above,  including  six  shafts,  was  about  $50,000.  The 
cost  of  the  600  feet  in  bed  rock  was  $8  per  lineal  foot. 
The  rock  being  firm  110  lining  of  any  kind  is  required. 
The  supplementary  tunneling,  above  bed  rock,  has  not 
progressed  far  enough  to  justify  a  statement  of  cost,  at 
this  date. 

Article  46.     Retaining  Walls. 

Various  complex  formuke  have,  from  time  to  time, 
been  given  for  finding  the  thickness  of  retaining  walls, 
and  they  differ  considerably  in  the  results  obtained  by 
them.  Engineering  Neivs ,  of  May  24th,  1890,  states  with 
reference  to  this,  for  thickness  of  wall  at  any  height: — 

"  We  have  our  own  pet  formula  which  we  want  to  air 
on  this  occasion.  It  is  short  and  simple:  '  three-seventh 
of  the  height,  and  throw  in  some  odd  inches  for  luck/ 
and  we  believe  this  to  be  more  strictly  arid  more  truly 
'  general ;  than  any  one  of  a  number  of  much  more  com- 
plex formulae  which  lie  before  us.  It  is  certainly  fool- 
hardy to  build  retaining  walls  much  thinner  than  this 
formula  calls  for  under  any  conditions.  While  expe- 
rience indicates  that  any  well-built  wall,  proportioned  in 
accordance  with  it?  is  pretty  sure  to  stand." 

There  is  more  practical  engineering  in  the  above 
extract  than  in  long  articles  discussing  the  pressure  of 
the  earth  on  the  wall,  under  various  conditions.  The 
odd  inches  in  the  above  formula  are  probably  intended 
to  meet  the  requirements  of  the  materials  composing  the 
wall,  having  different  specific  gravity.  Another  rule  is 
one-third  of  the  height  in  feet  plus  one  is  equal  to  the 
thickness.  This  rule  gives  almost  the  same  result  as  that 
given  above  by  Engineering  News . 

The  foundation  course  of  retaining  walls  has  its  width 
increased  beyond  the  thickness  of  the  wall,  by  a  series  of 


OTHER    IRRIGATION    WORKS.  239 

steps  in  front,  two  only  are  shown  in  Figure  172.  •  The 
objects  of  this  are  at  once  to  distribute  the  pressure  over 
a  greater  area  than  that  of  any  bed  joint  in  the  body  of 
the  wall,  and  to  diffuse  that  pressure  more  equally  by 
bringing  the  center  of  resistance  nearer  to  the  middle  of 
the  base  than  it  is  in  the  body  of  the  wall.* 


Fig.  172.    Cross-Section  of  Retaining  Wall. 

The  body  of  the  wall  may  be  either  entirely  of  brick, 
or  of  ashlar,  backed  with  brick  or  with  rubble,  or  of 
block-in-course  backed  with  rubble,  or  of  coursed  rubble, 
built  with  mortar,  or  built  dry.  As  the  pressure  at  each 
bed-joint  is  concentrated  towards  the  face  of  the  wall, 
those  combinations  of  masonry  in  which  the  larger  and 
more  regular  stones  form  the  face,  and  sustain  the  greater 
part  of  the  pressure,  and  are  backed  with  an  inferior 
kind  of  masonry,  whose  use  is  chiefly  to  give  stability  by 
its  weight,  are  well  suited  for  retaining  walls,  special 
care  being  taken  that  the  back  and  face  are  well  tied 
together  by  long  headers,  and  that  the  beds  of  the  facing 
stones  extend  well  into  the  wall. 

Along  the   base  and  in  front  of  the   retaining    wall 


'Rankine's  Engineering. 


240  IRRIGATION    CANALS    AND 

there  should  run  a  drain.  In  order  to  let  the  water  es- 
cape from  behind  the  wall,  it  should  have  small  upright 
oblong  openings  through  it  called  "  weeping  holes," 
which  are  usually  two  or  three  inches  broad,  and  of  the 
depth  of  a  course  of  masonry,  and  are  distributed  at 
regular  distances,  an  ordinary  proportion  being  one 
weeping  hole  to  every  four  square  yards  of  face  wall. 

The  back  of  the  retaining  wall  should  be  made  rough, 
in  order  to  resist  any  tendency  of  the  earth  to  slide 
upon  it.  This  object  is  promoted  by  building  up  the 
back  in  steps,  as  exemplified  in  Figure  172. 

When  the  material  at  the  back  of  the  wall  is  clean 
sand,  or  gravel,  so  that  water  can  pass  through  it  readily, 
and  escape  by  the  weeping  holes,  it  is  only  necessary 
to  ram  it  in  layers.  But  if  the  material  is  retentive  of 
water  like  clay,  a  vertical  layer  of  stones  or  coarse 
gravel,  at  least  a  foot  thick,  or  a  dry  stone  rubble  wall, 
must  be  placed  at  the  back  of  the  retaining  wall,  be- 
tween the  earth  and  the  masonry,  to  act  as  a  drain. 

A  catchwater  drain  behind  a  retaining  wall  is  often 
useful.  It  may  either  have  an  independent  outfall,  or 
may  discharge  its  water  through  pipes  into  the  drain  in 
front  of  the  base  of  the  wall. 

Article  47.     Combined  Irrigation  and  Navigation  Canals. 

It  has  been  found  impracticable  to  combine  irrigation 
and  navigation,  economically,  in  the  same  canal,  and  to 
make  it  a  good  working  machine  for  the  two  purposes. 

In  a  canal  intended  for  navigation  only,  a  still  water 
channel  is  the  most  suitable,  and  the  lower  its  velocity 
is,  the  less  obstruction  will  it  cause  to  boats  proceeding 
up  stream. 

In  an  irrigation  canal,  on  the  contrary,  the  greater 
the  velocity  of  the  water,  so  long  as  it  does  not  damage 
the  works,  the  more  economical  and  better  machine  it 
is.  The  cross-section  of  the  channel  can  be  diminished 


OTHER    IRRIGATION    WORKS.  241 

in  proportion  to  the  increase  in  velocity  of  the  water, 
and,  consequently,  all  the  works,  such  as  headworks, 
embankments,  cuttings,  bridges,  flumes,  falls  or  drops, 
etc.,  can  be  diminished  in  size  and  expense.  In  addi- 
tion, locks  to  pass  the  falls  would  be  required  for  naviga- 
tion. 

Mean  velocities  exceeding  4  feet  per  second  cause 
waves,  which  injure  the  banks  in  the  greater  number  of 
canals,  especially  in  sandy  loam. 

An  irrigating  canal  requires  at  least,  for  average 
ground,  a  velocity  of  2J  feet  per  second.  It  follows, 
therefore,  that  when  forcing  its  way  against  the  current 
at  the  rate  of  4  feet  per  second  the  boat  is  actually  mak- 
ing headway  only  at  the  rate  of  1J  feet  per  second, 
and  any  attempt  at  quicker  velocities  would  injure  the 
banks,  so  that,  irrespective  of  the  loss  of  power,  the 
banks  could  not  stand  if  there  was  quick  navigation. 
It,  therefore,  appears  evident  that  for  economical  work- 
ing and  the  safety  of  the  banks,  an  almost  still  water 
canal  is  required. 

Indian  experience  has  fixed  about  1|-  feet  per  second 
as  the  maximum  velocity  which  ought  to  be  allowed  in  a 
navigable  canal.  The  small  slope  would  increase  the 
number  of  falls  required  to  overcome  the  greater  surface 
slope  of  the  country,  and  in  addition,  the  greater  cost  of 
all  the  other  works  would  make  the  cost  of  a  navigable 
canal  almost  double  that  of  the  channel  required  for 
irrigation  alone. 

Again,  in  a  navigable  channel,  a  certain  minimum 
depth  and  width,  for  the  passage  of  canal  boats,  must 
be  allowed  everywhere;  and  the  amount  of  water  required 
for  this  minimum  must  be  allowed  over  and  above  the 
quantity  required  for  irrigation.  This  has  been  referred 
to  in  Article  5,  page  11,  entitled  Quantity  of  Water  Re- 
quired for  Irrigation. 
16 


242  IRRIGATION    CANALS    AND 

The  canal  of  Beruegardo,  in  Italy,  is  a  notable  exam- 
ple of  the  great  difficulty  of  combining  navigation  and 
irrigation  in  the  same  channel.  It  is  with  difficulty, 
and  only  by  the  strictest  measures,  that  the  supply  for 
navigation  is  secured  during  the  summer,  on  account  of 
the  urgent  demand  for  the  water  for  irrigation.  When 
boats  are  passing,  the  whole  of  the  irrigation  outlets, 
between  each  pair  of  locks,  are  necessarily  closed,  and, 
with  the  supply  accumulated  in  the  channel  by  this 
means,  the  passage  is  effected,  though  with  great  incon- 
venience, and  with  the  stoppage  of  irrigation  from  this 
reach  of  the  canal  during  the  time  of  the  boat's  transit. 

In  his  Report  on  the  Sutlej  Canal,  Major  Croftoii,  R* 
E.,  gives  some  of  the  items  which  cause  an  increase  of 
cost  for  navigation.  They  are,  the  necessity  of  provid- 
ing for  a  navigable  communication  throughout,  which 
involves,  besides  lockage  at  the  overfalls,  increase  of  ex- 
cavation in  the  formation  of  tow-paths,  and  considerable 
additions  to  every  bridge  to  give  towing  passages  on 
either  side,  as  well  as  extra  height  to  afford  headway  for 
laden  boats.  Navigation  appears  to  be  satisfactorily 
combined  with  irrigation  on  the  Madras  canals,  and 
here  again,  the  small  declivities  and  low  velocities  come 
into  their  aid.  In  a  Report  by  Sir  A.  Cotton,  on  some 
of  the  Godavery  channels,  he  mentions  a  mile  an  hour 
(or  1.47  feet  per  second)  as  the  maximum  velocity  which 
ought  to  be  allowed  in  the  current  of  a  navigable  chan- 
nel. Were  this  to  be  taken  as  the  basis  of  the  calcula- 
tions for  the  Sutlej  Canal  (see  List  of  Canals,  page  30), 
the  cost  of  the  works  in  excavation,  and  falls,  to  over- 
come the  superfluous  slope,  would  be  well  nigh  doubled. 
It  would  probably  be  a  cheaper  and  more  efficient  plan 
to  construct  an  entirely  separate  channel  for  navigation, 
alongside  the  canal,  to  which  the  latter  would  act  as  a 
feeder;  the  cost  of  the  irrigating  channel  might  then 


OTHER    IRRIGATION    WORKS.  243 

be  considerably  lessened  by  the  diminution  of  the  ex- 
cavation for  berms  or  tow-paths,  and  the  reduction  of 
the  width  of,  and  headway  under,  the  bridges,  to  that 
necessary  for  the  mere  passage  of  water  supply^  The 
latest  information  on  the  subject  of  Navigable  Canals, 
in  India,  is  strongly  in  support  of  the  above. 

In  the  Revenue  Report  of  the  Irrigation  Department 
of  the  Punjab,  India,  for  1889-90,  it  is  stated  with  re- 
ference to  the  Sirhind,  or  Sutlej  Canal,  that:  "On  this, 
as  on  the  other  irrigation  canals  of  Upper  India,  the 
cost  of  providing  navigation  is  not  likely  to  prove  re- 
munerative." This  is  conclusive. 

Article  48..    Survey. 

The  same  rules  which  govern  the  survey  of  a  railroad 
line  are  also  to  be  observed  in  the  survey  of  a  canal  line. 
There  are,  however,  a  few  points  which  it  is  well  to  re- 
fer to  here. 

The  level  of  the  floor  of  the  head  gate  of  the  canal 
is  a  good  datum  for  zero  for  levels,  and  the  face  of  the 
up-stream  head  wall  of  the  head  gate  is  suitable  for 
the  zero  of  longitudinal  measurement  for  the  central 
channel  of  the  canal,  and  the  same  plan  can  be  adopted 
on  their  respective  regulating  head  gates  in  fixing  the 
same  points  for  the  branches  and  laterals. 

Correct  levels  are  of  primary  importance  in  canal 
lines,  and  it  is  advisable  to  level  twice  over  the  same 
stations  with  the  same  instrument,  the  second  levels 
being  carried  in  the  reversed  direction  to  the  first.  In 
a  canal  carrying  over  1,000  cubic  feet  of  water  per  sec- 
ond, a  few  inches  more  or  less  in  a  mile  will  make  a 
serious  difference  in  the  velocity. 

It  is  advisable  to  have  frequent  bench  marks,  and  on 
permanent  objects  where  possible,  and  all  canal,  road, 
railroad  and  other  bench  marks  should  be  connected 


244  IRRIGATION    CANALS    AND 

with  the  line  of  levels.  A  bench  mark  should  be  es- 
tablished close  to  each  heavy  cut  and  fill,  crossings  of 
all  rivers,  canals,  bridges,  aqueducts  and  other  works 
on  the  line  of  canal. 

Where  possible  to  do  so,  without  extra  expense,  sharp 
curves  are  to  be  avoided.  In  India,  in  the  plains,  flat 
curves  are  adopted  varying  from  5,000  to  15,000  feet  in 
radius.  In  the  Isabella  II  Canal,  in  Spain,  a  recent 
work,  with  a  discharge  of  only  89  cubic  feet  per  second, 
the  maximum  radius  was  fixed  at  492  feet  and  the  mini- 
mum at  328  feet. 

Cross-sections  should  be  made  of  all  ravines  and 
water-courses  crossing  the  line  of  canal,  and  cross-sec- 
tions, at  right  angles  to  the  axis  of  the  stream,  should 
be  taken  in  all  channels  subject  to  flooding.  The  cross- 
sections  should  show  the  surface  of  the  water  at  the  date 
of  observation,  and  the  ordinary  and  highest  flood 
marks . 

The  waterway  of  all  bridges  and  culverts  and  the 
levels  of  their  floors,  if  any,  and  the  lowest  part  of  the 
superstructure  should  be  noted. 

The  nature  of  the  ground  should  be  noted,  and  en- 
quiries should  be  made  as  to  whether  the  country  is 
flooded,  and  as  to  whether  there  is  any  alkali  land 
passed  over  by  the  canal  line. 

In  India,  in  a  generally  level  country,  the  following 
plan  is  adopted  preliminary  to  the  survey  for  a  main 
canal.  Cross-sections  are  taken  at  intervals,  perpendic- 
ular to  the  supposed  water-shed.  For  the  general 
alignment  of  the  main  channels  between  two  large 
rivers,  the  interval  should  not  exceed  ten  miles.  For 
the  actual  location  and  for  the  minor  channels,  the  in- 
terval probably  should  not  exceed  five  miles,  or  possibly 
less.  The  cross-sections  should  be  connected  by  longi- 
tudinal lines  at  their  extremities,  to  test  the  accuracy  of 


OTHER    IRRIGATION    WORKS.  245 

the  work.  These  levels  being  platted  on  a  map  on  a 
large  scale,  the  line  of  canal  can.be  laid  down  approx- 
imately on  the  map  as  a  preliminary  to  the  location.  The 
levels  will  also  show  the  general  directions  of  branches 
and  laterals,  and  also  the  natural  drainage  lines  of  the 
country. 

If  the  levels  of  the  water-shed  admit  of  it,  the  nearer 
the  canal  line  approaches  to  it  the  better,  as  the  interfer- 
ence with  surface  drainage  of  the  country  will  then  be  the 
least  possible.  Having  determined  the  lines  of  the 
main  canal  and  its  branches  the  next  thing  to  do  is  to 
locate  the  distributaries. 

In  order  to  deliver  the  water  under  the  most  favor- 
able conditions,  it  is  clear  that  the  irrigating  channels 
must  everywhere  follow  the  water-sheds  of  the  country 
drainage. 

An  almost  perfect  arrangement  of  distributaries  is  ex- 
emplified in  Figure  173,  taken  from  a  paper  by  Mr.  H. 
M.  Wilson,  M.  Am.  Soc.  C.  E.*  This  arrangement 
shows  the  distributaries  following  the  water-shed  lines, 
of  the  country.  It  is  seldom  that  such  a  complete  dis- 
tributary system  can  be  located. 

The  first  step  then,  is  to  ascertain  how  many  water- 
shed lines  exist,  their  extent  and  relative  situations. 
This  knowledge  can  only  be  obtained  from  a  careful 
survey  of  the  country  it  is  designed  to  irrigate,  care 
being  taken  to  delineate  on  the  map  the  course  of  all 
rivers,  streams,  roads,  railroads,  canals,  etc.,  and  the 
position  of  all  hollows,  swamps  and  the  other  salient 
points  of  the  topography  of  the  country.  To  each 
water-shed  should  be  assigned  a  separate  channel  of 
capacity  apportioned  to  the  duty  it  has  to  perform, 
the  two  bounding  streams  or  drainage  channels  being 

*Irrigation  in  India  in  Transactions  of  the  American  Society  of  Civil 
Engineers.     Vol.  XXIII. 


246 


IRRIGATION    CANALS    AND 


OTHER    IRRIGATION    WORKS. 


247 


248  IRRIGATION    CANALS    AND 

considered  in  this  system  as  the  limits  to  which  irri- 
gation from  any  single  line  should  be  carried.  This 
is  very  plainly  shown  in  Figure  173.*  Figure  174 
shows  a  defective  location  of  a  distribution  system  and 
the  proposed  improvements.  The  difference  between 
the  location  of  the  laterals  on  the  two  Figures  173  and 
174  will  be  apparent  on  inspection.  On  the  former  the 
channels  are  kept  on  the  water-shed  lines  all  through, 
but  on  the  latter  the  original  channels  depart  so  much 
from  the  water-shed  that  large  tracts  of  land  cannot  be 
irrigated. 

Having  then  traced  out,  as  above  stated,  on  the  drain- 
age survey  map  the  general  course  of  the  proposed 
channels,  it  is  necessary  to  run  a  series  of  cross-levels 
in  order  to  fix  the  exact  position  of  the  water-shed. 
With  the  aid  of  the  information  thus  obtained,  the  en- 
gineer will  be  enabled  to  locate  the  distributary  to  the 
best  possible  advantage. 

Some  American  engineers  may  think  that  too  much 
time  and  labor  is  given,  by  the  above  method,  but  the 
experience  of  Indian  engineers,  on  thousands  of  miles 
of  badly  located  distributaries,  proves  that  too  much 
thought  and  care  cannot  be  given  to  the  location  of  these 
channels. 

For  the  more  complete  and  efficient  distribution  of 
the  water,  minor  distributaries  should  be  taken  out  from 
the  main  distributaries  where  they  may  be  most  re- 
quired; but  the  engineer  should  in  a  measure  be  guided 
by  the  nature  of  the  ground  and  the  character  of  the 
soil.  As  in  the  case  of  larger  works  he  should  endeavor 
to  secure  a  command  of  level  for  the  purpose  of  afford- 
ing every  facility  for  irrigation;  he  should  avoid  as  far 
as  possible  crossing  minor  drainages  or  stumbling  into 
hollows,  by  which  his  object  may  in  any  measure  be  de- 

*  Professional   Papers    on   Indian  Engineering.     Vol.  IV.     First  Series. 
Captain  W.  Jeffreys,  K.  E. 


OTHER    IRRIGATION    WORKS.  249 

feated;  he  should  banish  from  his  mind  any  idea  he 
may  entertain  of  the  relative  unimportance  of  this  class 
of  works;  for  he  may  be  assured  that  nothing  tends  so 
directly  to  an  economical  distribution  of  the  wrater  as  a 
carefully  constructed  system  of  minor  distributaries". 

In  the  system  advocated  above,  the  capacity  of  an 
irrigating  channel  should  everywhere  be  exactly  appor- 
tioned to  the  duty  it  has  to  perform,  the  section  decreas- 
ing as  the  line  advances  until  it  loses  itself  in  a  small 
water-course.  See  Article  8,  page  20. 

The  level  of  the  bed  of  the  distributary  should  be  fixed 
rather  with  reference  to  the  full  supply  level  of  the  canal, 
than  to  the  level  of  the  canal  bed,  chiefly  because  it  is 
an  object  to  keep  the  bed  of  the  distributary  at  a  suffi- 
ciently high  level  to  admit  of  surface  irrigation  on.  its 
whole  line  as  far  as  possible.  Moreover,  the  nearer 
to  the  surface  that  water  is  taken  off  by  a  distributary 
head,  the  less  will  be  the  silt  which  enters  the  distribu- 
tary, and  the  less  the  annual  labor  of  clearing  the  bed. 
The  bed  of  a  distributary  will,  therefore,  generally  be 
from  1  to  3  feet  higher  than  that  of  the  main  canal. 

When  the  Eastern  Jumna  Canal,  India,  was  laid  out, 
the  main  line  was  constructed  by  the  engineers,  the  dis- 
tribution channels  being  left  to  be  made  entirely  by  the 
cultivators.  That  led  to  such  great  evils,  that  when  the 
Ganges  Canal  was  made,  the  main  distribution  channels 
were  laid'  out  and  constructed  by  the  Government  engi- 
neers; but  the  minor  ones  were  still  left  to  the  cultiva- 
tors to  make;  arid  on  the  Agra  Canal  a  complete  system 
of  distributaries  was  carried  out  as  an  integral  part  of 
the  scheme. 

Mr.  Forrest*  had  charge  for  six  years  of  one  of  the 
divisions  of  the  Ganges  Canal.  It  was  a  tail  division, 


*  Mr.  K.  E.  Forrest,  M.  I.  C.  E.,  in   Transactions  of   the  Institution  of 
Civil  Engineers.     Vol.  LXXIII. 


250 


IRRIGATION    CANALS    AND 


where  the  supply  of  water  was  not  great,  while  the 
demand  was  large.  The  engineers  had  to  make  water 
go  as  far  as  possible.  When  he  first  went  there  the 
waste  of  water  was  enormous.  The  cultivators  had 
taken  their  channels  in  all  sorts  of  wrong  places,  down 
roads  and  hollows,  and  across  waste  lands,  and  waste 
water  was  lying  about  everywhere.  One  great  cause  of 
loss  was  this:  the  country  was  studded  with  barren 
plains,  and  when  a  main  distributary  ran  across  one  of 
them,  the  good  land  on  either  side  was  irrigated  by 
means  of  little  channels  across  the  plain,  as  shown  by 
the  dotted  lines  in  Figure  175,  some  of  them  over  a  mile 


Fig.   175.     Plan  Showing  Arrangement  of  Distributaries. 

long.  There  was  great  loss  in  having  so  many  chan- 
nels; and,  as  the  banks  were  made  of  the  silty  soil  of 
the  plains,  and  badly  made,  they  were  always  failing 
and  flooding  the  plain,  which  no  one  minded,  as  the 
land  was  barren.  For  these  channels  were  substituted 
properly  laid  out  channels,  AC,  A  E,  through  the 
middle  of  the  good  land,  which,  having  banks  made  of 
good  earth,  did  not  break  down,  and  if  they  did  good 
lands  were  flooded,  so  that  the  canal  establishment  and 


OTHER    IRRIGATION    WORKS.  251 

the  cultivators  had  to  take  pains  not  to  let  them  fail. 
The  effect  of  the  change  was  wonderful.  Mr.  Forrest 
had  two  channels,  one  40,  the  other  50  miles  long,  run- 
ning through  land  of  that  character;  and  whereas  he 
had  previously  not  been  able  to  get  the  water  half  way 
down  them,  he  then  got  it  down  to  the  very  tail.  That 
led  him  on  to  making  as  many  of  these  minor  distribu- 
tion channels  as  he  could.  Each  of  these  little  water- 
courses was  dealt  with  exactly  as  if  it  had  been  a  big 
canal.  Careful  surveys  were  made  and  levels  taken  for 
it.  The  line  was  located,  and  the  longitudinal  section 
and  cross-sections  carefully  fixed.  Badly  adjusted  cross- 
sections  caused  a  great  loss  of  water.  People  laughed  at 
so  much  pains  being  taken  with  such  small  channels, 
but  the  labor  was  not  thrown  away.  That  division  be- 
came one  of  the  best  paying  ones  on  the  canal,  and  some 
of  these  channels  gave  a  duty  of  400  acres  per  cubic  foot 
per  second. 

Thus,  then,  the  first  thing  was  to  make  the  distribution 
channels  properly,  and  the  next  thing  was  to  work  them, 
properly.  The  water  should  be  moved  about  and  distributed 
by  a  careful  system  of  rotation.  It  was  better  to  move 
the  water  in  as  large  volumes  as  possible.  By  a  good 
system  of  rotation,  it  might  be  possible  to  remedy  the 
loss  of  duty  from  the  water  not  being  used  at  night; 
the  water  could  be  run  on  at  night  to  the  more  distant 
points.  By  a  system  of  rotation,  the  evils  of  super- 
saturation  could  be  lessened.  The  water  was  made  to 
run  through  a  tract  only  when  it  was  wanted,  and  for  so 
long  as  it  was  wanted.  In  some  of  the  Ganges  canal 
channels,  the  water  ran  only  for  a  single  day  each  fort- 
night. The  water  should  be  completely  drawn  from 
every  tract  in  which  it  was  not  in  active  and  imme- 
diate demand. 


252 


IRRIGATION    CANALS    AND 


Article  49.     Distributaries — Laterals — Rajbuhas. 

These  channels  are  also  called  Distribution  Channels, 
Primary  Channels,  Ditches,  etc.,  and  they  derive  their 
supply  from  the  Main  Canal. 

These  channels  are,  in  every  respect,  a  counterpart  of 
the  main  canal,  and  require  the  same  class  of  works, 
though  on  a  smaller  scale,  as  the  main  canal. 


DETAILS    OF    DISTRIBUTARIES. 

As  defined  for  the  Soane  Ca**li. 

FcUl  on  &  Distributary  with  aqueduct  over  fail 


St/fjfwn  Urcu,n  for  paAstny  onz  J>istr' ouAeuy  under  another 
or  vi/ef  a  JnusHiyt 


Figs.  176,  177,  178. 

Figure  176  illustrates  a  section  of  a  fall  on  a  distributary 
with  a  small  aqueduct  over  its  tail  to  carry  another  small 
distributary,  and  Figure  177  is  a  plan  of  the  same. 

Figure  178  is  a  section  of  a  syphon  drain  for  passing 
one  distributary  under  another,  or  under  a  drainage 
channel. 


OTHER    IRRIGATION    WORKS. 


253 


The  design,  location,  construction  and  maintenance 
of  distributaries  should  be  as  carefully  carried  out  as 
that  of  the  main  canal,  for  on  all  these  details  the 
economical  use  of  the  water  will  chiefly  depend. 

Those  people  acquainted  with  irrigation  centers^  in 
America,  are  aware  that  proper  attention  to  the  minor 
channels  of  an  irrigation  system  is  very  seldom  given 
in  this  country. 

In  India,  on  the  older  canals,  irrigation  was  carried 
on  from  the  main  channel  itself,  that  is  the  small  irriga- 
tion outlets  were  fixed  in  the  canal  banks.  On  account 
of  the  leakage  along  the  outside  of  these  pipes,  frequent 
breaches  of  the  banks  took  place.  During  years  of 


"T 


Fig.  179.    Plan  of  Distribution  System. 

drought  the  villagers  cut  the  banks  and  attributed  the 
breach  to  some  other  cause.  The  loss  of  water  resulting 
from  these  practices  and  several  other  causes ,  were  found 
to  be  so  great,  that  the  distribution  (rajbuha)  system  is 


254  IRRIGATION    CANALS    AND 

now  generally  adopted.  In  this  system  all  pipes  or 
tubes  for  the  direct  irrigation  of  land,  must  be  taken 
from  the  lateral,  and  not  from  the  main  canal. 

Figure  179  is  intended  to  illustrate  the  system  of  locat- 
ing the  distribution  channels  in  use  in  Northern  India.* 
In  this  system,  as  remarked  by  Sir  Proby  Cautley,  the 
greatest  canal  engineer  that  ever  lived,  we  may  consider 
the  canal  as  answering  to  the  reservoir  or  supply  chan- 
nel, in  the  water  supply  of  towns,  the  distributaries  as 
the  mains,  and  the  village  water-courses  as  the  service 
channels.  The  village  water-courses  are  not  shown  in 
any  of  the  diagrams  in  this  article. 

A  and  B  show  the  methods  ordinarily  used  there 
where  the  slope  of  the  country  is  so  flat  as  seldom  to 
admit  of  the  waters  of  the  distributary  being  returned 
to  the  canal.  In  order  to  have  the  same  velocity  as  the 
main  canal  a  distributary  must  have  a  greater  grade, 
and  where  the  slope  of  the  canal  is  parallel  to  the  sur- 
face of  the  country,  it  is  evident  that  after  a  channel 
with  a  greater  grade  than  the  canal  has  left  the  latter,  it 
cannot  again  return  its  water  into  it.  In  order  to  have 
the  same  velocity,  the  grades,  required  for  a  canal  and 
distributary,  are  in  the  inverse  proportion  to  their  hy- 
draulic mean  depths. 

Where  the  slope  of  the  country  is  greater  than  that  of 
the  distributary,  Figure  180,  C  and  1),  show  different 
methods  by  which  the  tail  water  of  the  distributary  is 
returned  to  the  canal.  C,  in  the  diagram,  gives  an  ex- 
ample how  this  may  be  done  in  a  case  where  the  canal  is 
too  far  in  soil  to  afford  water  at  a  proper  level  to  irrigate 
close  to  its  banks.  After  leaving  the  canal  in  cutting 
at  a1,  a2,  etc.,  the  distributary  does  not  gain  sufficiently 
on  the  grade  of  the  country  to  be  able  to  give  surface 

*Sone  Canal  Project  by  Col.  C.  H.  Dickens. 


OTHER    IRRIGATION    WORKS. 


255 


elevation  until  it  arrives  at  61,  62,  etc.,  passing  there,  over 
a  syphon  or  fall  conveying  the  returning  upper  distrib- 
utary, which  from  loss  of  level  in  the  crossing  does  not 
irrigate  again  till  it  comes  to  d1,  c¥,  etc.,  whence  it 
passes  over  the  distributary  next  but  one  below  rty  and 
irrigates  the  land  close  to  the  bank,  before  it  returns  by 
a  drop  into  the  canal.  An  arrangement  of  this  kind 
could  only  be  effected  with  a  very  good  fall  of  country. 


Fig.  ISO.    Plan  of  Distribution  System. 

In  D,  in  diagram,  the  tail  water  from  the  upper  canal 
is  intercepted  and  utilized  by  the  canal  located  on  a 
lower  level. 

The  above  illustrations   are   given  to  show  what  has 


256 


IRRIGATION    CANALS    AND 


been  done  in  Northern  India,  where  irrigation  has  been 
carried  on  from  time  immemorial,  and  where  the  British 
Government  have  developed  it  to  an  extraordinary  ex- 
tent. 

In  locating  laterals  an  engineer  must  be  careful  not  to 
attempt  to  be  too  systematic,  but  to  be  guided  by  his  own 
ingenuity  and  the  nature  of  the  ground  in  each  case. 
In  the  American  plains,  distributaries  are  often  carried 
along  fence  lines,  which  form  sides  of  either  rectangular 
or  square  tracts  of  land. 

Fig.  181. 


Fig.  185. 


Figures  181   to  185  exemplify  distributaries  in  cut  de- 


OTHEK    IRRIGATION    WORKS.  257 

signed  for  the  Sone  Canals,  India. *  Only  half  the  bed 
width  is  shown.  These  illustrations  are  given,  not  only 
as  good  specimens  of  design,  but  also  to  show  the  care 
that  is  taken  in  India,  with  even  the  minutest  details  of 
design. 

Distributaries  may  be  cleared  of  silt  whenever  the 
water  is  least  required.  One,  or  at  most  two  clearances 
a  year  are  enough  for  a  well  designed  distributary.  The 
floorings  of  all  bridges  and  other  masonry  works,  built 
over  them,  will,  of  course,  have  been  carefully  laid  down 
to  the  proper  levels,  and  will  give  so  many  permanent 
bench-marks  for  restoring  the  correct  level  of  the  beds; 
besides  which,  stakes  or  masonry  bench-marks  should 
be  fixed  at  intervals,  not  exceeding  a  furlong. 

Major  Brownlow  states,  that  the  greater  the  amount 
discharged  by  a  distributary,  the  smaller  will  be  the 
proportion  of  cost  of  maintenance  to  revenue  derived. 
This  is  evident,  when  we  consider  that,  other  things 
being  equal,  a  channel  having  a  bed  width  of  12  feet, 
and  side  slopes  of  1  to  1,  discharges  almost  double  the 
volume  discharged  by  two,  each  having  a  bed  width  of  6 
feet,  while  the  cost  of  patrolling  and  repairs  to  banks  of 
the  12  feet  channel  will  be  about  half  of  that  on  the  two 
6  feet  channels.  When,  however,  the  channel  silts  up 
as  illustrated  in  Figure  7,  page  19,  and  the  side  slopes 
average  J  horizontal  to  1  vertical,  the  12  feet  channel 
discharges  more  than  two  6  feet  channels.  The  trans- 
porting power  of  large  volumes  of  water  being  also 
greater  than  small  volumes,  the  deposit  of  silt  in  the 
12  feet  channel  will  be  less  in  proportion  to  the  dis- 
charge than  in  the  two  6  feet  channels,  thus  doing  away 
with  the  necessity  of  frequent  clearances  required  in 
the  latter. 

*The  Sone  Canal  Project  by  Col.  C.  H.  Dickens. 

17 


258 


IRRIGATION    CANALS    AND 


The  following  table  based  011  Baziii's  formula  (37) 
Floio  of  Water,  for  channels  in  earth,  is  proof  of  what 
has  been  stated: — 

TABLE  17.  Giving  velocity  in  feet  per  second,  and  discharge  in  cubic 
feet  per  second,  of  channels  with  different  bed  widths,  but  all  other  things 
being  equal,  based  on  Baziii's  formula  for  earthen  channels. 


Bed 

width 
in  feet. 

Depth 
in 
feet. 

Grade. 

Side 
slopes. 

Velocity 
in  feet 
per  sec. 

Discharge  in  i       Side 
cubic  feet 
per  second.          slopes. 

Velocity 
in  feet 
per  sec. 

Discharge  in 
cubic  feet 
per  second. 

3 

3 

1  ill  2500 

1    to    1 

1.43 

25.65     'i  1  to  1 

1.39 

17.34 

•  .  -.  j, 

' 

6 

3 

1  in  '2500 

i  to  i 

1.65 

44.60     ;:    J   to  1 

1.58 

35  .  59 

9 

3 

1  in  2500 

t   to    1 

1.80 

64.66         i   to   1 

1.76 

55.34 

12 

3 

1  in  2500 

1    to    1 

1.90 

85.28      j  i  to  1 

1.87 

75.83 

15 

3 

1  in  2500 

1    to    1 

1.97 

106.26     :     MO   1 

1.05 

96.74 

18 

3 

1  in  2500 

I    to    1 

2.02 

127.46         |  to  1 

2  .  02 

117.90 

By  adopting  large  distributaries  the  actual  amount  of 
clearances  during  the  year  is  also  diminished,  for  a 
great  portion  of  the  silt  which  would  be  rapidly  de- 
posited at  the  head  of  a  small  line,  is  carried  along  and 
dropped  into  the  water-courses  branching  off  from  a 
large  one. 

In  Northern  India  distributaries  are  of  various  sizes 
discharging  from  4  to  200  cubic  feet  per  second,  but  ex- 
perience seems  to  prove,  that  irrigation  may  be  safely 
and  most  profitably  carried  on  from  channels  18  feet 
wide  at  bottom,  with  side  slopes  of  1  to  1,  the  depth  of 
water  being  from  3J  to  4  feet,  provided  that  the  depth 
be  kept  at  least  2  feet  below  soil  for  the  first  ten  miles  of 
its  course,  and  that  no  outlets  be  allowed  in  subsequent 
embanked  portions  of  the  line. 

On  the  Eastern  Jumna  Canal  during  1858-59  and 
1859—60,  the  revenue  from  all  distributaries  of  12  feet 


OTHER    IRRIGATION    WORKS.  259 

head  water-way  and  upwards,  amounted  to  $64,809,  while 
the  expenditure  on  their  maintenance  was  $8,019  or 
.123  of  the  revenue.  The  revenue  from  all  distri- 
butaries below  12  feet  water-way  at  the  head  was_1133,- 
524,  and  the  cost  of  maintenance  $28,289,  or  .223  of  the 
revenue,  being  very  nearly  double  the  proportion  in  the 
first  case. 

The  head  mentioned  is  the  width  of  water-way  of  the 
regulator  at  the  head  of  the  distributary.  For  example, 
if  a  regulator  at  the  head  of  a  distributary  has  one  clear 
opening  of  12  feet  between  the  abutments,  that  is  called 
a  12-foot  head,  but  if  there  is  a  pier  in  the  center 
making  two  clear  openings  of  six  feet  in  width  each, 
this  regulator  would  also  have  a  12-foot  head. 

The  economy  of  water  011  the  large  channels  is  equally 
marked,  for,  during  the  above-named  two  years,  the 
revenue  was,  from: — 

Seven  distributaries  of  12  feet  head  water-way  and  up- 
wards, $64,809; 

Forty-nine  distributaries  of  6  feet  head  water-way  and 
upwards,  $108,216; 

Twenty-nine  distributaries  of  3  feet  head  water-way 
and  upwards,  $25,308; 

Giving  an  average  revenue  per  annum  of: — 

$4,629  from  a  distributary  of  12  feet  head  water-way. 

$1,104  from  a  distributary  of  6  feet  head  water-way. 

$436  from  a  distributary  of  3  feet  head  water-way. 

Measurements  made  gave  90,  32  and  22  cubic  feet  per 
second  as  the  relative  discharges  from  12  feet,  6  feet  and 
3  feet  heads  oil  this  canal;  from  which  we  have  as  the 
relative  values  of  a  cubic  foot  of  water  per  annum: — 

$51  on  a  12  foot  distributary. 

$35  011  a  6  foot  distributary. 

$20  011  a  3  foot  distributary. 

The  increased  action  of  absorption  and  evaporation 


260  IRRIGATION    CANALS    AND 

over  the  greater  area  covered  by  water  of  the  smaller 
channels,  accounts  for  the  difference  above  shown. 

The  depth  of  water  in  distributaries  should  seldom 
exceed  4  feet;  but  in  carrying  out  a  new  line  of  irriga- 
tion, we  should  aim  at  keeping  the  surface  of  water  at 
about  1  to  1J  feet  above  the  general  surface  of  country, 
so  as  to  secure  irrigation  by  the  natural  flow  of  water. 
Under  these  conditions,  breaches  in  the  banks  need 
never  be  feared,  with  ordinary  care  in  their  construc- 
tion and  maintenance.  This  object,  however,  is  to  be 
kept  in  due  subordination  to  the  primary  desiderata  of  a 
reasonable  longitudinal  slope,  and  an  alignment  following 
the  watershed  of  the  country. 

Where  the  existing  supply  on  a  distributary  becomes 
insufficient  for  the  demand,  it  will  be,  in  the  end,  found 
more  economical  to  increase  the  discharge  by  widening 
the  original  channel  for  a  suitable  distance,  than  to 
do  so  by  carrying  the  required  additional  volume  down 
from  a  second  head,  as  used  to  be  often  done.  Against 
the  latter  course,  all  the  arguments  before  adduced  hold 
good,  while  the  back-water  from  the  head  which  is  run- 
ning the  strongest,  is  sure  to  check  the  velocity  of  the 
water  in  the  other,  and  so  immensely  accelerate  the  de- 
posit of  silt.* 

The  Roorkee  Treatise  states,  that  the  system  of  raising 
water  to  the  level  of  the  country,  where  it  runs  below 
the  surface  of  the  soil,  by  stop  dams  or  planks,  introduced 
into  grooves  constructed  for  that  purpose,  cannot  be  too 
strongly  condemned.  These  convert  what  should  be  a 
freely  flowing  stream,  into  a  series  of  stagnant  and  un- 
wholesome pools,  encourage  the  growth  of  weeds  and  the 
deposit  of  silt,  and  are  in  every  way  objectionable.  Be- 
sides, with  a  reasonable  slope  in  the  surface  of  the  coun- 
try, it  will  generally  be  found  that,  for  every  acre  of 

*Koorkee  Treatise  on  Civil  Engineering. 


OTHER    IRRIGATION    WORKS. 


261 


land  thus  secured,  ten  can  be  obtained  further  on  by  the 
natural  flow  of  water.  Be  this,  however,  possible  or  not, 
it  is  decidedly  better  to  resort  to  any  other  means  of 
raising  the  water  to  the  level  of  the  country  than  the 
above  wasteful  and  unhealthy  expedient. 

CROSS-SECTIONS  OF  DISTRIBUTARIES. 


The  writer  has  seen,  in  California,  land  irrigated  by 
the  use  of  stop  planks  that,  without  their  use,  could  not 
have  been  irrigated.  No  bad  results  whatever  followed 


262  IRRIGATION    CANALS    AND 

from  raising  the  water.  As  a  rule,  there  is  no  necessity 
to  keep  the  stop  planks  in  more  than  twelve  hours,  and 
in  this  short  time  little  if  any  damage  can  result.  It  is 
simply  a  question  of  utilizing  so  many- acres  of  land,  by 
raising  the  water  for  about  twelve  hours  at  certain  inter- 
vals of  time. 

Figures  186  to  189  show  distributaries,  not  drawn  to 
scale,  in  embankment  and  excavation.* 

Article  50.     Submerged  Dams. 

Submerged  dams,  also  called  sub-soil  dams,  are  fre- 
quently constructed,  across  and  under  the  beds  of 
streams,  with  the  object  of  intercepting  the  subterranean 
flow  of  water  in  channels  whose  beds,  after  rain  ceases, 
soon  become  dry  on  the  surface. 

In  the  construction  of  a  submerged  dam  a  trench  is 
excavated  through  the  sand  and  gravel  down  to  the  im- 
pervious material  underlying  them.  After  this  the 
trench  is  filled  with  puddle,  or  a  wall  of  masonry  or 
concrete  is  built  up  to,  or  nearly  as  far  as,  the  surface  of 
the  bed  of  the  channel.  Then,  if  there  is  no  leakage, 
the  water  rises  to  the  surface  and  is  conveyed  away,  by 
either  an  open  channel  or  a  pipe. 

If  the  rocky  sides  of  a  channel  or  its  bed  are  fissured, 
or  if  the  bed-rock  is  porous,  it  is  almost  certain  that  no 
water  can  be  intercepted.  The  foundation  for  a  sub- 
merged dam  should  be,  in  every  respect,  as  sound  and 
impervious  as  that  of  a  reservoir  dam,  but  too  often  this 
has  not  been  the  case  in.  Southern  California,  as  the 
numerous  failures  of  submerged  dams  there  prove  con- 
clusively. 

Colonel  Richard  J.  Hinton  states! : — 


*  Irrigation  by  Rajbtihas  (Distributaries)  by  Lieutenant  W.  S.  Morton. 
t  Irrigation  in  the  United  States.— Senate  Report. 


OTHER    IRRIGATION    WORKS.  263 

"  It  is  first  ascertained  by  sinking  shafts  across  the 
channel  whether  water  is  thus  passing  subterraneously. 
This  will  be  observable  in  some  cases  by  floating  sub- 
stances traversing  the  shaft,  but  if  the  flow  is  very  slow 
it  may  not  be  detected  by  this  means,  and  coloring-  the 
water  with  a  dye  will  show  it  by  a  replacement  of  the 
colored,  by  pure  water  passing  through  the  shaft.  A 
subterraneous  water  flow  is  frequently  brought  to  the 
surface  by  impervious  strata  traversing  its  course. 
Localities  in  which  this  occurs  are  the  best  sites  for 
weirs.  It  is  not  probable  that  such  natural  bars  are  to 
be  found  in  the  plains,  far  removed  from  the  sources  of 
supply,  and  to  produce  them  artificially  in  such  situa- 
tions would  necessitate  very  deep  and  probably  very  ex- 
tended walls.  The  trial  shafts  should  therefore  be  made 
where  the  valley  is  well  defined  in  character. 

11  Of  course  these  submerged  dams  can  only  bring 
water  to  the  surface  of  the  channel,  where  the  latter  is 
of  sand  or  gravel,  through  which  the  water  would  rise, 
forming  an  artesian  supply.  Where  the  surface  of  the 
bed  is  of  sand,  in  which  the  water  could  be  again  lost, 
the  elevated  water  would  of  course  be  diverted  to  an  im- 
pervious channel  provided  for  it.  Where  such  subter- 
ranean water  can  be  intercepted  a  considerable  supply 
might  be  expected  for  some  months  after  the  water 
ceased  to  flow  previous  to  the  interception,  for  doubtless 
in  many  cases  a  considerable  proportion  of  the  rainfall 
is  absorbed  and  given  off  gradually  to  subterranean 
strata." 

Article  51.     Construction — Canal  Dredger. 

The  following  brief  notes  are  given,  chiefly  for  the 
information  of  engineers  in  other  countries,  outside  of 
America,  and  who  have  never  seen  American  methods  of 
construction. 


264  IRRIGATION    CANALS    AND 

"To  begin  with  the  simplest  kind  of  construction,* 
that  of  field  ditching;  the  farmer  does  this,  as  a  rule, 
with  his  plow,  with  which  he  can  easily  run  a  ditch  of  a 
few  inches  capacity  across  his  field.  If  he  intends  to  widen 
it  while  keeping  it  shallow,  he  employs  the  ditch  plow, 
which  consists  of  a  blade  suspended  behind  the  shear  so 
as  to  push  the  earth  which  it  cuts  to  one  side.  In  many 
soils  this  is  found  to  be  an  invaluable  implement.  When 
the  work  is  more  roughly  done,  what  is  known  as  a  V 
scraper  is  brought  into  play.  This  varies  from  a  mere 
log  of  wood  with  a  couple  of  old  spade  heads  nailed  in 
front  forming  a  sharp  prow,  which  is  its  rudest  form,  to 
a  triangle  some  six  feet  wide  at  its  wooden  base,  from 
which  proceeds  two  long  iron  blades  forming  the  acute 
angle.  Its  use  is  always  the  same.  It  is  drawn  by 
horses  and  steadied  by  the  driver's  weight  so  as  to  push 
the  earth  outwards  from  a  simple  plow  furrow,  or  series 
of  furrows,  and  thus  form  a  ditch.  When  this  is  over 
six  feet  wide  a  "side  wiper"  is  generally  substituted, 
which  is  a  long  iron  blade,  lowered  from  a  frame  which 
rests  upon  four  wheels,  so  that  when  drawn  by  a  power- 
ful team  it  slants  the  plowed  soil  to  one  side.  In  light 
soils  and  for  large  ditches,  an  elaborate  machine  is  used, 
which  not  only  plows  the  earth,  but  takes  it  up  and 
shoots  it  out  upon  the  banks  a  distance  of  ten  or  twelve 
feet  on  either  side,  at  the  rate  of  from  600  to  1,000  cubic 
yards  per  day.  But  the  implement  most- in  use  for  oper- 
ations of  any  extent  is  the  iron  "  scraper,"  well  known 
in  Victoria  as  the  "  scoop/'  which  is  found  in  many 
forms,  sometimes  it  runs  sledgewise,  sometimes  upon 
wheels,  and  ingeniously  fitted  so  as  to  be  tilted  without 
effort.  For  a  long  pull,  wheels  are  considered  best,  and 
for  steep  banks  runners  have  the  preference.  The  kind 

^Irrigation  in  Western  America,  Egypt  and  Australia  by  the  Honorable 
Alfred  Deakin,  M.  P.,  Victoria. 


OTHER    IRRIGATION    WORKS.  265 

of  soil  to  be  moved  and  worked  upon,  and  the  length  of 
haul,  are  always  taken  into  account  in  determining  the 
class  of  scoop  used.  There  is  another  implement  known 
as  the  buck  scraper,  which  for  ordinary  farming  use  in 
light  soils,  and  in  practiced  hands,  accomplishcs^re- 
markable  results.  It  consists  of  a  strong  piece  of  two 
inch  timber,  from  six  feet  to  nine  feet  long,  and  one  foot 
three  inches  high,  with  a  six  inch  steel  plate  along  its  face 
projecting  two  inches  below  its  lower  edge,  and  is  strength- 
ened with  cross-pieces  at  the  back,  where  there  is  a  pro- 
jecting arm,  upon  which  the  driver  stands.  Like  the 
ordinary  scraper  it  is  also  found  on  wheels  and  runners, 
and  in  many  patterns,  and  is  drawn  by  a  pair  of  horses. 
Instead  of  taking  up  the  earth  as  the  scraper  does,  it 
pushes  the  soil  before  it,  and,  when  under  good  com- 
mand, does  such  work  as  check-making,  ditch  excavat- 
ing, or  field  levelling,  in  sandy  soils,  with  marvellous 
rapidity." 

A  novel  method  of  excavating  a  canal  has  been 
adopted  in  Northern  California.  It  is  illustrated  in 
Figure  190,  which  is  a  view  of  a  canal  dredger  invented 
and  operated  by  the  San  Francisco  Bridge  Company.  It 
is  now  in  use  digging  the  main  canal  of  the  Central  Ir- 
rigation District,  which  is  fifteen  feet  deep,  six  miles 
long,  sixty  feet  wide  at  the  bottom  and  one  hundred  feet 
wide  at  the  top. 

The  following  description  of  this  machine  is  taken 
from  the  California  Irrigations st  of  August  1,  1891: 

"The  bid  of  the  Bridge  Company  for  this  work  was 
about  thirty  thousand  dollars  lower  than  that  of  any  of 
their  competitors.  It  was  the  only  firm  of  contractors 
who  figured  on  doing  this  work  by  machinery;  the  other 
contractors  estimated  on  doing  it  by  the  old  method  of 
scrapers  and  horses. 

"  The  machine,  a  cut  of  which  is  herewith  presented, 


266 


IRRIGATION    CANALS    AND 


OTHER    IRRIGATION    WORKS.  2b  i 

was  conceived,  invented  and  designed  by  the  Bridge 
Company  for  the  carrying  out  of  its  contract,  and  it  has 
proved  remarkably  well  adapted  to  the  work  and  is  in  every 
way  a  success.  It  would  have  been  absolutely  impossi- 
ble to  have  excavated  this  ditch  in  the  oldiw^w-ith 
scrapers,  owing  to  the  presence  of  water,  which  in  the 
summer  months  stood  about  two  feet  deep  in  the  ditch, 
and  in  the  winter  months  was  often  as  deep  as  five  to 
seven  feet.  The  designers  of  the  machine  anticipated 
this  condition,  and  ingeniously  arranged  the  machine  to 
rest  on  the  original  ground  at  the  foot  of  the  spoil  bank 
at  the  top  of  the  ditch,  and  not  on  the  bottom  of  the 
ditch  as  steam  excavators  usually  do.  A  standard-gauge 
railroad  track  is  laid  011  either  side  of  the  ditch,  as  may 
be  seen  in  the  cut;  011  each  of  these  tracks  are  located 
three  very  heavy  railroad  trucks,  similar  to  flat  earsonly 
shorter;  on  these  trucks  are  rested  the  three  trusses  that 
span  the  ditch  and  carry  the  car,  which  runs  on  double 
track  standard-gauge,  and  on  which  is  located  all  the  ex- 
cavating and  transporting  machinery,  as  shown  in  the 
illustration.  The  cars  on  the  tracks  on  either  bank  are 
moved  forward  eight  or  ten  feet  at  each  shift  by  means 
of  wire  ropes  worked  by  steam  drums,  fastened  to  "  dead 
men/'  or  anchors  fixed  in  the  ground  100  or  200  feet 
ahead  of  the  machine;  then  the  excavating  chain  and 
buckets  are  lowered,  by  means  of  another  steam  gypsy, 
until  the  buckets  come  in  contact  with  the  ground,  and 
the  car  is  started  across  the  transverse  track  by  means 
of  another  steel  cable  worked  by  a  steam  drum;  and  the 
buckets,  as  the  machine  passes  transversely  across  the 
ditch,  take  a  cut  off  the  top  of  the  ditch  of  the  whole 
area  of  the  eight  or  ten  feet  which  the  machine  moved 
forward,  and  when  the  machine  arrives  at  the  other  side 
of  the  ditch,  the  boom  is  again  lowered  and  the  car 
started  back,  and  another  cut  is  excavated  by  the  buckets. 


268  IRRIGATION    CANALS    AND 

"  This  operation  is  repeated  until  this  section  of  the 
ditch  is  taken  out  clear  to  the  bottom,  then  the  ladder  is 
raised  hy  a  steam  drum  so  that  the  buckets  clear  the 
ground,  and  the  side  cars  are  again  run  ahead  another 
eight  or  ten  feet  as  before,  and  the  buckets  are  again 
lowered  until  they  come  in  contact  with  the  ground,  and 
the  car  started  on  the  transverse  track  again.  The 
buckets  dump  or  discharge  into  a  hopper,  the  bottom  of 
which  is  inclined  and  reversible,  and  the  material  after 
falling  into  a  hopper  falls  down  over  this  incline  bottom, 
which  delivers  it  on  the  rubber  belt  conveyor,  which 
carries  it  to  the  spoil  bank.  When  the  machine  passes 
the  center  of  the  ditch,  the  bottom  of  the  hopper  is 
tilted  to  the  other  side  and  the  material  is  thrown  011 
the  other  conveyor,  which  delivers  it  on  the  opposite 
bank." 

Article  52.     Water  Power  on  Irrigation  Canals. 

Water  power  is  utilized  to  a  far  greater  extent  on  the 
canals  of  France,  Spain  and  Italy  than  it  is  on  the  irri- 
gation canals  of  India  or  America. 

The  Hon.  Alfred  Deakiii,  M.  P.,  gives  an  account  of 
the  application  of  the  water  power  of  an  irrigation  canal 
for  the  purpose  of  irrigating  land  on  a  higher  level  than 
the  canal.*  He  states  that: — 

"  On  the  Cigliano  Canal,  above  Saluggia,  is  the  only 
instance  in  Italy  in  which  the  motive  power  of  water  is 
used  on  a  large  scale  in  connection  with  irrigation. 
Three  canals,  the  Rotto  carrying  565  cubic  feet  per  sec- 
ond; the  Cigliano,  carrying  1,766  oubic  feet  per  second; 
and  the  Ivrea,  carrying  600  cubic  feet  per  second,  round 
the  side  of  a  steep  hill,  one  above  the  other  in  the  order 
named.  The  waters  of  the  highest,  the  Ivrea,  feed  the 


*Irrigation  in  Western  America,  Egypt  and  Italy. 


OTHER    IRRIGATION    WORKS.  269 

Cigliano,  while  the  waters  of  the  Cigliano,  by  a  fail  of 
twenty-one  feet  into  the  Rotto,  generate  a  sufficient 
force  to  lift  part  of  the  waters  which  have  been  poured 
from  the  Ivrea  to  the  crest  of  the  hill  sixty-two  feet 
above  it,  and  130  feet  above  the  Cigliano.  From  This 
height  it  is  distributed  over  the  surrounding  plateau, 
which  is  164  feet  above  any  natural  water  supply.  The 
first  cost  of  the  machinery  employed  was  $140,000,  and 
a  further  outlay  of  $20,000  was  incurred  before  it  could 
raise  twenty-five  cubic  feet  per  second,  the  volume  de- 
sired. The  working  expenses  are  small,  but  capitalizing 
the  rent  paid  to  the  government  for.  the  water,  the  total 
cost  of  the  work  amounts  to  $200,000,  or  nearly  $8,100 
per  cubic  foot  per  second.  From  such  illustrations  it  is 
evident  that,  ingenious  and  economical  as  many  of  their 
works  are,  the  Italians  appraise  the  value  of  water  almost 
as  highly  as  the  Southern  Californians,  and  are  prepared 
to  undertake  the  most  expensive  and  difficult  works 
where  it  cannot  be  obtained  without  them." 

To  show  the  extent  to  which  the  water  power  of  irri- 
gation canals  has  been  utilized  in  other  countries  the 
following  examples  are  given: — 

The  Crappone  Canal  in  France,  having  a  capacity  of 
from  350  to  500  cubic  feet  per  second,  moves  thirty-three 
mills  situated  on  its  course. 

On  the  Marseilles  Canal  in  France,  the  owners  of  one 
hundred  and  seven  mills  use  the  fall  of  the  water  in  the 
canal  for  motive  power,  developing  about  2,000  horse- 
power. Probably  over  twenty  per  cent,  of  its  revenue  is 
derived  from  this  source,  and  the  tariff  for  the  use  of  the 
water  for  motive  power  at  the  numerous  falls  along  the 
canal  was,  a  few  years  since,  $40  per  horse-power  per 
annum.  A  horse-power  was  fixed  at  43,296  pounds  of 
water  falling  through  one  foot  per  minute.  The  water, 
after  being  used  for  motive  power,  had  to  be  returned 


270  IRRIGATION    CANALS    AND 

to  the  company's  canal  at  a  lower  level,  and  not  appro- 
priated for  any  other  purpose,  except  by  special  arrange- 
ment. When  the  water  was  not  used  by  subscribers  for 
irrigation,  it  could  be  employed  temporarily  for  motive 
power  at  the  rate  of  $5  per  horse-power  per  month. 

On  the  Verdon  Canal  in  France,  there  existed,  some 
time  since,  at  the  numerous  falls  along  the  canal,  water 
power  to  the  extent  of  2,000  horse-power,  which  was 
fixed  to  be  let  at  $40  per  horse-power  per  annum. 

The  water  power  of  the  Henares  Canal  in  Spain,  has 
been  estimated  at  3,630  horse-power  for  nine  months, 
and  1,450  horse-power  for  the  rest  of  the  year. 

Article  53.     Cost  of   Pumping  and  of  Water.* 

Fearing  the  failure  of  the  immense  masonry  barrage 
(described  at  page  97),  which  crosses  both  branches  of 
the  Nile,  a  short  distance  below  Cario  at  the  head  of  the 
Delta,  upon  which  the  supply  of  water  to  the  perennial 
canals  largely  depends,  the  Government  in  1885  made 
an  agreement  with  the  Irrigation  Society  of  Behera,  by 
which 'it  undertook  to  pay  $210,000  a  year  for  thirty 
years  for  a  supply  up  to  a  certain  level,  with  a  maximum 
of  about  2,604  cubic  feet  per  second  at  Low  Nile,  lifted 
by  two  powerful  sets  of  steam  pumps  into  the  Western 
Canal  or  Rayah  Behera.  The  weir  has  since  been  ren- 
dered secure,  but  the  agreement  indicates  the  value  of 
water  and  the  difficulty  of  obtaining  it,  even  in  parts  of 
Egypt.  Owing  to  the  defective  alignment  of  some,  and 
the  silting  up  of  other  canals,  the  task  of  raising  the 
water  a  second  time  from  the  channels  to  the  fields  has 
been  cast  upon  a  large,  if  not  the  largest,  body  of  the 
cultivators.  In  1864,  according  to  Figari  Bey,  the 


*  Irrigation  in  Western  America,   Egypt  and  Italy,   by  the  Honorable 
Alfred  Deakin,  M.  P.  of  Victoria,  Australia. 


OTHER    IRRIGATION    \VORKS.  271 

number  of  sakiyehs  or  wooden  water-wheels  used  in 
Central  and  Lower  Egypt  was  about  50,000,  turned  by 
200,000  oxen  and  managed  by  100,000  persons,  who 
watered  4,500,000  acres.  The  water-wheels  are  of  sev- 
eral varieties,  costing  011  the  average,  with  the~~well, 
$150  each,  that  most  in  use  sufficing  for  five  acres,  or 
ten  acres  if  worked  day  and  night,  and  employing  three 
bullocks  and  two  men  on  each  shift. 

In  the  estimate  of  Figari  Bey,  some  steam  pumps  were 
probably  overlooked;  for  twenty  years  later  there  were 
2,000  of  these  at  work  in  lower  Egypt,  with  coal  ranging 
from  $10  to  $20  per  ton.  It  can  now  be  bought  in 
Alexandria  for  $5  per  ton.  The  cost  of  steam  pumping 
is  about  $1.50,  but  the  price  at  which  it  can  be  hired 
varies  from  $2  up  to  $5  per  acre.  If  paid  in  kind  the 
charge  is  often  one-fifth  of  a  cotton,  and  one-quarter  of 
a  rice  crop,  as  the  latter  requires  more  water.  A  ten- 
horse  power  engine  gives  an  ample  supply  for  100  acres 
during  the  season.  There  are  also  "shadoofs"  (Egyp- 
tian water-lifters  or  swing  buckets)  innumerable  in  con- 
stant employ,  which  require  six  men  to  keep  watered 
one  acre  of  cotton  or  sugar-cane  or  two  of  barley.  "  If 
the  thin  deposit  of  mud  left  by  the  departing  river  is 
kept  moist  its  value  remains  at  par.  If  the  hot  sun  is 
allowed  to  play  upon  it  unopposed,  it  soon  becomes 
baked,  and  curls  up  into  tiny  cylinders;  then,  breaking 
into  fragments,  it  falls  dead  and  worse  than  useless. 
Therefore,  the  process  of  irrigation  must  begin  at  once. 
The  rude  sakiyeh  and  the  ruder  shadoof  are  kept  going 
night  and  day,  and  give  employment  to  tens  of  thous- 
ands of  people,  and  cattle  as  well.* 

The  cost  of  this  incessant  labor  cannot  be  estimated. 
(t  There  is  the  greatest  dearth  of  accurate  statistics, "f 
and  especially  of  statistics  which  would  show  what  is 

*  "The  Modern  Nile,"  G.  L.  Wilson,  Scribner,  September,  1887. 
t  Public  Works  Report  1884. 


272  IRRIGATION    CANALS    AND 

paid  for  the  water  and  what  is  produced  by  it.  Though 
twenty-eight  taxes  were  repealed  in  1880,  and  others 
have  been  removed  since,  the  taxation  now  ranges  from 
$5  to  $10  per  acre,  and  sometimes,  in  Upper  Egypt, 
amounts  to  more  than  twenty  per  cent,  of  the  gross  an- 
nual value  of  the  farm.  Over  1,000,000  acres  of  the 
irrigated  land  belongs  to  the  State,  the  Fellahin  upon 
them  being  its  tenants,  with  a  life  interest  and  a  title 
to  their  improvements;  half  as  much  is  included  in 
great  estates,  while  the  balance  is  in  the  hands  of  small 
proprietors.  Omdehs,  or  notables,  and  sheiks,  who 
control  the  village  communes,  often  own  estates  of  1,000 
or  even  2,000  acres,  but  the  holdings  of  the  great 
majority  of  their  constituents,  who  are  working  pro- 
prietors, are  very  small.  The  Crown  tenants,  of  course, 
pay  rent,  but  all  pay  a  "  land  tax  "  of  from  $1  to  $8  per 
acre,  which  might  be  more  properly  named  a  water 
rent,  as  no  tax  is  levied  if  no  water  is  given.  It  is  clear 
that,  if  in  addition  to  the  taxes,  there  is  the  cost  of 
pumping,  and  four  months'  labor  taken  by  the  corvee,  the 
produce  must  be  great  to  yield  any  profit  to  the  culti- 
vator. The  cost  of  the  crop,  including  taxes  and  pump- 
ing, averages  $25  per  acre.  The  value  of  land  averages 
$60  per  acre  in  Upper  Egypt,  and  from  $100  to  $125  in 
Lower  Egypt,  but  it  not  unfrequently  reaches  $100  in 
the  one  and  $300  to  $350  in  the  other.  Its  variation 
may  be  judged  from  the  fact  that  rents  run  from  50 
cents  to  $50  per  acre.  Labor,  of  course,  is  plentiful  and 
cheap — wages  averaging  from  32  cents  to  14  cents  per 
day — but,  on  the  other  hand,  the  agricultural  imple- 
ments employed  are  of  the  most  primitive  character; 
the  plough  used  is  made  on  the  same  model  as  is 
delineated  upon  monuments  thousands  of  years  old,  and 
the  Nile  mud,  though  freely  and  easily  worked  after  the 
subsidence  of  the  water,  requires  constant  attention 
throughout  the  year. 


OTHER    IRRIGATION    WORKS.  273 

Article  54.      Maintenance   and  Operation   of  Irrigation 

Canals. 

The  defective  design  and  construction  of  the  greater 
number  of  irrigation  canals  in  this  country,  haye_been 
already  referred  to.  But  this  is  not  all,  for  the  mainte- 
nance is  equally  bad.  Repairs  are  seldom  carried  out 
in  a  thorough  and  workmanlike  manner.  Weeds, 
bushes,  and  even  trees,  are  allowed  to  grow  in,  and 
obstruct  the'  channels.  Brush  is  allowed  to  collect  and 
form  obstructions  to  the  flow.  In  some  places  the  chan- 
nel gets  silted  up  and  bars  are  formed,  and  in  other 
places  extensive  erosion  takes  place.  A  great  loss  of 
water  takes  place  from  defective  banks  and  leaky  flumes. 
The  channel,  in  some  cases,  floods  large  areas  of  land, 
causing  serious  loss  of  water.  The  side  slopes  arid 
grades  of  the  canals  are  allowed  to  take  care  of  them- 
selves, and  when  breaches  occur  in  the  banks,  the  re- 
pairs are  done  in  a  hurried  and  slipshod  way.  Any- 
thing is  good  enough  to  fill  in  the  breach  in  the  banks. 

When  drops  are  washed  out  they  are  seldom  replaced,, 
then  retrogression  of  levels  takes  place,  and  the  surface 
of  the  water  gets  lower  and  lower,  until  the  velocity  of 
the  current  has  adjusted  itself  to  the  material  cut  through, 
and  the  channel  has  established  its  regimen.  In  conse- 
quence of  the  scouring  out  of  the  bed  of  the  channel, 
the  sub-soil  water  passed  through  is  lowered,  causing  in 
some  cases,  great  injury  to  the  land.  If  the  channel 
has  fall  enough,  and  it  usually  has  too  much  fall,  it  is 
assumed  that  the  canal  can  take  care  of  itself. 

For  the  proper  conservancy  of  the  canal  it  should  be 
closed  once  a  year,  at  least,  for  repairs.  Stakes  should 
be  set  in  the  bed,  to  grade,  and  the  silt  removed  to  this 
level.  The  banks  should  be  trimmed  up,  and  all  weeds, 
brush  and  other  obstructions  removed.  Weirs,  head- 
works,  bridges,  flumes,  sluices,  drops.,  etc.,  should  be 
18 


274  IRRIGATION    CANALS    AND 

put  in  thorough  repair.  This  will  be  found  the  cheap- 
est method  in  the  end,  and,  by  this  means,  the  water 
can  be  kept  in  better  control,  and  the  canal  worked  to 
much  better  advantage,  than  when  it  is  allowed  to  fall 
into  bad  repair. 

Telephone  service  should  be  established  along  the 
line  of  the  canal,  and  a  roadway  on  one  bank  will  be 
found  useful.  The  official  in  charge,  whether  engineer 
or  superintendent,  should  be  informed  every  day  by  the 
patrolman  of  the  quantity  of  water  flowing  into  the 
canal  at  the  head  works,  and  also  the  quantity  discharged 
at  each  irrigation  outlet.  He  should  also  be  immediately 
informed  of  any  breach  in  the  canal  banks,  or  anything 
else  likely  to  cause  damage,  or  a  partial  obstruction  to, 
or  complete  stoppage  of  irrigation  in  its  main  or  dis- 
tributary channels. 

The  Indian,  Egyptian  and  Italian  Irrigation  Canals 
are  closed,  at  least  once  a  year,  for  clearance  of  silt  and 
repairs  in  general.  Some  of  the  Indian  canals .  are 
closed  for  about  six  weeks  annually.  The  Naniglio 
Grande,  or  Grand  Canal  of  the  Ticino  in  Italy,  is  closed 
twice  a  year.  An  instance  of  frequent  closing  is  given 
on  one  of  the  small  Indian  canals.  In  the  Irrigation 
Revenue  Report  of  the  Bombay  Presidency,  for  1889-90, 
it  is  stated  that: — 

"The  Palkhed  Canal  was  closed  six  times  during  the 
year  for  clearance  of  silt,  aquatic  plants,"  etc. 

Mr.  Walter  H.  Graves,  C.  E.,  has  made  some  remarks 
on  this  subject  which  will  be  found  useful  here.  He 
states: — * 

"  Maintenance  and  superintendence  are  matters  of 
considerable  importance  in  the  management  and  success 
of  any  enterprise,  but  especially  important  in  irrigation 

^Irrigation  and  Agricultural  Engineering  in  Transactions  of  the  Denver 
Society  of  Civil  Engineers  for  June,  1886. 


OTHER    IRRIGATION    WORKS.  275 

plants,  for  obvious  reasons.  The  roadbed  and  rolling 
stock  of  a  railroad  might  be  allowed  to  deteriorate  for 
some  length  of  time  without  seriously  impairing  the 
operation  of  the  road,  but  deterioration  in  the  head- 
works  and  channel  of  a  canal  means  speedy  paralysis . 

"  The  sources  of  impairment  of  canal  property  are: — 

"  First.  As  to  the  channel.  The  water  itself  carried 
by  the  canal,  by  the  erosion  of  the  banks  and  channel, 
and  the  filling  of  the  channel  by  the  deposition  of  sedi- 
ment. 

"  This  is  a  process  of  self  destruction. 

"Second.  From  the  storm  or  flood  water.  The  de- 
nuding of  the  banks  by  the  erosive  action  of  the  elements 
is  a  constant  source  of  destruction,  although  it  is  a  com- 
paratively small  item.  From  the  very  nature  of  the 
alignment  or  location  of  the  canal  it  must  intercept  to 
a  greater  or  less  extent  the  slope,  and  consequently  the 
drainage  of  the  country  it  traverses.  If  ample  provis- 
ion is  made  to  transfer  the  flood  or  drainage  water  across 
the  canal  by  means  of  flumes,  culverts,  etc.,  destruction 
from  this  source  is  largely  prevented.  But,  as  a  rule, 
provisions  of  this  character  are  wholly  neglected.  In 
many  cases,  where  the  slope  of  the  country  is  sufficient, 
there  is  no  upper  bank  to  the  canal,  and  the  drainage 
channels  are  allowed  to  empty  directly  into  it.  Thus 
the  surface  water  of  the  entire  country  above  the  canal 
is  gathered  into  it,  and  the  result  is,  in  such  cases,  a 
constant  rebuilding  and  repairing  of  banks. 

"  Third.  The  destruction  of  the  channel,  and  espec- 
ially the  banks,  by  the  range  cattle,  which  can  only  be 
prevented  by  fencing  the  canal. 

"  The  deterioration  in  the  structures  of  a  canal  are: 

"First.  The  head  works.  If  these  are  of  such  a 
character  as  to  be  proof  against  the  strain  and  force  of 
the  annual  floods,  and  to  meet  the  requirements  of  the 


276  IRRIGATION    CANALS    AND 

wide  range  of  the  fluctuations  of  the  average  mountain 
stream  they  must  be  very  complete  and  expensive  struc- 
tures, and  quite  out  of  the  reach  of  the  average  company. 
The  class  of  work  usually  adopted,  however,  is  such  as 
to  make  the  liability  of  destruction  and  the  cost  of  re- 
pair important  items  in  the  subject  of  maintenance. 

"Second.  Applying  to  all  structures  is  decay.  Tim- 
ber intervening  between  water  and  earth,  and  alter- 
nately soaked  and  dried,  is  particularly  subject  to  decay, 
and  the  life  of  wooden  structures  can  scarcely  be  pro- 
longed beyond  six  or  eight  years. 

11  Third.  Incendiarism.  Strange  as  it  may  appear, 
this  has  proven,  in  the  experience  of  the  larger  canal 
companies,  an  item  of  considerable  importance. 

11  The  subject  of  maintenance  directly  involves  that 
of  superintendence.  An  ignorant  or  an  indifferent 
superintendent  can  increase  the  cost  of  maintenance 
many  fold. 

"  Where  incipient  disaster  may  easily  and  cheaply  be 
curtailed  by  intelligent  vigilance  on  the  part  of  the 
superintendent,  serious  calamities  often  occur  by  reason 
of  his  carelessness  and  ignorance.  As  a  case  in  point, 
a  leak  of  apparently  insignificant  proportions  was 
allowed  to  exist  for  some  time  through  the  embankment 
adjoining  the  head-gate  of  one  of  the  largest  canals  in 
Colorado,  when  it  suddenly  assumed  a  magnitude  beyond 
control,  until  it  had  almost  completed  the  destruction  of 
the  head-gate,  a  structure  costing  several  thousand  dol- 
lars. In  this  case  as  in  many  others  similar,  bad  super- 
intendence was  credited  to  bad  engineering. 

11  It  seems  to  be  quite  the  custom  in  Colorado  to  select 
canal  superintendents  from  among  any  class  of  men  ex- 
cept engineers,  the  very  men  best  fitted  by  experience 
and  training  for  such  work." 

In  India  the  irrigation  canals  are  always   under   the 


OTHER    IRRIGATION    WORKS.  277 

control  of  the  engineers  of  the  Public  Works  Depart- 
ment. They  control  the  movement  and  distribution  of 
the  water,  and  carry  out  all  repairs  and  additions  to  the 
works.  In  order  to  know  at  all  times  the  quantity  of 
water  available  they  have  numerous  gauges,  the  read- 
ings of  which  reach  the  controlling  office  every  day,  and 
it  is  a  rule  that  he  should  write  them  into  his  gauge 
book  with  his  own  hand. 

There  is  one  arrangement,  however,  which,  though  it 
works  well  in  India,  is  not  suited  for  this  country,  that 
is,  executive  and  assistant  engineers  engaged  on  the 
canals  there,  usually  have  powers  of  an  assistant  magis- 
trate for  the  protection  of  canal  property. 

The  following  extract  is  pertinent  to  this  subject:* 
"  It  is  too  commonly  supposed  that  when  the  canal  is 
once  constructed,  there  remains  little  for  the  executive 
engineer  to  do  worthy  of  a  man  of  any  experience,  abil- 
ity or  education.  This  is  a  very  great  mistake.  There 
may  be  no  great  works  left  to  construct,  but  there  are 
sure  to  be  many  small  ones  requiring  much  experience 
and  precision  to  execute  properly.  There  are  many 
points  of  the  purest  science  still  undetermined,  such  as 
the  true  formulae  for  the  discharge  of  large  bodies  of 
water  in  open  .channels,  or  over  weirs,  the  amount  of 
loss  by  percolation  and  evaporation;  the  effect  on  the 
velocity  of  a  stream  of  a  large  percentage  of  silt  carried 
along.  The  executive  engineer  may  have  besides,  to 
train  and  do  battle  with  rivers  of  great  size,  or  the  not 
less  troublesome  hill  torrents.  He  may  have  in  his 
charge  a  series  of  weirs  which  have  to  be  constantly 
watched  and  protected,  while  repairs,  often  of  the  most 
important  character  have  to  be  executed  within  the  space 
of  only  a  few  days  when  the  canal  can  be  closed. 


*ltoorkee  Treatise  011  Civil  Engineering. 


278  IRRIGATION    CANALS    AND 

Alongside  of  his  weirs  he  may  have  locks  to  superin- 
tend. His  rajbuhas  (laterals  or  distributaries)  ought 
to  be  a  source  of  constant  interest,  requiring  extension 
and  improvements,  while  he  will  find,  as  he  goes  on 
irrigating,  that  drainage  has  to  be  attended  to  and  arti- 
ficial cuts  to  be  laid  out,  to  correct  the  over-saturation 
which  only  the  best  administration  can  prevent  from 
taking  place,  and  to  ward  off  the  malaria  which  over- 
saturation  produces. 

11  Besides  all  this,  no  man  should  consider  it  beneath 
his  attention  to  exercise  almost  independent  control  over 
a  large  body  of  water,  bringing  in  a  revenue  every  year 
of  $200,000  to  $300,000,  and  also  of  being  a  source  of 
wealth  to  the  country  of  at  least  four  times  that  amount. 

"  He  should  possess  a  general  knowledge  of  the  agri- 
culture of  the  district,  and  know  at  what  season  the  va- 
rious crops  most  want  watering,  and  what  soils  most 
require  it.  If  he  is  fond  of  forestry,  he  will  find  room 
for  gratifying  his  taste  in  cherishing  and  extending  the 
plantations  along  the  banks  of  his  canal,  and  may  render 
lasting  benefits  to  the  country  by  the  introduction  of 
new  trees. 

"  Among  lesser  matters,  he  may  turn  his  attention  to 
utilizing  the  water  power  of  his  canal,  a  subject  which 
must  claim  attention  as  the  country  progresses.  If  the 
above  subjects  do  not  possess  sufficient  interest  for  the 
engineer,  he  had  better  choose  some  other  line  than  the 
irrigation  department. 

"  Nor  ought  he  to  look  for  employment  on  a  running 
canal  if  he  is  not  prepared  for  a  life  of  constant  moving 
about,  at  all  seasons  of  the  year.  He  must  expect  but 
little  of  the  pleasures  of  society,  or  domestic  life,  and 
be  prepared  for  many  a  long,  hot  day,  by  himself,  in  the 
canal  inspection  house." 


OTHER    IRRIGATION    WORKS.  279 

Article  55.     Methods  of  Irrigation. 

The  methods  of  irrigation  are  generally  classed  under 
four  heads,  as  follows:— 

1st.  .Flooding. 

2d.      By  distribution  through  furrows  or  ditches. 

3d.     Sub-surface  irrigation  by  pipes. 

4th.    Sprinkling. 

Of  the  four  methods  mentioned,  only  the  first  two  will 
be  referred  to  in  the  following  pages,  as  almost  all 
irrigation  011  a  large  scale  is  carried  011  under  these 
heads. 

Of  the  above  four  methods,  flooding  is  most  generally 
practiced,  and  on  the  most  extensive  scale.  The  flood- 
ing is  usually  done  in  embanked  compartments.  These 
compartments  vary  in  size.  In  India,  they  are  some- 
times as  small  as  400  square  feet,  whilst  in  Egypt,  they 
are  often  several  square  miles  in  extent. 

The  following,  on  methods  of  irrigation,  is  compiled 
mainly  from  a  paper  in  the  Minutes  of  Proceedings  of 
the  Institution  of  Civil  Engineers  for  1883,  by  P. 
O'Meara,  C.  E.,  on  Irrigation  in  Northeastern  Colorado, 
and  also  from  a  paper  by  the  Hon.  Alfred  Deakin,  M. 
P.,  of  Victoria,  Australia,  on  American  Irrigation. 

FLOODING. 

The  easiest,  simplest  and  cheapest  method  of  irriga- 
tion is  by  flooding.  By  this  method,  the  water  is 
directed  to  cover  the  whole  area  under  cultivation  to  a 
depth  varying  according  to  the  crop  and  the  quality  of 
the  soil.  This  plan  is  the  most  wasteful  of  water,  but 
cannot  be  avoided  in  the  cultivation  of  cereals.  The 
only  work  it  involves  in  the  field  is  that  necessary  to 
permit  an  even  flow  of  water.  With  a  regular  slope 
this  work  is  sometimes  trifling,  but,  as  a  rule,  some 
preliminary  outlay  is  required  for  leveling  irregu- 


280 


IRRIGATION    CANALS    AND 


larities,  or  else  providing  for  the  equal  distribution  of 
the  stream  from  points  of  vantage. 


m  4i 

To  secure  the  highest  degree  of  economy  under  the 


OTHER    IRRIGATION    WORKS.  281 

flooding  method,  inequalities  are  removed  from  the  sur- 
face of  the  land,  which  is  then  divided  by  small  raised 
mounds,  called  "  checks,"  into  compartments,  each  of 
which  is  connected  with  a  lateral  or  branch  drain,  lead- 
ing from  a  lateral  by  one  or  more  rudely  constructed 
sluice  boxes,  or  other  cheap  contrivances.  The  objects 
of  these  compartments  are  threefold,  namely: — 1,  To 
check  the  water  and  to  cause  it  to  flow  laterally;  2,  To 
arrest  the  flooding  as  soon  as  the  amount  supplied  is 
sufficient  for  moistening  the  soil  to  the  extent  deemed 
beneficial;  3,  To  diminish  the  inequality  in  the  depths 
moistened,  which  necessarily  arises  in  the  circulation  of 
water  from  a  central  point. 

Figure  191  exhibits  the  distributing  ditch  taken  from 
the  main  canal,  the  gates  leading  from  the  distributing 
ditch  to  the  compartment.'*  The  compartment  flooded 
is  the  third  from  the  main  canal,  and  in  case  the  two 
upper  compartments  were  first  flooded,  their  surplus 
water  would  flow  through  the  gates  shown  in  the  checks, 
into  the  third  compartment.  Small  gates  are  shown  in 
the  three  checks  for  draining  the  compartments  when 
it  is  deemed  they  have  had  sufficient  water. 

The  smaller  the  compartments  the  less  will  be  the  re- 
sulting inequality,  but  the  greater  the  expense  of  con- 
structing and  the  labor  of  using  them.  Lands  nearly 
level  and  lands  with  retentive  soil  admit  of  the  largest 
compartments,  with  a  given  margin  for  inequality  of 
moistening.  The  maximum  of  size  is  perhaps  obtain- 
able when  the  slope  from  the  point  of  application  is 
about  1  inch  in  100  feet.  On  nearly  level  lands  the 
size  of  the  compartments  may  be  directly  proportioned 
to  the  volume  of  water  in  application.  The  extent  of 
this  volume  is  limited  by  the  difficulty  of  controlling  it, 

*Report  of  the  Senate  Committee  on  the  Irrigation  and  Reclamation  of 
Arid  Lauds. 


282  IRRIGATION    CANALS    AND 

and  the  damage  it  would  do  to  the  soil  or  crop  if  too 
large.  Laterals  of  three  or  four  cubic  feet  per  second 
for  broken  land,  and  of  six  or  seven  cubic  feet  when  the 
land  is  unbroken,  are  manageable  under  favorable  cir- 
cumstances, by  one  irrigator,  although  those  which  are 
in  use  where  compartments  have  been  tried  in  Colorado 
are  much  smaller.  The  whole  of  the  volume  in.  appli- 
cation may  be  admitted  into  one  compartment  through 
several  openings,  or  into  several  compartments  through 
one  or  more  openings.  In  the  former  case  the  com- 
partments may  be  larger,  because  the  inequality  of 
absorption  depends  011  the  time  of  flooding.  This,  to 
come  within  the  margin  fixed  for  inequality  of  absorp- 
tion, must,  in  the  absence  of  statistics  for  different  soils, 
be  arrived  at  by  a  tentative  process,  and  the  size  of  the 
compartments  then  proportioned  to  the  volume  or  vol- 
umes in  application. 

When  the  fall  is  slight,  shallow  ditches  are  run,  in 
Colorado,  from  50  feet  to  100  feet  apart  in  the  direction 
of  the  fall;  when  the  land  is  steeper  they  are  carried 
diagonally  to  the  slope,  or  are  made'  to  wind  around  it, 
and  from  there,  by  throwing  up  little  dams  from  point 
to  point,  the  whole  field  is  inexpensively  flooded.  When 
the  fall  is  still  greater  and  the  surface  irregular,  ridges 
are  thrown  up  along  the  contour  lines  of  the  land, 
marking  it  off  into  plots  called  "checks,"  on  the  whole 
of  the  interior  of  which  water  will  readily  and  rapidly 
reach  an  equal  depth  on  the  contour  line.  When  one 
plot  is  covered  the  check  is  broken  and  the  water  ad- 
mitted so  as  in  the  same  way  to  cover  the  next  plot. 

Figure  192  shows  the  contour  checks  beginning  at 
the  main  canal,  and  compartments  supplied  by  a  ditch 
or  distributary  running  almost  parallel  on  each  side  of 
the  compartments.  Figure  193  shows  a  cross-section  of 
main  canal;  Figure  194,  a  cross-section  of  distributary, 


OTHER    IRRIGATION    WORKS. 


283 


and  Figures  195  and  196,  cross-sections  showing  checks.* 
The  ridges,  checks  or  levees  must  have  rounded  crests 
and  easy  slopes,  or  else  they  interfere  with  the  use  of 
farming  machinery,  such  as  plows,  headers,  etc.  By 


means  of  diagonal  furrows  and  checks,  remarkable  re- 
sults are  obtained,  even  in  very  broken  country.  By 
their  means  it  is  claimed  that,  in  Colorado  one  man  can 
irrigate  twenty-five  acres  per  day.  Where  checks  have 
not  been  used  upon  ground  with  an  acute  incline  the 
water  has  soon  worn  deep  channels  through  it,  utterly 
ruining  it  for  agricultural  purposes;  or  again,  where 
the  water  has  been  allowed  to  flow  too  freely,  the  conse- 
quence has  been  that  all  the  fertilizing  elements  of  the 
soil  have  been  washed  away.  In  flooding,  the  aim  is, 
therefore,  to  put  no  more  water  upon  the  land  than  it 
will,  at  once  and  equally,  absorb  or  can  part  with  with- 
out creating  a  current  sufficient  to  carry  off  sediment. 
The  neglect  of  these  precautions  has  caused  the  aban- 
donment of  several  settlements  made  in  Utah  before  the 
art  of  Irrigation  was  properly  understood.- 


*Beport  of  the  Senate  Committee  ou  the  Irrigation  and  Reclamation  of 
Arid  Lands. 


284  IRRIGATION    CANALS    AND 

Both  the  depth  and  number  of  floodings  are  varied 
according  to  soil  and  crop.  With  a  clay  the  water- 
ings are  light  and  frequent,  while  with  a  sandier 
quality  they  are  heavier  and  rarer.  Much,  too,  depends 
upon  the  distance  and  nature  of  the  sub-soil.  There  is 
considerable  uncertainty  with  regard  to  the  measure- 
ments given  for  flooding.  It  is  sometimes  so  low  that  it 
will  give  a  depth  of  only  two  or  three  inches,  and  at  other 
times  it  will  give  a  depth  of  five  to  ten  inches  at  a  single 
watering.  There  are  cases  in  which  as  many  feet  have 
been  used.  The  number  of  waterings  is  best  deter- 
mined by  the  crop  itself,  and  the  most  skillful  irrigators 
are  those  who  study  its  needs  and  take  care  to  supply 
these  needs,  without  giving  an  excess  of  water.  The 
quantity  used  alters,  therefore,  from  season  to  season,  so 
that  only  an  average  can  be  given.  See  Article  58. 

In  Colorado,  where  water  is  used  more  lavishly  than 
in  any  other  State,  some  good  judges  have  agreed  that 
an  average  of  14  inches  should  be  ample,  and  this  is 
certainly  not  too  low.  Where  the  soil  is  liable  to  be- 
come hard,  and  will  retain  moisture,  wheat  is  often 
grown  with  two  floodings,  one  before  the  ground  is 
ploughed  and  the  other  when  it  is  approaching  the  ear. 
When  two  waterings  are  given  after  sowing,  one  is 
given  when  the  wheat  commences  to  "tiller,"  and  the 
other  when  it  reaches  the  milky  stage.  Where  irriga- 
tion does  not  precede  the  plowing,  it  is  postponed  as 
long  after  the  appearance  of  the  crop  as  possible. 
Sometimes  wheat  has  three,  or  even  as  many  as  four, 
floodings,  but  this  is  unusual,  as  over-watering  occasions 
"rust."  Experience  shows  that  it  is  easy  to  exceed  the 
quantity  required  by  the  crop,  and  that  every  excess  is 
injurious.  Extravagance  is  the  common  fault,  so  much 
so  that  the  most  successful  irrigators  are  invariably 
those  who  use  the  least  water.  The  less  water,  indeed, 


OTHER    IRRIGATION    WORKS.  285 

with  which  grain  can  be  brought  to  maturity,  the  finer 
the  yield. 

Colonel  Charles  L.  Stevenson  states,  with  reference  to 
the  methods  of  irrigation  in  use  in.  Utah: — * 

"Each  farmer  has  canals  leading  from  the  main  one 
to  every  field,  and  generally  along  the  whole  length  of 
the  upper  side  of  each  field.  Each  field  has  little  fur- 
rows, a  foot  or  more  apart  and  parallel  with  each  other, 
running  either  lengthwise  or  crosswise  or  diagonally 
across,  as  the  slope  of  the  land  requires.  Into  these 
furrows  the  water  is  turned,  one  or  more  at  a  time,  as 
the  quantity  of  water  permits,  until  it  has  flowed  nearly 
to  the  other  end,  when  it  is  turned  into  the  next  fur- 
rows, and  so  on  until  all  are  watered. 

11  This  is  the  usual  custom,  but  where  the  soil  is  made 
of  clay  this  method  is  not  so  good  and  another  is  used. 
This  method  is  to  throw  up  little  embankments  six 
inches  high  around  separate  plats  of  land  that  are  of 
uniform  level,  and  turn  the  water  in  until  the  plat  is 
full  to  the  top,  when  the  water  is  drawn  off  to  the  next 
lower  plat,  and  so  on  to  the  end.  This  enables  the 
water  to  soak  in  more  and  so  does  more  good,  but  where 
the  soil  is  porous,  as  is  generally  the  case,  it  is  not  so 
good  a  method  as  it  wastes  water." 

FLOODING    IN    INDIA. 

In  India,  and  also  Egypt,  flooding  is  universally 
practiced.  There  are  two  methods  adopted  in  India  in 
supplying  water  for  irrigation,  known  as  flush  and  lift. 
In  flush  irrigation  the  water  flows  by  gravitation  on  to 
the  land  to  be  irrigated.  In  lift  irrigation  the  water 
reaches  the  land  at  such  a  low  level  that  it  cannot  flow 
over  the  surface  of  the  land  to  be  irrigated.  This 

*  Irrigation  Statistics  of  the  Territory  of  Utah,  by  Colonel  Charles  L. 
Stevenson,  C.  E. 


286  IRRIGATION    CANALS    AND 

necessitates  power  of  some  kind,  usually  manual  labor, 
to  raise  the  water  sufficiently  to  enable  it  to  flow  over 
the  land.  It  is,  therefore,  to  the  interest  of  the  irri- 
gator  to  economize  water,  and  in  view  of  this  fact  the 
officials  of  the  Ganges  and  Jumna  Canals  charge  for  lift 
irrigation  only  two-thirds  of  the  rates  charged  for  flow. 

The  proportion  of  flow  to  lift  irrigation,  on  the  Sone 
Canals,  in  Bengal,  in  1889-90,  was  96.3  to  3.7.  During 
the  same  period  on  the  Mazzafargarh  Canals,  in  the 
Punjab,  the  proportion  of  flow  to  lift  was  as  96.1  to  3.9, 
but  on  the  Shahpur  Inundation  Canals,  in  the  same 
Province,  the  proportion  of  flow  to  lift  irrigation  was 
85  to  15.  There  is  usually  more  lift  irrigation  on  inun- 
dation canals  than  on  perennial  canals. 

So  great  was  the  loss  from  waste  of  water  in  India, 
some  years  since,  that  it  was  seriously  proposed  to  sup- 
ply all  the  water  at  such  a  level  that  it  should  be  raised 
some  height,  however  small,  in  order  to  bring  it  to  the 
surface  of  the  land  to  be  irrigated.  It  would  then  be  to 
the  interest  of  the  irrigators  to  prevent  waste,  and  the 
duty  of  water  would,  in  this  way,  be  materially  increased. 

FURROWS. 

Peas  and  potatoes  are  not  irrigated  by  flooding,  but 
from  furrows  four  feet  to  ten  feet  apart,  and  this  is 
found  the  most  economical  and  most  successful  system 
for  vines  and  fruit  trees.  The  direction  of  the  furrows 
is  chosen  so  as  to  give  a  fall  of  from  one  inch  to  three 
inches  per  100  feet.  The  expenditure  of  water  is  much 
less  under  this  than  under  the  flooding  method.  When 
the  furrows  are  deep  and  narrow  the  practice  is  similar 
in  principle,  though  less  effective  than  the  pipe  method 
of  irrigation,  which  will  be  described  further  on.  Irri- 
gation can,  in  fact,  be  carried  on  without  flooding  the 
intervening  soil,  moistening  in  the  latter  case  taking 
place  beneath  the  surface,  and  losses  from  evaporation 


OTHER    IRRIGATION    WORKS. 


287 


being  thereby  largely  diminished.  It  is  evident  that 
the  depth  of  the  furrows  should  be  in  some  degree  pro- 
portioned to  the  depth  of  the  roots  of  the  crop  culti- 
vated. Figure  197  illustrates  how  land  is  irrigated  by 
furrows.* 


Fig.  197.    Plan  Showing  Method  of  Furrow  Irrigation. 

Under  the  flooding  system  the  ground,  if  not  pro- 
tected from  the  sun,  cakes  quickly.  When  the  water  is 
run  down  furrows  drawn  by  a  plow  between  the  plants, 
this  caking  is  avoided  and  the  water  soaks  quickly  to 
the  roots.  When  flooding  was  practiced  in  orchards  it 


*Irrigatioii  by  W.  H.  Graves,  C.  E.     Transactions  of  Denver  Society  of 
Civil  Engineers,  1886. 


288  IRRIGATION    CANALS    AND 

was  found  to  bring  the  roots  to  the  surface  and  enfeeble 
the  trees,  so  that  they  needed  frequent  waterings. 

Sometimes  the  furrows  feed  a  small  hole  at  the  foot  of 
the  tree,  from  which  the  water  soaks  slowly  in.  When 
this  is  done  mulching  is  found  desirable  over  the  hole 
to  reduce  the  loss  by  evaporation.  The  general  rule  is 
to  protect  the  trees  by  small  ridges,  so  that  the  water 
does  not  affect  the  surface  within  three  or  four  feet  of 
them.  The  simple  furrow,  however,  is  most  generally 
in  use. 

Oranges  are  watered  three  or  four  times  in  summer; 
vines  once,  twice,  or  often  not  at  all  after  the  first  year 
or  two;  and  other  fruits  according  to  the  caprice  of  the 
owner,  the  necessities  of  the  season  and  the  nature  of 
the  soil,  one  to  four  times.  It  is  impossible  to  be  more 
exact. 

An  even  greater  difference,  comparatively,  in  the 
quantity  of  water  used  obtains  in  the  furrow  irrigation 
of  fruit  trees  and  vines,  than  has  been  noted  in  regard 
to  cereals.  To  such  an  extent  does  this  prevail  that, 
not  only  do  districts  differ,  but  of  two  neighbors  who 
cultivate  the  same  fruits  in  contiguous  orchards,  having 
exactly  the  same  slope  and  soil,  one  will  use  twice  or 
thrice  as  much  water  as  the  other.  To  attain  the  best 
results  the  trees  must  be  carefully  watched,  and  sup- 
plied with  only  just  enough  water  to  keep  them  in  a 
vigorously  healthy  condition. 

Another  all  important  principle,  as  to  which  there  is 
no  question,  and  which  is  testified  to  on  every  hand  is, 
that  the  more  thoroughly  the  soil  is  cultivated,  the  less 
water  it  demands,  a  truth  based  partly  y  110  doubt,  upon 
the  fact  that  the  evaporation  from  hard,  unbroken  soil 
is  more  rapid  than  from  tilled  ground,  which  retains 
the  more  thoroughly  distributed  moisture  for  a  longer 
period. 


OTHER    IRRIGATION    WORKS.  289 

Major  Corbett  published  some  articles  in  the  Profes- 
sional Papers  on  Indian  Engineering  to  prove  that,  by 
the  adoption  of  superior  cultivation,  the  necessity  of 
irrigation  would  be  very  much  diminished- in-iidia. 
The  native  plow  enters  the  ground  for  only  a  few  inches, 
and  below  that  depth  there  is  a  hard  crust  that  prevents 
the  water  from  filtering  down.  He  contended  that  by 
breaking  up  this  hard  crust  by  deep  plowing,  and  by 
carrying  the  cultivation  deeper,  that  there  would  not  be 
the  same  necessity  for  irrigation  as  was  required  after 
shallow  plowing,  for  the  reason  that  evaporation  from 
the  land  would  not  take  place  to  the  same  extent. 

For  the  irrigation  of  cereals,  works  are  required  on  a 
larger  scale,  proportionately,  than  for  fruit,  because  in 
the  first  case  the  water  is  demanded  in  greater  quantities, 
at  particular- times,  while  in  the  latter  the  supply  can 
be  more  evenly  distributed  throughout  the  year,  though, 
of  course,  the  irrigating  season  with  both  is  much  the 
same. 

Winter  and  autumn  irrigations  are  growing  in  favor. 
Land  which  receives  its  soaking  then,  needs  less  in  sum- 
mer, and  is  found  in  better  condition  for  plowing.  It 
is  argued  that  moisture  is  more  naturally  absorbed  in 
that  season  and  with  greater  benefit.  Everywhere  the 
verdict  of  the  experienced  is,  that  too  much  water  is  be- 
ing used,  and  the  outcry  against  over-saturation  in 
summer  is  but  one  of  its  forms. 

Article  56.     Duty  of  Water  for  Irrigation. 

The  duty  of  water  is  that  quantity  required  to  irrigate 
a  certain  area  of  land.  In  English-speaking  countries, 
it  is  usually  expressed  by  stating  the  number  of  acres 
that  a  continuous  flow  of  one  cubic  foot  per  second. will 
irrigate.  Thus,  if  a  stream  discharging  40  cubic  feet  of 
19 


290  IRRIGATION    CANALS    AND 

water  per  second  is  all  expended  in  irrigating  8,000 
acres  of  land,  then  its  duty  is  equivalent  to  200  acres, 
that  is,  each  cubic  foot  per  second  irrigates  200  acres. 
The  duty  varies  from  35  to  2,200  acres  per  cubic  foot 
per  second. 

The  duty  is  sometimes  expressed  by  the  average 
depth  of  water  over  the  whole  land,  and  again,  by  the 
cubic  contents,  as,  for  instance,  the  number  of  cubic 
yards  per  acre. 

The  duty  of  water  is  influenced  by  different  circum- 
stances and  varies  according  to  the  following  condi- 
tions:— 

1.  With  the  character  and  conditions  of  the  soil  and 
sub-soil. 

2.  Configuration  of  the  land. 

3.  The  depth  of  water-line  below  surface  of  ground. 

4.  Rainfall. 

5.  Evaporation  and  temperature. 

6.  The  method  of  application  employed. 

7.  Length  of  time  the  land  has  been  irrigated. 

8.  Kind  of  crop. 

9.  The  quantity  of  fertilizing  matter  in  the  water. 

10.  The  experience  of  the  irrigators. 

11.  The  method  of  payment  for  the  water,  whether 
by  the  rate   per  acre  irrigated   or   by  payment  for  the 
actual  quantity  of  water  used. 

Payment  according  to  the  actual  quantity  of  water 
used  is  a  good  method  to  make  the  irrigators  use  the 
water  with  economy. 

Mr.  J.  S.  Beresford,  C.  E.,  in  a  paper  on  the  Duty  of 
Water,*  enters  very  fully  into  all  the  causes  of  waste  of 
water.  He  states,  under  the  heading: — 

"  Efficiency  of  a  Canal. — Take  the  Ganges  Canal.      We 


*  Professional  Papers  on  Indian  Engineering,  Vol.  V,  Second  Series. 


OTHER    IRRIGATION    V^ORKS.  291 

may  look  on  it  as  a  great  machine  composed  of  many 
parts,  and  go  about  calculating  its  efficiency  in  the  same 
way  as  that  of  a  steam  engine.  This  irrigating  machine 
is  made  up  of  four  important  parts,  which  are—quite 
separate,  and,  as  things  stand  at  present,  at  least  two 
of  them  depend  on  different  interests.  They  are  as 
follows: — 

11  1.     Main  Canal. 

"  2.     Distributaries. 

"  3.     Village  water-courses. 

"  4.     Cultivators  who  apply  the  water  to  the  fields. 

"Each  cubic  foot  of  water  entering  the  head  of  a 
canal  is  expended  as  below: — 

"  1st.  In  waste  by  absorption  and  evaporation  in 
passing  from  canal  head  to  distributary  head. 

"  2d.  In  waste  from  same,  cause  in  passing  from  dis- 
tributary head  to  village  outlet. 

"  3d.  In  waste  from  same  cause  in  passing  along 
village  water-course  to  the  fields  to  be  watered. 

"  4th.  In  waste  by  cultivators,  through  carelessness 
in  not  distributing  the  water  evenly  over  the  fields, 
causing  evaporation,  and  the  ground  to  get  saturated  to 
an  unnecessary  depth  in  places.  (See  page  250.) 

"  5th.     In  useful  irrigation  of  land. 

"  Our  object  is  plainly  to  increase  the  fifth  by  the  re- 
duction of  all  the  rest." 

All  over  the  irrigating  districts  of  America,  where 
irrigation  is  carried  on  from  earthen  channels,  the  duty 
is  low.  We  see  in  Table  18  that  the  average  duty  in 
India  is  over  200  acres,  and  it  is  doubtful  if  the  average 
in  America  is  half  of  that  quantity.  There  is  one  fact 
that  may  account  for  this  great  difference.  In  America 
the  greater  part  of  the  land  irrigated  is  virgin  soil,  and 
this  may  account  for  the  great  quantity  of  water  used. 
In  India,  on  the  contrary,  the  land  has  been  irrigated 


292  IRRIGATION    CANALS    AND 

for  centuries  and  the  average  rainfall  is  greater  than  in 
the  arid  region  of  America.  A  great  portion  of  the 
land  now  irrigated  by  canal  water  in  India  was  irriga- 
ted from  wells  before  the  construction  of  the  canals. 
Whatever  the  cause  may  be,  the  fact  is  apparent,  that 
the  duty  of  water  in  America  is  far  below  that  of  India. 

We  have  already  seen,  in  page  249,  how  Mr.  A.  E. 
Forrest,  C.  E.,  by  simply  improving  the  distributaries, 
raised  the  duty  of  water  in  one  of  the  divisions  of  the 
Ganges  Canal  to  400  acres. 

There  is  no  good  reason  why  such  a  duty  of  water 
should  not  be  reached  in  many  districts  of  America. 
As  the  area  of  irrigated  land  increases  so  will  the  value 
of  water  increase,  and  irrigators  will  then  be  compelled 
to  keep  their  main  and  distributing  channels  in  good 
order,  to  use  the  water  at  night  to  prevent  all  waste  and 
to  put  no  more  on  the  land  than  is  sufficient  to  mature 
a  crop. 

The  following  table,  showing  the  duty  of  water  in 
different  countries,  is  compiled  from  various  sources 
and  includes  a  table  given  by  Mr.  A.  D.  Foote,  C.  E.,  in 
his  Report  on  Irrigating  Desert  Lands  in  Idaho: — 


TABLE 


OTHER    IRRIGATION    WORKS. 


Giving  the  duiy  of  water  iu  different  countries. 


293 


LOCALITY. 

COUNTRY. 

Duty  of 
water. 

REMARKS. 

Eastern  Jumna  Canal  

India..  .  . 
India   .     . 

Acres. 

306 
240 

E.  B.  Dorsey,  C.  E. 
F  C  Danvers. 

Ganges  Canal  
Canals  of  Upper  India  
Canals  of  India  —  average  
Bari  Doab  Canal  

India  
India  
India  
India  

232 
267 
250 
155 

E.  B.  Dorsey,  C.  E. 
E.  B.  Dorsey,  C.  E. 
Lieut.  Scott  Moncrieff,  R.  E. 
F  C.  Danvers. 

Madras  Canals  (Rice)  
Tanjore  'Rice)  
Swat  River  Canal,  1888-89. 
Swat  River  Canal,  1889  90. 
Western  Jumna  Canal,  1888-89. 
Western  Jumna  Canal,  1889-90. 
Bari  Doab  Canal,  1888-89. 
B'iTi  Doab  Canal,  1889-90 
Sirhind  Canal,  1888-83. 
Sirhind  Canal,  1889-90. 
Chenab  Canal,  1888-89. 
Chenab  Canal,  1889-90 
Nira  Canal,  1888-S9. 
Genii  Canal  ... 

India  
India  
India  
India  
India  
India  
India  
India  
India  
India  
India  
India.  ..  . 
India  

66 
40 
216 
177 
143 
179 
201 
227 
180 
180 
154 
154 
186 
240 

George  Gordon. 
Roorkee  Treatise  Civil  Engineering. 
Revenue  Report  of  the  Irrigation  Dep't, 
Punjab,  1889-90. 

Bombay  Report,  1889-90. 
E  B  Dorsey  C  E 

Elche  

Spain...  . 
Spain  ...  . 

1072 
2200 

George  Higgin,  C.  E. 
George  Higgin,  C.  E 

Jucar  (Rice) 

Spain 

35 

George  Higgin  C  E 

Spain 

157 

George  Higgin  C  E 

Canals  of  Valencia  

Spain  ...  . 

242 
140 

E.  B.  Dorsey,  C.  E. 
Transactions  ICE    vol  65 

Canals  south  of  France  
Sen,  or  Lower  Nile  Canals  
Sen,  or  Lower  Nile  Canals  
Canals,  Northern  Peru  
Canals,  Northern  Chili  
Canals,  Lombardy  
Canals,  Piedmont  <  
Marcite  

France  .  . 
Egypt  ..  . 
Egypt  .  . 
Peru  
Chili  
Italy  
Italy  
Italy 

70 
350 
274 
160 
190 
90 
60 
1  to  18 

George  Wilson,  C.  E. 
London  Times,  18  Sept.,  1877. 
Russian  Pasha,  1883. 
E.  B.  Dorsey,  C.  E.    No  rainfall. 
E.  B.  Dorsey,  C.  E.    No  rainfall. 
Baird  Smith,  R.  E.    Including  Rice. 
Baird  Smith,  R.  E.    Including  Rice. 
Columbani  and  Brioschi. 

Sen  Canals,  Southern  France  
Sen  Canals,  Victoria 

France  .  .  . 
Australia 

60 

200 

Lieut.  Scott  Moncrieff,  R.  E. 
The  Honorable  Alfred  Deakin,  M.  P 

Sweetwater,  San  Diego  
Pomona,  San  Bernardino  

California. 
California. 
California 

500 
500 
500 

William  Fox,  M.  Inst.,  C.  E.  ~)       -p. 
William  Fox,  M.  Inst,,  C.  E.    V      ' 
William  Fox,  M  Inst..  C.  E.  )    systenL 

California 

California 

80  to  150 

San  Diego 

California 

1500 

James  D  Schuyler,  C.  E. 

Canals  of  Utah  Territory  
Canals  of  Colorado  
Canals  of  Cache  la  Poudre  ,  

Utah  
Colorado.. 
Colorado.  . 
Colorado 

100 
100 
193 
55 

C.  L.  Stevenson,  C.  E. 
Nettleton,  State  Engineer,  Colorado. 
Prof  Mead,  C.  E. 
P  O'Meara  C  E 

Article  57.     Pipe  Irrigation. 

Four  things  are  necessary  in  order  to  get  the  greatest 
possible  duty  of  water.     They  are: — 

1.  That  the  water   should  he   sold    or    supplied    by 
measurement. 

2.  That  it  should  he  conveyed  to  the  actual  point   of 
use  in  impervious  channels,  and  best  of  all  in  pipes. 

3.  That  its  use  should  he  continuous,  that  is,  at  night 
as  well  as  by  day. 


21)4  IRRIGATION    CANALS    AND 

4.  That  it  should  be  used  intelligently  and  with  a 
dvie  regard  to  economy. 

The  use  of  pipes  refers  only  to  small  supplies  of  water. 
For  large  supplies  earthen  channels  are  the  most 
economical,  not  o^  water,  but  of  money. 

If  the  above  four  conditions  are  observed  the  duty  of 
water,  especially  for  fruit  land,  will  be  increased  to  a  great 
extent,  with  a  corresponding  increase  in  the  area  of  land 
irrigated. 

The  use  of  pipes  made  of  plate  iron,  vitrified  clay, 
concrete,  wood  bound  with  iron  bands,  open  channels 
made  of  asphalt  or  concrete,  and  reservoirs  lined  with 
asphalt  or  concrete,  is  steadily  increasing  in  Southern 
California. 

The  pipe  system  has  been  adopted  with  great  success 
in  Bear  Valley,  Pomona,  Ontario,  Riverside,  San  Ber- 
nardino, Los  Angeles,  and  many  other  localities  in 
Southern  California,  and  this  is  conclusive  proof,  that 
the  great  expense  attending  their  construction,  is  more 
than  counterbalanced  by  the  great  saving  of  water 
effected  by  their  use.  By  the  pipe  system  the  distribu- 
tion of  water  is  better  under  control,  and  easier  man- 
aged, than  by  open  channels. 

Fred.  Eaton,  M.  Am.  Soc.  C.  E.,  of  Los  Angeles,  has 
supplied  the  following  relative  to  irrigation  by  pipes: — * 

"  The  duty  of  our  streams  would  be  extended  by  ex- 
tending the  present  ditches  by  pipe  systems.  Experi- 
ence has  taught  us  that  by  economizing  the  water  it  is 
not  only  the  water  that  we  save  in  seepage  alone,  but  the 
distribution.  The  convenience  that  these  pipe  systems 
offer  in  the  distribution  of  water  is  a  great  economizer. 
We  find  that  we  can  get  along  with  a  half  or  a  third  the 


*  Quoted  in  Irrigation  in  the  United  States  by  Richard  J.  Hiiitou. — U.  S. 
Department  of  Agriculture. 


OTHER    IRRIGATION    WORKS.  295 

water  that  we  get  in  running  it  around  in  ditches.  It 
was  thought  that  the  San  Gabriel  was  being  used  up  by 
irrigating  2,000  acres,  but  it  has  been  used  since  for 
irrigating  12,000  acres,  and  it  can  be  increased  by  the 
pipe  system.  The  duty  of  one-fiftieth  of  a  cubicToot  per 
second  throughout  the  valley,  under  the  pipe  system, 
would  be  one  inch  to  ten  acres;  that  is,  for  vegetables 
and  all  kinds  of  crops.  It  depends  altogether  on  the 
character  of  the  soil.  A  soil  that  is  well  sub-drained, 
that  is,  composed  of  gravel,  will  require  much  less  water. 
Such  sub-soil  is  a  natural  drain,  and  for  that  reason 
water  will  go  a  great  deal  farther  on  that  kind  of  land 
than  it  will  on  an  impervious  sub-soil.  Taking  the  aver- 
age in  the  San  Gabriel  Valley,  with  ten  acres,  you  can 
irrigate  all  kinds  of  crops,  orange  trees,  and  all  kinds  of 
vegetables. 

"  The  cost  runs  from  $15  to  $50  per  acre.  The  cement 
pipes  are  not  cheaper  than  the  pressure  pipes,  because 
it  requires  a  good  many  more  of  them,  arid  they  are  not 
so  convenient  as  the  pressure  pipes.  We  generally  use 
sixteen  iron.  It  is  practically  the  sixteenth  of  an  inch 
thick.  A  four-inch  pipe  is  more  difficult  to  make  than 
a  sixteen-inch.  We  put  asphaltum  on,  but  it  is  impos- 
sible to  keep  it  from  being  knocked  off  in  spots,  and 
these  spots  rust  there.  We  cannot  inspect  them  closely 
enough  to  get  at  them  all  and  paint  them  over.  In  or- 
dinary soil  where  there  is  no  alkali,  it  will  wear  fif- 
teen or  sixteen  years.  I  put  in  pipes  fifteen  years  ago 
that  are  doing  service  now.  The  Pasadena  pipes  were 
eleven  inches  with  eighteen  iron.  That  system  was  put 
in  in  1873  and  served  up  to  this  year.  We  have  not 
many  storage  facilities  up  in  the  mountains,  they  are 
confined  practically  to  the  foothills  and  the  valleys.  We 
have  to  bring  our  water  down  and  make  our  reservoir  in 
the  valley/' 


2"96  IRRIGATION    CANALS    AND 

The  following  description  of  the  pipe  system  of  Onta- 
rio, California,  is  by  F.  E.  Trask,  Chief  Engineer  of  the 
Ontario  Land  Improvement  Company:— 

PIPE  IRRIGATION    SYSTEM,    ONTARIO,    CALIFORNIA. 

A  portion  of  the  Ontario  tract  of  11, 000  acres  is  under 
cultivation  receiving  its  water  supply  from  San  Antonio 
Canon  by  means  of  a  pipe  system  of  main,  sub-mains 
and  laterals.  The  accompanying  plat  shows  only  a  por- 
tion of  the  north  end  of  the  tract,  the  letters  A  Az  A3, 
B  B  B3,  and  C  C  C,  marking  the  location  of  mains,  sub- 
mains  and  laterals  respectively.  Lots  are  696  feet  by  627 
feet,  or  about  ten  acres  each  in  area. 

The  general  slope  of  the  land  is  southeast,  and  the 
grade  varies  from  thirteen  (13%)  per  cent,  at  the  north 
end — shown  on  plat — to  one  (1%)  per  cent,  at  the  south 
end  of  the  tract,  which  is  not  included  in  the  plat. 

The  principal  main,  A  A  Az,  brings  the  water  from 
the  canon,  around  the  foothills,  and  down  the  same,  to 
the  head  of  the  colony  land,  where,  running  east  and 
west,  this  main  supplies  the  laterals  C  C  C. 

Sub-mains  BB  Bs,  or  as  commonly  designated,  the  sup- 
plementary mains,  take  water  from  the  main  line,  A  A  A^ 
near  the  foothills  and  run  diagonally  through  the  colony, 
.furnishing  water  to  the  laterals,  C  C  C,  at  points  some 
miles  south  of  their  heads,  to  compensate  for  that 
already  expended  by  the  latter.  For  example — the  lat- 
teral  A$  B$  has  supplied  four  lots  by  the  time  it  reaches 
B$.  At  $3  a  new  supply  is  received  into  the  lateral  A3  B3 
from  the  sub-main  B  B  B?,,  which  is  used  to  irrigate  land 
lying  south  of  B^. 

Laterals  C  C  C  are  designed  to  carry  water  without 
pressure  and  deliver  the  same  at  the  highest  corner  of 
each  lot.  They  are  parallel  to  each  other  and  average 
about  six  miles  in  length.  Each  line  is  designed  to  irri- 


OTHER    IRRIGATION    WORKS. 


297 


gate  one  tier  of  lots  and  is  located  three  feet  within  the 
boundary    of  such    tier,    as    shown    on    diagram.     The 


diameter  and  grades  of  the  laterals  C  C  C  are  given  on 
the  plat  for  the  section  it  represents;  below  which  the 


2U8  IRRIGATION    CANALS    A\:> 

grade  constantly  decreases  to  the  south  end  of  the  tract 
where  the  grade  is  flattened,  i.  e.,  about  one  per  cent.; 
but  the  diameter  of  pipes  remain  the  same. 

Stand  pipes  of  fourteen  (14")  or  sixteen  (16")  inches 
diameter  are  placed  in  the  pipe  lines,  C  G  0,  at  points 
where  water  is  to  be  delivered  to  the  land.  In  each 
stand  pipe  an  iron  slide  gate  is  set;  this  can  be  dropped 
to  close  the  whole  pipe  line  or  to  a  sufficient  depth  to  in- 
tercept the  required  volume  of  water,  as  the  case  may  be. 

The  greater  portion  of  the  pipe  used  in  this  system 
has  been  manufactured  from  cement  concrete  at  conven- 
ient points  in  the  tract. 

Properly  located  and  designed,  the  pipe  system  for  the 
irrigation  of  fruit  lands  is  much  more  economic  than 
any  of  the  older  methods,  and  irrigators  can  ill  afford  to 
adopt  flume  or  ditch  systems  where  the  topography  admits 
of  the  pipe  system  being  used. 

Article  58.     Number  and  Depth  of  Waterings. 

The  number  and  depth  of  waterings  given  to  land 
vary  very  much  in  different  countries. 

The  greatest  quantity  is  used  in  the  Marcite  cultiva- 
tion of  Italy  and  the  south  of  France,  where  water  is 
poured  over  the  meadow  lands  during  the-  winter,  in 
quantity  sufficient  to  cover  them  to  a  depth  of  more  than 
300  feet,  and  where  the,  duty  has  been  as  low,  in  some 
cases,  as  one  acre  to  one  cubic  foot  of  water  per  second. 
(See  Table  18.) 

The  other  extreme  is  reached  of  a  small  expenditure 
of  water  by  the  pipe  system  of  orchard  agriculture  in 
Southern  California,  where  a  cubic  foot  of  water  per 
second  was  estimated  to  irrigate  from  500  to  1,500  acres. 

The  Henares  Canal,  in  Spain,  gives  twelve  waterings. 
Each  watering  is  equal  to  about  916  cubic  yards,  which 


OTHER    IRRIGATION    WORKS.  299 

gives  a  depth  of  0.57  foot  for  one  watering,  equal  to  6.8 
feet  in  depth  for  twelve  waterings. 

The  Esla  Canal,  also  in  Spain,  gives  twelve  waterings. 
Each  watering  is  equal  to  about  850  cubic  yards,  which 
gives  a  total  depth  on  the  land  of  about  6.3  feel.~ 

In  Valencia,  in  Spain,  where  it  is  vory  hot,  wheat  is 
watered  four  or  five  times,  giving  about  200  acres  per 
cubic  foot  per  second.  In  other  parts  of  Spain  a  depth 
of  two  and  one-half  to  three  inches  was  considered  ample 
for  an  irrigation,  and  two  irrigations  in  the  seasons 
were  held  to  be  sufficient. 

In  some  of  the  gardens  of  Valencia,  Spain,  only  from 
13  to  20  acres  per  foot  are  irrigated.  Here,  however, 
there  are  at  least  two  crops  a  year  and  a  part  is  devoted 
to  rice. 

In  the  new  canal  from  the  Rhone,  in  France,  the 
summer  waterings  will  generally  be  twenty  in  number, 
given  once  a  wreek,  and  representing  a  total  depth  of  one 
metre  or  3.28  feet. 

In  the  south  of  France  the  time  for  irrigation  com- 
mences on  the  1st  of  April,  and  terminates  on  the  30th 
of  September.  The  standard  quantity  of  water  adopted 
in  the  country  is  one  litre  (.0353  cubic  feet)  of  water  sup- 
posed to  flow  continuously  for  six  months,  per  hectare 
(2.471  acres).  This  quantity  of  water  would  cover  the 
ground  to  a  depth  of  about  62J  inches;  consequently  it 
gives  fourteen  irrigations,  each  of  about  four  and  one- 
half  inches;  twenty  irrigations  of  about  three  inches,  or 
forty-three  irrigations  of  about  one  and  one-half  inch 
depth  of  water. 

There  is  no  fixed  rule  in  the  south  of  France  as  to  the 
number  of  irrigations  for  such  crops  which  require 
periodical  irrigating,  during  the  whole  season,  as  this 
must  necessarily  depend,  to  a  great  extent,  upon  the 
nature  of  the  land,  whether  light  or  heavy,  whether  fiat 


300  IRRIGATION    CANALS    AND 

or  sloping.  In  most  cases  the  water  is  given  by  the 
companies  once  a  week,  which  would  be  equal  to  twenty- 
six  irrigations  during  the  season.  The  Marseilles  Canal 
gives  the  water  forty-three  times  during  the  season. 

Experiments,  near  the  Bari  Doab  Canal,  in  India, 
showed  that  an  average  depth  of  0.24  feet  on  the  whole 
surface  represents  a  thorough  watering  of  the  average 
soil  of  the  district,  sandy  loam,  and  that  for  sandy  soils 
0.31  feet  in  depth,  and  therefore  the  amount  of  water 
necessary  for  an  average  watering  of  one  acre  is  0.24  X 
43,560  =  10,454  cubic  feet. 

Wheat  in  a  dry  season  requires  five  waterings;  the 
first  for  preparing  the  land  for  plowing  at  10,500  cubic 
feet,  and  four  for  the  standing  crop  of  8,000  cubic  feet, 
gives  42,500  cubic  feet  in  all  necessary  for  each  crop  of 
wheat  that  is  an  average  depth  of  less  than  one  foot. 

In  Madras  6,000  cubic  yards  of  water  are  usually 
given  to  irrigate  an  acre  of  rice.  This  is  equivalent  to 
a  depth  of  3.7  feet. 

In  Colorado  the  expenditure  of  water  for  a  single 
irrigation  is  generally  reckoned  at  about  twelve  inches 
in  depth.  Of  irrigations  the  number  applied  to  the 
land  in  one  season  is  about  three,  in  exceptionally  dry 
ones,  four.  The  English  company  in  Colorado  has  a 
water  right  equivalent  to  a  depth  of  42.84  inches. 

Professor  George  Davidson,  of  San  Francisco,  says 
that  the  best  authorities  assume  a  depth  of  from  10  to 
12  inches  of  water  to  the  production  of  a  crop  of  wheat, 
barley  and  maize,  when  applied  in  waterings  of  four 
times  two  and  a  half  inches  or  three  times  four  inches. 
The  smaller  of  these  results  is  almost  identical  with  the 
amount  deduced  from  observation  in  the  great  valley  of 
California,  where  a  rainfall  of  10J  inches,  fairly  distri- 
buted, has  insured  a  large  crop  of  wheat,  etc. 


OTHER    IRRIGATION    WORKS.  301 

Colonel  Charles  L.  Stevenson,  C.  E.,  states,  with 
reference  to  Utah*: — 

"  Each  farm  generally  has  the  right  to  use  the  water 
so  many  hours  once  a  week  or  once  in  10,  12  or  l^days, 
as  the  particular  valley  and  the  time  of  year  require. 
The  crops  are  supposed  to  get  a  good  soaking  at  every 
watering." 

General  Scott  Moncrieff  states,  with  reference  to  irri- 
gation in  India: — 

"  For  the  wheat  crop  which  is  grown  in  the  cold 
season,  four  waterings  are  quite  enough,  and  almost  110 
other  crop  requires  more,  except  rice  and  sugar-cane, 
which  are  sometimes  irrigated  as  often  as  twelve  times, 
and  are  watered  by  a  rainy  season  as  well.  From  actual 
experiments  in  the  Northwest  Provinces  of  India,  in  the 
months  of  December  and  February,  when  it  is  by  no 
means  very  warm  weather,  I  found  that  one  cubic  foot 
of  water  per  second  would  irrigate  in.  twenty-four  hours 
4.57  acres  of  rough,  uncleaned  ground  previous  to  plow- 
ing, and  that  this  same  discharge  was  enough  for  5.64 
acres  of  a  well-cleaned  and  level  field  of  young  wheat. 
These  results  give  depths  of  water  of  5.1  inches  and  4.1 
inches.  A  safe  mean  in  Northern  India  is  to  reckon 
five  acres  in  twenty-four  hours  as  the  area  to  be  watered 
by  one  cubic  foot  per  second,  where,  as  is  general,  the 
soil  is  light. 

"  We  may  further  take  fifty  oays  as  about  the  greatest 
interval  there  allowed  to  elapse  between  two  waterings, 
and  so  we  shall  obtain  5  X  50  -—  250  acres  as  the  duty  to 
be  got  out  of  each  cubic  foot  per  second,  that  is,  .28 
litre  (.009886  cubic  feet)  per  hectare  (2.47  acres),  sup- 
posing it  can  be  used  at  this  rate  all  the  year  round,  and 
this  is  not  more  than  has  been  done  more  than  once  on 

*  Irrigation  Statistics  of  the  Territory  of  Utah. 


302  IRRIGATION    CANALS    AND 

the  Eastern  Jumna  Canal.  The  discharge  then  is 
measured  at  the  head  of  the  canal,  and  the  water  prob- 
ably runs  on  an  average  more  than  300  miles  before  it 
actually  reaches  the  field  to  be  watered.  It  is  usual  to 
deduct  twenty  per  cent,  for  the  loss  by  filtration,  evap- 
oration, etc.,  en  route,  and  yet  a  duty  as  high  as  this 
has  been  proved  attainable  without  making  allowance 
for  the  deduction.  Of  these  250  acres,  about  eighteen 
per  cent,  usually  consists  of  rice,  and  as  much  more  of 
sugar-cane,  each  requiring  a  large  amount  of  water; 
fifty  per  cent,  of  wheat  and  barley,  and  the  rest  of  in- 
ferior crops,  only  watered  once  or  twice.  The  rain,  of 
which  for  the  greater  part  falls  in  June,  July  and  Au- 
gust, consists  of  about  40  inches  a  year — more  certainly 
than  in  Castile.  The  heat  and  consequent  evaporation 
must  be  considerably  greater." 

Article  59.     Horary  Rotation. 

Water  is  supplied  for  purposes  of  irrigation: — 

1.  By  fixed  outlet  or  by  measurement. 

2.  By  the  area  of  land  irrigated  to  certain  crops. 

3.  By  Horary  Rotation. 

The  latter  method  of  supply  will  be   now  considered. 

In  order  to  obtain  the  greatest  duty  from  water,  it 
should  be  used  at  night  as  well  as  during  the  day. 

An  irrigating  channel  passes  through  the  lands  of  sev- 
eral proprietors.  A  period  of  rotation- is  fixed  for  this 
channel.  This  period  varies  according  to  the  nature  of 
the  crop,  rice  for  example  requiring  a  more  rapid  rota- 
tion than  wheat.  Each  landowner  can  then  have  the  full 
volume  of  the  channel  turned  011  to  his  land,  once  in 
the  period  of  rotation,  for  a  certain  number  of  hours, 
according  to  the  quantity  to  which  he  is  entitled. 

This  method  is  applicable  only  to  laterals  or  distribu- 


OTHER    IRRIGATION    V/ORKS.  oO«T> 

taries,  having  a  small  discharge,  which  a  landowner  can 
handle  with  economy. 

It  is  clear  that  the  quantity  of  water  to  which  any  sin- 
gle employer  of  a  canal,  common  to  several,  ajn.d_jregu- 
lated  by  horary  rotation,  is  entitled,  is  in  direct  propor- 
tion to  the  total  volume  of  the  canal,  and  the  number  of 
hours  during  which  he  is  entitled  to  possess  it,  and  in 
inverse  proportion  to  the  number  of  days  over  which 
rotation  extends.  Hence  we  have  the  following  general 
formula:  — 


N 
where:  — 

Q  —  the  quantity  appertaining  to  a  single  consumer 
in  continued  discharge. 

T  ===  the  number  of  hours  or  days  during  which  he 
has  the  right  to  the  whole  volume  of  the  canal. 

Ql  =  the  volume  of  channel  in  cubic  feet  per  second, 
or  any  other  fixed  measure. 

N  =  the  number  of  days  over  which  the  rotation  ex- 
tends. 

Example.  —  Let  10  days  be  the  period  of  rotation,  and 
the  channel  has  a  supply  of  20  cubic  feet  per  second,  of 
which  a  consumer  is  entitled  to  a  continuous  supply  of 
one-twentieth  part  or  one  cubic  foot  per  second.  He 
wishes  to  change  this  continuous  for  an  intermittent  sup- 

ply— 

^Q_10XJ 
=  Qi   :         20 

Therefore,  he  is  entitled  to  the  full  supply  for  half  a 
day  or  twelve  hours.  His  name  is  placed  on  the  list,  say 
sixth,  and  he  gets  the  full  supply  turned  on  at  a  fixed 
hour  and  turned  off  at  a  fixed  hour.  also.  Arrangements 
can  be  made  to  have  another  consumer's  gate  opened  as 
this  one  is  being  closed,  and,  in  this  manner,  the  full 


304  IRRIGATION    CANALS    AND 

supply  of  the  channel  is  delivered  on  the  land  continu- 
ously. 

Mr.  R.  E.  Forrest,  C.  E.,*  states:—  "  That  by  a  good 
system  of  rotation  it  might  be  possible  to  remedy  the  loss 
of  duty  from  the  water  not  being  used  at  night;  the 
water  could  be  run  on  at  night  to  the  more  distant 
points.  By  a  system  of  rotation  the  evils  of  supersat- 
uration  could  be  lessened.  The  water  was  made  to  run 
through  a  tract  only  when  it  was  wanted  and  for  so  long 
as  it  was  wanted.  In  some  of  the  Ganges  Canal  chan- 
nels the  water  ran  only  for  a  single  day  each  fortnight. 
The  water  should  be  completely  withdrawn  from  every 
tract  in  which  it  was  not  in  active  and  immediate  de- 
mand." 

Article  60.     Forestry  and  Irrigation. 

The  preservation  of  the  forests,  and  the  extensive 
planting  of  trees,  should  proceed  simultaneously  with 
the  development  of  irrigation  in  this  country.  A  stop 
should  be  put,  and  at  an  early  date,  to  the  ruthless  de- 
struction of  the  forests  of  this  country,  especially  at  the 
head-waters  of  the  rivers,  for  if  this  is  not  done,  what 
has  happened  in.  other  countries  is  sure  to  happen  here, 
and  districts  which  are  now  fertile  will,  in  the  lapse  of 
time,  become  barren  wastes. 

A  large  forest,  is  in  fact,  an  immense  reservoir,  which 
slowly  but  surely  gives  out  its  supply  for  the  wants  of 
man.  The  greater  part  of  its  loss  by  percolation  is 
again  utilized  to  supply  the  streams,  and  it  requires  no 
dams  or  other  expensive  works.  The  Government  send 
out  engineering  parties  to  locate  the  sites  of  reservoirs, 
whilst,  at  the  same  time,  they  permit  nature's  own  reser- 


*  Transactions  of  the  Institution  of  Civil  Engineers,  Volume  LXXHI — 
1883. 


OTHER    IRRIGATION    WORKS.  305 

voirs,  the  forests,  to  be  destroyed  in  the  interest  of  a  few 
individuals. 

Parts  of  Persia  that  are  now  desert  were,  within  his- 
toric times,  fertile  lands,  which  supported  deftse___riopu.- 
lations  and  yielded  large  revenues.  During  long  periods 
of  time,  different  large  armies,  with  their  countless  hosts 
of  camp  followers,  passed  across  the  country  and  cut- 
down  the  trees  for  fuel.  The  inhabitants  of  the  country 
did  the  same  thing,  and  no  trees  were  planted  to  replace 
those  that  were  destroyed.  During  the  existence  of  the 
forests  the  rain  fell  at  regular  intervals,  and  in  moderate 
quantities,  and,  in  this  way,  was  an  aid  in  the  cultiva- 
tion of  the  land  and  in  maturing  the  crop.  After  the 
destruction  of. the  forests  the  rain  fell,  in  dense  showers, 
at  irregular  intervals,  thus  doing  more  harm  than  good, 
and  as  a  result  of  this  the  population  gradually  dimin- 
ished until  the  land  became  a  desert. 

In  America,  an  army  of  wood-cutters  is  constantly  em  - 
ployed  in  destroying  the  forests.  It  takes  a  short  time 
to  destroy  a  forest,  but  many  a  year,  equal  to  several 
generations  of  men,  to  reproduce  it. 

Mr.  Allan  Wilson,  Mem.  Inst.  C.  E.,  states*  with  ref- 
erence to  Southern  India: — 

"  In  former  times  when  the  tanks  (reservoirs)  were  in 
good  repair,  trees  were  largely  planted,  and,  as  is  always 
the  case,  vegetation  attracted  the  moisture,  and  the  mon- 
soon could  always  be  depended  upon.  Now,  since  these 
works  have  fallen  into  decay,  the  vegetation  has  disap- 
peared, and  the  monsoon  has  been  precarious  and  insuf- 
ficient." 

Every  year  we  read  in  the  press  of  destructive  floods 
taking  place  in  the  old  country,  and  these  floods  are 
almost  all  due  to  the  destruction  of  the  forests. 


*  On  Irrigation  in  India  in  Transactions  of  the  Institution  of  Civil  En- 
gineers.     Vol.  XXVII.— 1867-68. 
20 


306  IRRIGATION    CANALS    AND 

The  Indian  Government,  some  years  since,  recognized 
the  importance  of  this  matter,  and  organized  a  Forest 
Department,  somewhat  on  the  hasis  of  the  Public  Works 
Department,  and  already  the  good  results  of  this  policy 
are  admitted  by  all  those  in  India  who  have  given  any 
attention  to  the  subject. 

The  following  extract  on  the  Objects  of  Forest  Manage- 
ment* are  pertinent  here. 

"  Forest  management  has  two  objects  in  view: — 

"  1.  To  produce  and  reproduce  certain  useful  mate- 
rial. 

"2.  To  sustain  or  possibly  improve  certain  advan- 
tageous natural  conditions. 

"  In  the  first  case  we  treat  the  forest  as  a  crop,  which 
we  harvest  from  the  soil,  take  care  to  devote  the  land  to 
repeated  production  of  crops.  As  agriculture  is  prac- 
ticed for  the  purpose  of  producing  food  crops,  so  forestry 
is  in  the  first  place  concerned  in  the  production  of  wood 
crops,  both  attempting  to  create  values  from  the  soil. 

"  In  the  second  case  we  add  to  the  first  conception  of 
the  forest  as  a  crop,  another,  namely,  that  of  a  cover  to 
the  soil,  which,  under  certain  conditions,  and  in  certain 
locations,  bears  a  very  important  relation  to  other  con- 
ditions of  life. 

"  The  favorable  influence  which  the  forest  growth 
exerts  in  preventing  the  washing  of  the  soil  and  in  re- 
tarding the  torrential  flow  of  water,  and  also  in  checking 
the  winds  and  thereby  reducing  rapid  evaporation,  fur- 
ther in  facilitating  subterranean  drainage  and  influenc- 
ing climatic  conditions,  on  account  of  which  it  is  desirable 
to  preserve  certain  parts  of  the  natural  forest  growth 
and  extend  it  elsewhere;  this  favorable  influence  is  due 
to  the  dense  cover  of  foliage  mainly,  and  to  the  mechan- 

*  What  is  Forestry,  by  B.  E.  Fernow,  Chief  of  the  Division  of  Forestry, 
U.  S.  Department  of  Agriculture. 


OTHER    IRRIGATION    WORKS.  307 

ical  obstruction  which  the  trunks  and   the   litter  of  the 
forest  floor  offer. 

"  Any  kind  of  tree  growth  would  answer  this  purpose, 
and  all  the  forest  management  necessary  wotild^be  to 
simply  abstain  from  interference  and  leave  the  ground 
to  nature's  kindly  action. 

"  This  was  about  the  idea  of  the  first  advocates  of  for- 
est protection  in  this  country;  keep  out  fire,  keep  out 
cattle,  keep  out  the  ax  of  man,  and  nothing  more  is 
needed  to  keep  our  mountains  under  forest  cover  forever. 

"But  would  it  be  rational  and  would  it  be  necessary 
to  withdraw  a  large  territory  from  human  use  in  order 
to  secure  this  beneficial  influence?  It  would  be,  indeed, 
in  many  localities,  if  the  advantages  of  keeping  it  under 
forest  could  not  be  secured  simultaneously  with  the  em- 
ployment of  the  soil  for  useful  production,  but  rational 
forest  management  secures  both  the  advantages  of  favor- 
able forest  conditions  and  the  reproduction  of  useful 
material.  Not  only  is  the  rational  cutting  of  the  forest 
not  antagonistic  to  favorable  forest  conditions,  but  in 
skillful  hands  the  latter  can  be  improved  by  the  judi- 
cious use  of  the  ax. 

"  In  fact  the  demands  of  forest  preservation  on  the 
mountains  and  the  methods  of  forest  management  for 
profit  in  such  localities  are  more  or  less  harmonious; 
thus  the  absolute  clearing  of  the  forest  on  steep  hill- 
sides, which  is  apt  to  lead  to  dessicatioii  and  washing  of 
the  soil,  is  equally  detrimental  to  a  profitable  forest  man- 
agement, necessitating,  as  it  does,  leplaiitiiig  under  dif- 
ficulties. 

"Forest  preservation,  then,  does  not,  as  seems  to  be 
imagined  by  many,  exclude  proper  forest  utilization, 
but,  on  the  contrary,  these  may  we'll  go  hand  in  hand, 
preserving  forest  conditions  while  securing  valuable  ma- 
terial; the  first  requirement  only  modifies  the  manner, 
in  which  the  second  is  satisfied." 


308  IRRIGATION    CANALS    AND 

Article  61.     Rainfall. 

In  considering  the  growth  of  any  crop,  the  annual 
rainfall  should  not  so  much  bo  taken  into  account  as 
the  particular  portion  of  the  rainfall  that  fell  during  the 
irrigating  season,  and  its  distribution  during  that  time. 
In  the  majority  of  irrigation  countries  it  was  not  the 
deficiency  of  rainfall  throughout  the  year,  but  the  fact 
that  the  rain  fell  at  unsuitable  times,  that  rendered 
irrigation  essential.  In  some  famine  years  in  India,  the 
aggregate  of  the  rainfall  throughout  the  year  was  more 
than  ample  to  mature  the  crops,  but  it  was  almost  useless 
for  purposes  of  cultivation,  as  it  fell  at  the  wrong  time. 

The  Honorable  Alfred  Deakin,  M.  P.,  of  Victoria, 
states*: — 

"  The  arid  area  of  the  United  States,  by  the  terms  of 
Major  Powell's  definition,  includes  only  lands  where  the 
rainfall  is  under  20  inches  per  annum.  Over  the  great 
belt  in  which  irrigation  has  so  far  had  its  chief  develop- 
ment, the  record  for  a  series  of  years  gives  but  little 
more  than  half  that  quantity,  so  that  10  to  12  inches 
may  be  taken  as  a  fair  average,  though  the  extremes 
show  a  much  wider  variation.  In  Northern  California, 
and  among  the  mountains  to  the  east,  the  rainfall  rises 
to  40  inches,  while  in  the  deserts  of  Southern  California 
it  falls  to  four  inches. 

"In  Western  Kansas  the  fall,  not  infrequently, 
reaches  20  inches;  but  there,  as  with  us,  this  is  so 
irregular  that  the  farmer  who  relies  solely  upon  a 
natural  supply  loses  more  by  the  dry  seasons  than  he 
can  make  in  those  which  are  more  propitious.  The 
question  as  to  whether  settlement  increases  the  rainfall 
in  the  West,  as  it  has  increased  it  in  the  Mississippi 
Valley,  is  still  undetermined;  for,  though  popular 


Irrigation  in  Western  America,  Egypt  and  Italy. 


OTHER    IRRIGATION    WORKS.  309 

opinion  is  decidedly  in  the  affirmative,  the  State  En- 
gineer of  Colorado  points  out  that  official  records  so  far 
do  not  support  the  assertion.  The  exceptions  to  this 
are  that  Salt  Lake,  Utah,  appears  to  be  steadily_gaining 
in  depth,  and  that  dew  is  now  observed  at  Greeley,  in 
Northern  Colorado,  a  phenomenon  quite  unknown  until 
irrigation  had  been  practiced  for  some  years.  Nor  does 
the  mere  amount  of  rainfall  indicate  sufficiently  the 
necessity  for  an  artificial  supply  of  water,  unless  also 
the  seasons  in  which  it  falls  are  taken  into  account. 
In  parts  of  Dakota  and  Minnesota,  where  the  rainfall 
only  averages  about  20  inches,  dry  farming  is  carried 
on;  while  in  districts  of  Texas,  where  the  figures  are  as 
high,  it  would  be  impossible  to  obtain  the  same  results 
without  irrigation.  The  explanation  is  that  in  Dakota 
nearly  seventy-five  per  cent,  of  the  rain  falls  in  the 
season  when  the  farmer  needs  it,  as  against  about  fifty 
per  cent,  in  Texas.  Indeed,  a  gradation  may  be  ob- 
served in  this  scale  from  north  to  south,  since  in  Kansas 
some  sixty-five  per  cent,  of  the  rain  falls  in  the  spring, 
and  summer,  while  in  the  extreme  south,  as  at  San 
Diego,  only  half  of  the  whole  rainfall,  nine  inches,  falls 
in  the  spring,  and  is  consequently  useless  for  agricul- 
ture. There  is  some  irrigation  in  Dakota,  as  also  in 
Iowa  and  Wyoming,  but  not  nearly  so  much  as  in  the 
States  to  the  southward,  where,  even  if  the  rainfall  were 
as  high,  its  distribution  would  render  it  insufficient.  A 
glance  at  the  rainfall  statistics  of  Victoria  will  show 
that,  roughly  speaking,  one-half  of  it  might  be  included 
in  the  arid  area,  or  in  that  portion  of  the  sub-humid 
area  in  which  irrigation  is  little  less  essential. 

"  The  valleys  of  the  north  and  the  great  plains  of  the 
northwest,  as  well  as  the  belt  of  level  country  imme- 
diately to  the  north  and  west  of  Port  Phillip  and  the 
eastern  coast  of  Gippsland,  all  feel  the  need  of  a  regular 


310  IRRIGATION    CANALS    AND 

rainfall.  Still,  there  is  little  of  what  would  be  called  in 
America,  desert  land.  The  irrigated  districts  of  South- 
ern California  are  hotter  and  drier  than  any  portion  of 
our  colony,  resembling,  indeed,  the  climate  of  Algiers, 
rather  than  that  of  Southern  Europe.  There  it  is 
always  grassless  and  almost  rainless  in  many  seasons, 
while  in  the  country  beyond  Swan  Hill,  though  the 
rainfall  drops  to  ten  inches  and  even  less,  there  are  still 
numerous  seasons  in  which  a  fair  crop  of  grass  can  be 
obtained. 

In  Victoria,  the  difficulty  for  the  most  part  is,  that 
the  supply  is  sometimes  insufficient,  often  irregular,  or 
distributed  so  as  to  leave  the  crops  unsupplied  at  a  par- 
ticular period.  The  critical  season  is  generally  that  in 
which  the  crop  is  ripening,  toward  the  end  of  spring 
and  beginning  of  summer.  A  glance  at  our  rainfall 
statistics  for  the  last  four  years  gives  Horsham  an 
average  fall  of  about  sixteen  inches,  and  Kerong  of 
about  ten  inches,  of  which  at  the  first  rather  more,  and 
at  the  second  rather  less,  than  twenty-five  per  cent,  falls 
in  the  three  months,  September,  October  and  Novem- 
ber. If  an  emergency  watering  could  always  be  obtained 
during  this  period,  our  northern  farmers  would  be  sure 
of  a  harvest,  while,  as  it  is,  they  run  the  risk  of  a  com- 
plete failure  every  two  or  three  years.  So  far  as  rainfall 
is  concerned,  then,  Victoria  appears  to  be  in  as  good  a 
position  as  any  of  the  irrigated  States  except  Western 
Kansas.  Enough  rain  can  be  calculated  upon  to  ma- 
terially decrease  the  quantity  of  water  required  to  be 
artificially  supplied,  and,  in  exceptional  years,  to  ren- 
der irrigation  unessential.  Though  there  have  been, 
at  long  intervals,  years  in  which  this  state  of  things  has 
been  reached  in  South-western  America,  yet  they  are  so 
few  as  to  but  little  affect  the  average.  To  make  the 
comparison  perfect,  the  fall  in  the  various  seasons  in 


OTHER    IRRIGATION    WORKS.  311 

Victoria  would  need  to  be  tabulated  for  a  number  of  years. 
The  soil  of  its  several  districts  would  also  have  to  be 
carefully  analyzed,  for  it  is  to  be  remembered  that  one 
lesson  of  American  experience  is  that  soils  wrhich  to  the 
'  dry  farmer '  gave  but  faint  promise  of  any  productive- 
ness, have  proved  extremely  fertile  when  exposed  to  fre- 
quent saturation  and  continuous  cultivation.  The  quan- 
tity of  water  needed  is  also  affected  by  temperature,  for 
the  higher  it  reaches  the  more  water  is  demanded.  The 
loss  by  evaporation  has  not  yet  been  determined  for  the 
several  States,  but,  it  is  stated,  that  in  very  arid  tracts, 
it  rises  to  over  sixty  inches  per  annum. 

As  favored  in  rainfall  as  America,  Victoria  is  less 
favored  than  India,  Italy  or  France,  where  the  precipi- 
tation is  often  twice  as  great.  The  fact  that  irrigation 
is  resorted  to  under  such  conditions  should  be  borne  in 
mind,  when  we  consider  the  wisdom  of  securing  an 
artificial  supply  in  places  where  the  yearly  fall  is  often 
sufficient." 

The  Statistical  Review  of  the  Irrigation  Works  of 
India  for  1887-88,  has  the  following  on  rainfall: — 

"  It  has  not  infrequently  been  assumed  that  the 
probabilities  of  the  success  of  a  new  irrigation  project 
can  be  gauged  by  a  consideration  of  the  incidence  of 
the  rainfall  on  the  tract  commended.  The  rainfall  is, 
no  doubt,  one  of  the  chief  factors  to  be  considered,  but 
the  statistics  of  rainfall*  show  conclusively  that  there 
must  be  other  factors  of  at  least  equal,  if  not  greater, 
weight,  which  must  be  taken  into  account  in  determin- 
ing the  success  or  failure  of  an  irrigation  system.  For 
example,  the  rainfall  in  Bombay  is  generally  scanty, 
while  at  Madras  it  is  copious,  but  in  the  former  case  the 
irrigation  works  are  entirely  unremuiierative,  whereas 
in  Madras  they  are,  with  one  exception,  most  lucrative. 


Not  given  in  this  work. 


312  IRRIGATION    CANALS    AND 

"  Even  a  more  striking  instance  can  be  found  in 
Madras  itself.  The  Gauvery  Canals,  which  irrigate  a 
larger  area  and  pay  a  far  higher  percentage  on  capital 
than  any  other  system  in  India,  lie  in  a  district  where 
the  average  rainfall  is  53.9  inches  in  the  year;  whilst 
the  Kurnool  Canal,  which  is  the  most  conspicuous 
failure  of  all  irrigation  works  in  India,  lies  within  300 
miles  of  the  Cauvery,  in  the  same  Province,  in  a  tract 
where  the  average  rainfall  is  28.9  inches,  or  ->nly 
slightly  more  than  half  that  which  falls  on  the  Cauvery 
Canals.  The  causes  which  produce  these  striking  dif- 
ferences are  but  little  understood,  and  the  available 
statistics  afford  no  clue  to  them.  It  may,  however,  be 
said  that  in  Madras  the  temperature  is  generally  so 
equable  that  it  is  possible  to  grow  two,  and  even  three, 
crops  of  rice  on  the  same  field  during  the  year;  this  is 
not  possible  in  the  more  variable  climate  of  Bengal, 
where  the  total  rainfall  is  not  greatly  different  from  that 
of  Madras.  It  may  be  that  this  climatic  difference  ex- 
plains the  great  discrepancy  in  the  results  obtained  in 
the  two  Provinces.  It  should  also  be  noted  that  the 
actual  amount  of  the  rainfall  is  of  less  importance  than 
its  distribution.  Differences  in  soil  and  in  methods  of 
cultivation  have  also  great  weight  in  determining  the 
success  of  an  irrigation  project.  *  *  *  *  What- 
ever the  causes  may  be  which  should  determine  the 
results  obtained,  it  must  be  admitted  that  much  ignor- 
ance has  prevailed  concerning  them,  and  this  has  led  to 
the  construction  of  many  works  :vhich  have  signally 
failed  to  produce  the  results  which  were  anticipated  by 
their  projectors." 

The  following  extract  is  taken  from  Engineering  News 
of  May  11,  1889:- 

"  There  is  no  part  of  California  where  the  people  are 
more  in  earnest  about  irrigation  than  in  Colusa  County, 


OTHER    IRRIGATION    WORKS.  313 

California  (see  page  175),  where  they  have  an  annual 
rainfall  of  30  inches.  There  are  twro  classes  of  lands 
requiring  irrigation  here — one,  lands  which  will  yield 
crops  without  irrigation,  but  which  will  double  their 
yield  under  the  influence  of  a  regular  supply  of  wafer- 
say  a  cubic  foot  per  second  to  150  acres — during  the 
growing  season;  the  other,  desert  lands,  which  will 
yield  nothing  at  all  without  an  artificial  supply  of  water, 
either  from  a  system  of  irrigation  works  or  artesian 

wells." 

The  following  table  is  from  a  paper  by  Mr.  P.  O'Meara, 
M.  Inst.  C.  E.,  in  the  Transactions  of  the  Institution  of 
Civil  Engineers,  Vol.  LXXIII:— 


314 


IRRIGATION    CANALS    ANL> 


TABLE  19.     Statistics 


CROP. 

COUNTRY  OR  LOCALITY. 

4> 

P  ^  < 

tr**  85 
•     £.E2 
P 

*l 

l»| 

I 

IP 
53.1? 

Cereals,  wheat,  oats,  etc  
Cereals,  wheat,  oats,  etc  
Cereals,  wheat,  oats,  etc  
Cereals,  wheat,  oats,  etc  
Cereals,  wheat,  oats,  etc  
Cereals,  wheat,  oats,  etc  

Lower  Bengal,  Patna  
Southern  India,  Madras  .... 
Punjab,  Lahore  
North  Italy,  Piedmont  
Bouches-tlu-Rhone  
Hungary,  Debreczin  

Inches. 
2.21 
7.33 
4.29 
17.50 
6.30 
14  26 

Inches 
9 
9 
None 
None 
5 
None 

Inches 
11.21 
16.33 
4.29 
17.50 
11.30 
14  26 

2  to  4 
2  to  1 

None 
None 
1  to  3 

Cereals,  wheat,  oats,  etc  
Cereals,  wheat,  oats,  etc  
Cereals,  wheat,  oats,  etc  
Cereals,  wheat,  oats,  etc  .... 

Spain,  Alcalti  
Yorkshire,  Ferry  Bridge.  .  .  . 
Ireland,  Dublin  
Minnesota      

6 
12.73 
13.04 
10  35 

None 
None 
None 
None 

6. 
12.73 
13.04 
10  35 

None 
None 
None 
None 

Cereals  wheat  oats  etc  . 

11  23 

11  23 

None 

Cereals,  wheat,  oats,  etc  

Missouri,  Lower  

13 

None 

13 

None 

Cereals,  wheat,  oats,  etc  .... 

11  25 

None 

11  25 

None 

Cereals,  wheat,  oats,  etc  
Cereals,  wheat,  oats,  etc  
Rice  A  crop 

Colorado,  Poudre  Valley... 
(  Colorado,    Fort    Collins  ) 
i   Agricultural  College.       y 

5.67 
4.50 
25  33 

43 

None 
26 

48.67 
4.50 
51  33 

3 
None 

Rice,  B  crop   

Lower  Bengal,  Patna  

30  44 

40 

70  44 



Rice,  A  crop  
Rice,  B  crop  

Southern  India,  Madras.  .  .  . 
Southern  India,  Madras.  .  .  . 

10.31 
38  06 

26 

40 

36.31 
78  06 



Rice 

Spain,  Valencia  

7  29 

139 

146  29 

Rice  

North  Italy,  Piedmont  

25  19 

62 

87  19 

100 

Rice,  upland  

Japan,  Yeddo  
Lower  Bengal  Patna 

51. 

45  83 

None 
60 

51. 

105  83 

None 

•Sugar  Cane  

Southern  India,  Madras.  .  .  . 

48  56 

60 

108  56 

Sugar  Cane  

Sub  Himalayas,  Ranikhet.. 

48  56 

43  56 

None 

Sugar  Cane  

Jamaica  

40  80 

40  80 

None 

Natal  Ottawa  Estate 

38  78 

None 

38  78 

Sugar  Cane  

Mauritius  

47  to  90 

17  to  90 

Potatoes 

Colorado  Poudre  Valley  •  • 

6 

6 

12 

2 

Potatoes        

Ireland,  Dublin  

16 

None 

16 

Summer  Meadows          

Colorado,  Poudre  Valley... 

6 

43 

49 

Summer  Meadows            .... 

South  of  France  

9 

60 

69 

Italy  

22 

42 

64 

18 

Summer  Meadows    .   

Ireland,  Dublin  

8  22 

8  22 

Bouches-du-Rhone  

9 

37  5 

46  50 

g 

5 

11 

Indian  Corn  

North  Italy  

22. 

23.58 

45.58 

6 

Indian  Corn   

Hungary,  Debreczin  

12  79 

12  79 

Natal  Coast  Districts 

24  59 

24  59 

Cotton 

Central  India,  Sutna  

43 

43 

g 

None 

g 

None 

33  48 

None 

33  48 

None 

Vines               

California,  San  Bernardino.. 

2. 

3  to  12 

5  to  15 

2  to  4 

California,  Riverside  

10  05 

10. 

20  05 

California,  Riverside  

10.05 

.5 

10.55 

Orange  Trees 

Natal   Durban  

49  74 

None 

49.74 

None 

OTHER    IRRIGATION    WORKS. 


315 


of  Irrigation. 


IRRIGATION 

SKA.,  ON. 

HM 

*|f 

Mean 
Temper- 
ature. 

AUTHORITY. 

REMARKS. 

j 

Satn.  100. 
60  2 

0 

70  6 

Allan  Wilson 

Blandford's  rainfall  tables 

Dec.  to  Apr.,  inc  
Oct  to  Mar    inc 

65.6 
51 

79.7 
63 

Allan  Wilson  

Blandford's  rainfall  tables. 
Blandford's  rainfall  tables 

Col.  Baird  Smith  

George  Wilson  

Chiolich's  rainfall  tables 

George  Higgin  

Feb  to  July  inc 

50. 

Beardmore's  rainfall  tables 

Signal  Officers'  ramf'll  returns 

Signal  Offiders'  rainf  '11  returns 

Signal  Officers'  rainf  '11  returns 

Signal  Officers'  rainf  '11  returns 

The  Author 

Prof  Blount 

73 

86 

Allan  Wilson 

Aug.  to  Dec.,  inc  
June  to  Aug  ,  inc  

57! 
60. 

76.1 
86. 

W.  W.  Hunter  
Allan  Wilson  

63 

81. 

W  W.  Hunter  

Mar.  to  Sept.,  inc  
Mar.  to  Aug.,  inc  
Mar  to  Aug.,  inc  

*59 

72.3 

77  8 

George  Higgin  
Col.  Baird  Smith  
Con.  Gen  Van  Buren  .... 
Allan  Wilson 

139  refers  to  dotation,  not  to 
Total  annual  rainfall  given. 

Jan.  to  Dec.,  inc  

65. 

82.3 
60  3 

Allan  Wilson  
Col  Greathead                 , 

4  Mem.  of  Geological  ^ 

Manual  of  Geology. 

Jan.  to  Dec.,  inc..  — 





("Natal    Colonist,'') 
I         Oct.,  1879.         / 
The  Author 

The  Author  

The  Author 

The  Author  — 

(  One  cutting,  flooding  without 

George  Wilson  !  .  .  ! 

Col.  Baird  Smith  

Beardmore's  tables. 

George  Wilson 

Six  cuttirgs. 

'  'Colorado  Farmer"  .... 

/  Four  cuttings  in  third   and 

Col  Baird  Smith 

Chiolich. 

The  Author  

(  Rainfall  Returns  of  Durban 

65 

84  9 

Col.  Greathead  ... 

In  black  cotton  soil. 

May  to  Aug.,  me  

"  Colorado  Farmer".  .  .  . 

June  to  Aug.,  inc  
/  March  to  May,  and  > 

63. 

85.1 

George  Higgin  

f  W.    W.    Hunter,    "Imperial 
\     Gazetter,"  vol.  iv,  p.  48  J. 

(  one  irrigation  in  Oct  j 
Mar.  to  Sept.,  inc  

Report  

/Ordinary   flooding  system. 

Mar  to  Sept    inc 

Report 

J  Asbestine  sub-irrigation  sys- 

(     tern. 
Total  annual  rainfall. 

316  IRRIGATION    CANALS    AND 

Article  62.     Evaporation. 

In  countries  where  irrigation  is  conducted  on  an  ex- 
tensive scale,  the  evaporation,  that  is,  the  depth  of  water 
evaporated  annually,  does  not  materially  differ.  The 
records  of  experiments  given  below  in  America,  Italy, 
France,  Spain,  India  and  Egypt,  prove  this. 

The  records  of  evaporation  published  by  the  State 
Engineering  Department  of  California,  show  that  the 
mean  annual  evaporation  at  Kingsburg  bridge,  Tulare 
County,  California,  for  the  four  years  from  1881  to  1885 
was  3.85  feet  in  depth,  when  the  pan  was  in  the  river, 
which  is  equal  to  an  average  depth  of  one-eighth  of  an 
inch  per  day  for  a  whole  year. 

For  the  same  period  the  evaporation,  when  the  pan 
was  in  air,  was  4.96  feet  in  depth,  that  is,  equal  to  a 
mean  daily  depth  of  evaporation  throughout  the  year, 
of  less  than  three-sixteenths  of  an  inch  per  day. 

The  greatest  evaporation  was  in  the  month  of  August, 
when  it  was  more  than  one-sixth  of  the  evaporation  for 
the  whole  year.  The  average  for  this  month  is  one-third 
of  an  inch  per  day. 

During  the  months  when  the  largest  quantity  of  water 
is  used  for  irrigation  in  this  district,  the  table  shows 
that  the  mean  evaporation  was: — 

For  March  one-twelfth  of  an  inch  per  day. 

For  April  one-twelfth  of  an  inch  per  day. 

For  May  one-fifth  of  an  inch  per  day. 

Mr.  Walter  H.  Graves,  C.  E.,  states:—* 

lt  Evaporation  is  very  nearly  a  constant  quantity. 
*  *  *  *  *  *  *  * 

Observation  and  experiment  by  the  writer  in   various 
parts  of  Colorado  tend  to  show  that  evaporation  ranges 

*  Irrigation  and  Agricultural  Engineering  in  Transactions  of  the  Den- 
ver Society  of  Engineers — 1886. 


OTHER    IRRIGATION    WORKS.  317 

from  .088  to  .16  of  an  inch  per  day,  during  the  irrigat- 
ing season. " 

To  some  people  these  depths  of  evaporation  may  ap- 
pear very  small.  Let  us,  therefore,  examine_the_result 
of  observations  in  other  countries: — 

Colonel  Baird  Smith,  in  his  work  011  Italian  Irrigation 
states  that,  in  the  north  of  Italy  and  center  of  France, 
the  daily  evaporation  varies  from  one-twelfth  to  one- 
ninth  of  an  inch  per  day;  while  in  the  south  and  under 
the  influence  of  hot  winds  it  increases  to  between  one- 
sixth  and  oiie-fifth  of  an  inch  per  day. 

In  1867  the  total  evaporation  in  Madrid,  8pain,*»was 
sixty-five  inches  in  depth.  In  July  of  the  same  year 
according  to  the  returns  of  the  Royal  Observatory,  it  was 
13J  inches  in  depth  or  less  than  half  an  inch  per  day, 
and  in  May  of  the  same  year  it  was  only  one-quarter  of 
an  inch  per  day.  July  was  the  hottest  month  in  1867, 
and  it  was  estimated  that  during  this  month  the  total 
evaporation  of  the  Henares  Canal,  carrying  105  cubic 
feet  per  second,  or  5,250  miner's  inches,  under  a  fo-ur 
inch  head,  amounted  to  only  three-fourths  of  one  per 
cent,  of  the  total  flow. 

W.  W.  Culcheth,  C.  E.,f  states  as  the  result  of  his  in- 
vestigation on  the  Ganges  Canal  in  Northern  India,  that 
for  evaporation,  one-quarter  of  an  inch  per  day  over  the 
wetted  surface  may  be  taken  as  the  average  loss  from,  a 
canal. 

Dr.  Murray  Thompson's  J  experiments  in  the  hot  sea- 
son in  Northern  India,  with  a  decidedly  hot  wind  blow- 
ing, gave  an  average  result  of  half  an  inch  in  depth 
evaporated  in  twenty-four  hours. 


*  Irrigation  in  Spain,  by  George  Higgin,  M.  Inst.  C.  E.,   in  Transac- 
tions of  the  Institution  of  Civil  Engineers.     Volume  XXVII. — 1867-68. 
t  Transactions  of  the  Institution  of  Civil  Engineers.    Volume  LXXIX. 
J  Professional  Papers  on  Indian  Engineering.     Vol.  V.  Second  Series. 


318  IRRIGATION    CANALS    AND 

In  Hyderabad  in  the  Dec-can,  in  India,  it  was  found 
that  the  mean  evaporation  from  a  tank  or  reservoir  was 
0.165  inch  per  day. 

In  Nagpur,  in  India, *  the  total  depth  evaporated  from 
October,  1872,  to  June,  1873,  was  four  feet,  which,  dis- 
tributed over  the  period  of  the  experiment,  242  days, 
gives  an  average  depth  of  .0165  feet,  or  0.198  inch,  being 
about  one-fifth  of  an  inch  per  day. 

Colonel  Fyfe,  R  E.,f  states  that  in  large  reservoirs 
in  India,  about  two  square  miles  in  area,  the  amount  of 
evaporation,  that  he  made  allowance  for  was  about  three 
feet  in  depth  per  annum  in  the  Deccan,  and  something 
less  in  the  Concan  district  in  India. 

Major  Allan  Cunningham,  R.  E.,J  conducted  experi- 
ments, lasting  twenty-five  months,  from  1876-79,  to 
measure  the  evaporation  from  the  Ganges  Canal.  He 
states  that,  the  most  remarkable  feature  of  the  results  is 
their  extreme  smallness,  amounting  to  only  about  one- 
tenth  of  an  inch  per  day  on  the  average  near  Roorkee; 
whereas  one-half  inch  per  day  is  said  to  be  a  common 
rate  in  India  for  evaporation  on  land.  This  led  at  first 
to  the  suspicion  of  the  introduction  of  water  from  with- 
out; but  after  considering  the  possible  sources  of  this, 
namely,  leakage,  spray,  rain,  dew,  wilful  tampering,  it 
still  seems  that  the  results  may  be  accepted  as  substan- 
tially correct.  The  real  cause  of  the  small  evaporation 
appears  to  be  the  unusual  coldness  of  the  canal  water, 
for  instance,  on  May  22,  1877,  at  2:30  p.  M.,the  temper- 
ature of  the  air  was  165°  in  the  sun,  and  105°  in  the 
shade,  whilst  that  of  the  water  was  only  66°  inside  the 


*  The  Nagpur  Waterworks,  by  A.  E.  Binnie,  M.  Inst.  C.  E.,  in  Trans- 
actions Institution  of  Civil  Engineers.  Vol.  XXXIX. 

t  Transactions  Institution,  of  Civil  Engineers.    Vol.  XXXIX. — 1874-75. 

t  Kecent  Hydraulic  Experiments  in  Transactions  of  the  Institution  of 
Civil  Engineer:}.  Vol.  LXXI.— 1883. 


OTHER    IRRIGATION    WORKS.  319 

pan  and  65°  in  the  canal;  also  the  highest  recorded  tem- 
perature of  the  canal  water  was  only  75i°.  The  canal, 
in  fact,  takes  its  supply  from  the  Ganges,  a  snow-fed 
river,  at  its  exit  from  the  hills. 

It  was,  indeed,  found  that  the  canal  evaporation  in- 
creased with  distance  from  the  head  of  the  canal  at 
Hurdwar  on  the  Ganges.  Thus,  out  of  the  forty  results, 
twenty-eight  were  taken  near  Roorkee,  and  twelve  near 
Kamhera,  at  distances  of  eighteen  and  fifty-two  and  one- 
half  miles  from  the  head-works;  the  evaporation  at  the 
latter  was  much  the  larger,  comparing,  of  course,  sim- 
ilar seasons,  being  about  0.15  inch  against  0.10  inch  on 
an  average.  This  is,  no  doubt,  due  to  the  gradual  heat- 
ing of  the  water  under  the  hot  sun,  with  increased  dis- 
tance from  the  head. 

Taking  the  Roorkee  estimate  of  one-tenth  of  an  inch 
per  day,  the  total  evaporation  from  the  whole  surface  of 
the  canal  and  its  branches,  about  487,000,000  square  feet, 
amounts  to  about  forty-seven  cubic  feet  per  second, 
which  is  about  T|^  part  of  the  full  supply  of  the  canal, 
or  in  other  words,  ten  minutes  full  supply  daily. 

Little  connection  could  be  traced  between  the  evapor- 
ation and  the  meteorological  elements;  the  temperature 
of  the  water,  which  depends  chiefly  on  the  amount  of 
snow  water  in  the  Ganges,  being  probably  the  governing 
elemont. 

M.  Lemairesse's*  observations  at  Pondicherry,  in 
French  India,  give  a  daily  evaporation  of  from  three- 
tenths  to  half  an  inch  in  depth  per  day. 

Trautwine  made  observations  in  the  Tropics  and  he 
found  the  evaporation  from  ponds  of  pure  water  to  be  at 
the  rate  of  one-eighth  of  an  inch  per  day,  but  he 


*  The  Irrigation  of  French  India  in  Professional  Papers  on  Indian  En- 
gineering, Volume  I.     Second  Series. 


320 


IRRIGATION    CANALS    AND 


observes  that  the  air  in  that  region  is  highly  charged 
with  moisture. 

Mr.  Willcocks,  C.  E.,  in  his  work  on  Egyptian  Irriga- 
tion, states  that  Linant  Pasha  considered  the  evapora- 
tion in  Upper  Egypt,  as  about  equal  to  one-third  of  an 
inch  per  day  throughout  the  year.  As  a  result  of  his 
own  observations,  Mr.  Willcocks  gives  the  evaporation 
for  one  year  in  Upper  Egypt,  as  equal  to  six  feet  in 
depth,  and  in  Lower  Egypt,  as  equal  to  2.4  feet  in  depth. 

The  following  table  given  by  General  Scott  Moncrieff, 
R.  E.,  shows  the  general  conditions  of  temperature  and 
rainfall,  as  measured  at  Orange,  eighteen  miles  north  of 
Avignon,  and  at  Marseilles  in  France,  for  periods  of 
thirty  and  twenty  years  respectively: — 

TABLE  20.     Giving  temperature  and  rainfall  in  the  South  of  France. 


MEAN  TEMPEKATURE. 

Greatest  !  Greatest 

Annual    I    No.  of 

Summer 

Winter. 

Whole  y'r. 

degrees. 

degrees. 

in 
inches. 

in  the 
year. 

Orange  .  .  . 

71 

41 

56 

104 

5 

26.6 

96 

Marseilles. 

70 

45 

59 

87 

22 

12.8 

59 

This  table  shows,  in  a  striking  way,  the  modifying  in- 
fluence which  the  sea  has  over  climate,  the  extreme 
range  at  Marseilles  being  only  65°,  while  at  Orange, 
ninety-three  miles  distant,  it  is  99°.  The  annual  rain- 
fall, scanty  as  it  is,  does  not  fully  denote  the  extent  to 
which  this  part  of  France  suffers  from  drought,  for  at 
Avignon  it  often  happens  that  there  is  not  a  shower  of 
rain  during  the  three  hottest  months  of  June,  July  and 
August.  The  evaporation  in  the  plains  of  Languedoc, 
not  far  distant,  has  been  estimated  at  .079  inch  per  diem, 
and  it  is  probably  about  the  same  in  Provence. 


OTHER    IRRIGATION    WORKS.  321 

Article  63.     Percolation. 

Taking  a  broad  view  of  percolation  in  channels  and 
reservoirs,  through  their  beds  and  banks,  it  denotes 
infiltration,  seepage,  absorption  and  even  leakage.—  If 
the  leakage  is  of  a  large  quantity  through  a  bank  of 
earth,  that  bank  is  not  likely  to  last  long. 

"  In  every  new  canal,  through  sandy  loam,  the  loss 
by  percolation  at  first  is  very  serious.  Gradually  the 
ground  gets  saturated,  and  at  the  same  time  the  inter- 
stices of  the  porous  material  of  the  bed  and  banks  get 
filled  up  with  particles  of  clay,  which  diminish  the  per- 
colation. The  bed  of  a  canal  acts  as  an  elongated  filter, 
It  is  well  known  that  the  sand  of  a  water  works  filter 
bed,  if  not  periodically  washed,  or  if  not  replaced  with 
clean  sand,  the  interstices  between  the  particles  of  sand 
get  filled  with  silt,  and  the  filter  ceases  to  act,  or  acts  so 
slowly  as  to  be  practically  useless.  The  same  thing 
takes  place  in  a  canal,  but  at  a  slower  rate  than  in  a 
filter  bed.  There  is  less  deposit  in  an  irrigation  canal, 
in  the  same  time,  than  in  a  filter  bed,  as  the  greater 
part  of  the  finer  particles  of  silt  do  not  deposit  in  it,  but 
are  carried  in  suspension  until  the  water  reaches  the 
land  to  be  irrigated."* 

Mr.  Walter  H.  Graves,  C.  E.,  in  a  paper  read  before 
the  Society  of  Engineers  in  Denver,  Colorado,  in  1866, 
states: — 

"  The  factor  of  seepage  is  a  variable  one,  depending 
mostly  upon  the  nature  of  the  soil,  and  gradually  grows 
less  through  a  long  term  of  years.  Evaporation  is  very 
nearly  a  constant  quantity,  depending  on  the  altitude  of 
the  locality  and  the  prevailing  meteorological  conditions. 
In  calculating  for  the  loss  from  these  sources,  evapora- 

*  Report  on  the  proposed  Works  of  the  Tulare  Irrigation  District,  Cali- 
fornia, by  P.  J.  Flynii,  C.  E. 

21 


322  IRRIGATION    CANALS    AND 

tion  and  seepage,  in  the  older  canals  about  twelve  per 
cent,  should  be  deducted  from  the  carrying  capacity." 

Mr.  P.  O'Meara,  in  a  paper  in  the  Minutes  of  Pro- 
ceedings of  Inst.  C.  E.  for  1883,  states:— 

"  From  a  short  time  after  irrigation  is  established  in 
any  district,  the  quantity  of  water  required  will  grad- 
ually become  less,,  till  an  equilibrium  is  established 
between  the  amount  of  water  supplied  in  the  irrigating 
season,  and  the  quantity  removed  by  filtration  and 
evaporation. 

11  It  is  a  question  whether,  supposing  irrigation  were 
carried  out  to  its  full  extent  in  Colorado,  there  would  be 
any  loss  of  irrigating  power  other  than  that  due  to 
evaporation.  Losses  occurring  through  absorption  and 
surface  flow  are  not  final.  The  waters  absorbed  or 
wasted  reappear,  probably  with  undiminished  volume, 
lower  down  in  the  streams." 

Mr.  Boyd,  President  of  the  State  Board  of  Agriculture 
of  Colorado,  in  a  communication  to  the  Institution  of 
Civil  Engineers  in  1883,  states: — 

"  In  a  volume  of  six  cubic  feet  per  second  of  water 
flowing  in  a  lateral  two  miles  in  length,  not  less  than 
one-tenth  would  be  lost  by  soaking  and  evaporation." 

Mr.  E.  B.  Dorsey,  C.  E.,  in  a  paper  in  the  Transac- 
tions of  the  Am.  Soc.  C.  E.,  Volume  16,  1887,  states: — 

"That  in  some  of  the  Colorado  canals  the  loss  from 
evaporation  and  seepage  is  estimated  at  fifty  per  cent., 
which  is  excessive,  and  shows  that  the  canal  is  con- 
structed in  bad  soil,  or  that  there  must  be  something 
the  matter  with  the  construction.  Twenty  per  cent, 
ought  to  be,  under  ordinary  circumstances,  a  liberal  loss 
from  these  causes,  and  this  should  largely  diminish  as 
the  banks  and  bottom  of  the  canal  become  compact." 

Mr.  George  G.  Anderson,  C.  E.,*  made  measurements 

*  Transactions  of  the  American  Society  of  Civil  Engineers.  Volume 
XVI,  1887. 


OTHER    IRRIGATION    WORKS. 

on  the  High  Line  Canal,  in  Colorado,  in  the  middle  of 
July,  1886,  and  found  that  where  156  cubic  feet  per 
second  were  passing  into  the  head-gates  only  80  cubic 
feet  per  second  were  passing  a  point  45  miles  from  Jhe 
head-gates,  and  110  water  was  used  for  any  purpose  in 
the  intermediate  distance.  This  was  during  the  very 
hottest  and  driest  period  of  an  unusually  hot  and  dry 
summer  in  Colorado.  The  soil  through  which  this 
canal  passes  is  in  many  places  very  pervious.  There 
are  long  stretches  of  fine  sand,  and  in  places  the  canal 
bottom  is  in  rock  badly  fissured.  The  alignment  of  the 
canal  is  very  crooked,  and,  no  doubt,  a  great  loss  is  ex- 
perienced from  this  source.  It  is  to  be  expected  that 
this  serious  loss  will  gradually  diminish  as  the  canal 
bed  and  sides  become  compact  and  puddle  naturally. 
But  to  estimate  a  smaller  loss  from  these  causes  than 
twenty-five  per  cent,  would  scarcely  be  wise." 

In  a  paper  by  Mr.  C.  Greaves,*  he  showed  that  the  per- 
colation through  ordinary  soil,  as  compared  with  sand, 
was  only  about  one-third,  whereas  the  evaporation  from- 
a  surface  of  ordinary  soil  was   four  times  that  from  a 
surface  of  sand. 

Mr.  G.  F.  Kitso,  C.  E.,  in  his  description  of  the  irri- 
gation of  the  Canterbury  Plains,  New  Zealand,  states: — t 

"  Of  the  canals  in  alluvial  soil  that  the  percolation  is 
small,  as  the  constant  tendency  of  channels  is  to  silt  up 
and  to  become  more  water-tight." 

The  Martesana  Canal,  in  Italy,  of  a  capacity  of  981 
cubic  feet  per  second  and  twenty-eight  miles  in  length, 
was  estimated  to  have  lost  from  evaporation,  seepage, 
and  illegal  abstraction,  3.75  cubic  feet  per  second  per 
mile  of  canal.  We  have  here,  however,  an  additional 
source  of  loss,  that  by  illegal  abstraction. 


*  Transactions  of  the  Institution  of  Civil  Engineers.     Vol.  XLV,  1876. 
t  Transactions  of  the  Institution  of  Civil  Engineers.     Vol.  LXXIV,  1883. 


324  IRRIGATION    CANALS    AND 

Engineers  in  Lombardy  calculate  the  absorption  in 
each  watering,  of  about  four  inches  in  depth,  as  ranging 
from  one-third  to  one-half  of  the  total  quantity  of  water 
employed.  This  is  when  the  general  period  of  rotation 
is  about  fourteen  days.  From  observation,  it  has  been 
concluded  that  the  balance  of  the  water  reaches  chan- 
nels at  a  lower  level,  and  is  again  available  for  the  irri- 
gation of  lower  lands. 

On  the  Marseilles  Canal,  in  France,  the  losses  by  per- 
colation, evaporation,  and  at  the  settling  or  silt  basins, 
was  estimated  at  58  cubic  feet  per  second,  or  sixteen  per 
cent,  of  the  full  supply  of  353  cubic  feet  per  second. 

Ribera  estimated  the  total  loss  from  evaporation  and 
percolation  on  the  Isabella  Canal,  in  Spain,  a  masonry- 
lined  channel,  at  two  per  cent. 

Nadault  de  Buffoii  gives  the  average  percentage  of  loss 
on  canals  from  evaporation  and  percolation  at  15  per 
cent,  of  the  total  volume  carried.  He  does  not,  how- 
ever, mention  under  what  circumstances  such  a  percent- 
age may  be  expected. 

In  a  project  for  a  canal  from  the  Rhone,  in  France, 
of  over  2,000  cubic  feet  per  second,  it  was  calculated 
that  one-sixth  would  be  lost  by  evaporation,  percola- 
tion, etc. 

In  designing  the  Agra  Canal,  India,  the  loss  by  ab- 
sorption and  percolation  was  estimated  at  0.23  cubic  feet 
per  100  cubic  feet  per  mile  of  canal. 

After  the  completion  of  the  Ashti  Tank,  in  India,  ob- 
servations were  made,  and  it  was  found  that,  out  of  a 
supply  of  1,348,192,450  cubic  feet,  the  loss  from  evapora- 
tion, percolation  and  seepage  through  the  subsoil  of  the 
tank  combined,  amounted,  in  a  year,  to  233,220,240 
cubic  feet,  or  about  18  per  cent,  of  the  supply. 

In  the  Irrigation  Revenue  Report  of  Bombay  for 
1889-90,  it  is  stated,  as  the  result  of  gaugings,  that  the 


OTHER,    IRRIGATION    WORKS.  325 

Ashti  Tank  lost  during  the  year  by  evaporation,  absorp- 
tion, etc,  7.08  feet  in  depth  of  water  over  its  mean  area. 

In  the  same  Report  the  result  of  some  experiments 
in  the  loss  of  water  in  small  canals  was  given:— __ 

"  On  the  Palkhed  Canal,  14.87  miles  in  length,  there 
was  a  loss  by  leakage  and  evaporation  of  0.44  cubic  feet 
per  second  per  mile,  or  nearly  forty-eight  per  cent,  of 
the  supply. 

"  Before  taking  observations  for  leakage  experiments 
all  the  irrigating  outlets  were  closed;  gaugings  were  made 
with  ordinary  floats  and  were  read  in  each  mile,  which 
gave  the  average  result  of  loss  as  forty-eight  per  cent. 
The  only  feasible  way  of  reducing  the  leakage  seems  to 
be  to  keep  the  canals  clear  of  silt  arid  weeds.  No  other 
precautions  seem  practicable,  unless  in  the  way  of  man- 
aging all  outlets  better,  escapes  included. 

"  On  the  Ojhar  Tambat  Canal  (1.75  miles  in  length) 
there  was  a  loss  of  0.49  cubic  foot  per  second,  or  nearly 
thirty  per  cent,  of  the  supply." 

The  percentage  of  loss  on  the  above  canals  is  very 
great,  and  it  is  seldom  that  the  loss  is  so  great  in  a 
channel  carrying  silt,  and  that  has  been  in  use  for  some 
years. 

When  the  Ganges  Canal  was  flowing  at  least  6,000  cubic 
feet  per  second,  during  October,  1868,  a  year  of  drought, 
Colonel  H.  A.  Brownlow,  II.  E.,  estimated  the  loss  by 
absorption  at  twenty  per  cent.  He  states  that  the  es- 
timate of  loss  by  absorption  (twenty  per  cent.)  may  be 
considered  somewhat  low  for  a  year  of  drought,  but  that 
the  long  continued  high  supply  in  the  canal  must,  after 
some  time,  have  checked,  in  a  great  measure,  the  drain 
upon  itself  by  fully  saturating  the  adjacent  ground.  In 
fact,  the  greater  ease  with  which  the  gauges  were  kept 
up  during  October  and  November,  as  compared  with 
August  and  September,  was  a  matter  of  common  re- 
mark at  the  time. 


326  IRRIGATION    CANALS    AND 

In  the  original  design  of  the  Ganges  Canal  its  dis- 
charge, at  full  supply,  was  fixed  at  6,750  cubic  feet  per 
second.  Of  this  quantity,  it  was  assumed  that  1,000 
cubic  feet  per  second  would  be  lost  by  evaporation,  ab- 
sorption and  navigation,  and  that  the  remainder  would 
be  available  for  irrigation. 

Mr.  J.  S.  Beresford,  C.  E.,  states  as  the  result  of  In- 
dian experience,  that  old  canals  give  higher  duties  of 
water  than  new  canals,  or,  in  other  words,  that  there  is 
less  loss  of  water  through  the  material  forming  the 
channel  in  old  than  in  new  canals. 

Sir  B.  Baker,  C.  E.,  has  stated:—* 

"In  a  porous  soil  like  that  of  Egpyt,  ii  was  impossi- 
ble to  confine  water  simply  by  raising  the  bank,  because 
it  would  find  its  way  by  percolation  underneath,  and  it 
came  up  to  the  surface  and  washed  the  salt  out  and  killed 
vegetation.  He  had  ascertained  that  the  water  percola- 
ted at  the  rate  of  about  one  mile  from  the  river  in  a  week. 
That  is  to  say,  the  water  in.  a  well  one  mile  from  the 
river  would  begin  to  rise  about  a  week  after  the  water  in 
the  river  had  begun  to  rise.  It  would  be  seen  that  that 
was  an  exceedingly  important  matter  as  affecting  many 
questions  of  drainage  in  London.  If  the  tide  were  not 
of  twelve  hours  but  a  week's  interval,  the  greater  part 
of  the  low-lying  districts  in  London  would  be  much  in- 
jured by  the  percolation  of  tidal  water;  but  at  present 
it  did  not  follow  up  quickly  enough  to  exert  a  destructive 
hydrostatic  pressure  upon  the  thin  basement  walls  of 
houses  near  the  river." 


Transactions  of  the  Institution  of  Civil  Engineers.  Vol.  LXXIII,  1883. 


OTHER    IRRIGATION    WORKS.  327 

Article  64.     Drainage. 

As  a  rule,  the  drainage  of  irrigated  land  will  take  care 
of  itself,  if  the  natural  drainage  channels  are  left  free 
and  unobstructed.  If  it  is  found  that,  before  irrigation 
is  introduced  into  a  district,  the  country  is  flooded  and 
water-logged  after  rains,  then  it  is  likely  to  be  in  a  worse 
condition  after  the  land  is  irrigated,  and  drainage  will 
be  absolutely  necessary  for  the  success  of  the  irrigation 
and  the  health  of  the  district. 

In  many  cases  in  this  country,  although  irrigation 
dates  back  but  a  few  years,  the  natural  drainage  outlets 
have  been  converted  into  irrigation  channels,  with  the 
very  worst  results.  In.  this  way,  while  the  supply  to  be 
drained  off  had  been  increased  in  quantity,  the  drain- 
age channels  have  been  diminished  in  carrying  ca- 
pacity. 

If  the  subsoil  and  surface  water  cannot  escape  freely 
by  the  natural  channels,  super-saturation  follows,  and  the 
ground  becomes  water-logged.  Stagnant  water  is  very 
injurious  to  crops,  and  it  generates  disease  and  pesti- 
lence. Many  irrigation  districts  in  this  country  show 
the  evil  effects  of  too  much  irrigation  combined  with 
defective  drainage.  One  of  the  least  evils  is  a  dense 
and  troublesome  growth  of  weeds,  and  as  a  consequence 
waste  land.  The  cultivator  suffers  in.  health  and  pocket. 

To  construct  irrigation  canals  without  efficient  surface 
drainage,  and,  as  has  sometimes  been  the  case,  to  obstruct 
the  natural  drainage  of  the  country,  by  the  mproper 
location  of  canals,  without  making  adequate  provision 
for  allowing  the  surface  drainage  to  pass  away,  tend  to 
the  certain  formation  by  artificial  means,  of  those  evils 
that  exist  in  the  neighborhood  of  natural  swamps,  and 
hence,  the  importance  of  paying  every  attention  in  the 
preparation  of  projects,  and  the  construction  of  works, 


328  IRRIGATION    CANALS    AND 

with  the  view  of  avoiding  those -defects  which,  if  per- 
mitted in  the  first  instance,  will  certainly  have  to  be 
remedied  at  some  future  time,  at  considerable  cost,  both 
direct  and  indirect.  Whatever  excuses  may  have  been 
admissible  in  past  years,  when  the  science  of  construct- 
ing irrigation  works  was  less  understood  than  it  is  at  the 
present  day,  no  justification  can  now  be  pleaded  for  the 
repetition  of  similar  errors. 

On  the  reconstruction  of  the  Western  Jumna  Canal  in 
1820,  after  a  suspension  of  its  usefulness  for  more  than 
half  a  century,  the  original  mistake  of  a  bad  location 
was  repeated.  Instead  of  being  carried  along  the  water- 
shed lines  it  was  taken  through  the  drainage  of  the  coun- 
try, by  interfering  with  which,  serious  consequences  re- 
sulted in  the  creation  of  swamps  and  the  occasional  sub- 
mergence of  lands  which  might,  by  a  proper  location, 
have  been  brought  under  cultivation.  But  besides  ren- 
dering lands  uncultivatable,  and  so  curtailing  the  extent 
of  area  capable  of  growing  for  a  poor  and  highly  taxed 
people,  the  healthfulness  of  the  neighborhood  of  these 
swamps  became  seriously  impaired,  and  the  population 
was  found  to  be  on  the  decrease  in  the  vicinity.  In 
some  cases  land  became  waterlogged,  and  therefore  use- 
less, for  cultivation,  whilst  in  others  it  became  covered 
with  a  peculiar  saline  efflorescence,  known  as  alkali  in 
America,  and  reh  in  India.  After  investigating  the  above 
state  of  affairs,  the  Indian  Government  adopted  meas- 
ures to  abate  the  evils  of  the  defective  irrigation. 

Egypt  is  now  suffering  from  the  super-saturation  of 
its  land  and  want  of  proper  drainage.  Mr.  W.  Willcocks, 
Asso.  Inst.  C.  E.,  states: — * 

"  The  canals  are  so  disproportionately  large  during 
flood,  that  they  send  down  into  the  lower  lands  further 

*  Irrigation  in  Lower  Egypt  in  Transactions  of  the   Institution  of  Civil 
Engineers.     Vol.  LXXXVIII.— 1886-87. 


OTHER    IRRIGATION    WORKS.  329 

north  such  an  excessive  volume  of  water,  that  all  the 
canals,  escapes,  and  drainage  cuts  are  full  to  overflowing 
with  flood  water,  and  are  in  consequence  unable  to  per- 
form their  proper  functions.  The  country  daring  jlood 
is  divided  into  a  number  of  islands  surrounded  by  water 
at  a  high  level.  The  natural  consequence  is  that  salt 
efflorescence  is  greatly  on  the  increase  in  the  lands  under 
cultivation.'7 

Again  he  states:— 

"  The  conversion  of  all  the  drainage  cuts  into  irriga- 
tion canals,  was  all  that  was  needed  to  destroy  the  higher 
lands.  This  soon  followed." 

There  are  several  districts  in  California  where  a  few 
years  since  the  great  want  was  water,  but  where,  at  the 
present  time,  the  pressing  want  is  drainage.  A  small 
percentage  of  the  quantity  of  water  required  a  few  years 
since  to  irrigate  a  certain  area,  is  now  sufficient  to  insure 
a  crop,  as  the  sub-soil  is  so  saturated  with  water,  that 
very  little  flooding  is  now  required  in  comparison  with 
the  first  few  years  after  the  introduction  of  irrigation. 

The  same  thing  has  happened  in  Colorado.  Mr.  Gr. 
G.  Anderson,  C.  E.,  states: — * 

"  In  Colorado,  as  in  most  other  irrigation  countries, 
the  necessity  of  carrying  on  drainage  and  irrigation 
simultaneously  is  being  impressed  upon  practical  men 
more  and  more  every  year.  Although  it  is  a  rare  oc- 
currence when  these  works  are  successfully  conducted 
together,  it  is  regrettable  to  note  the  large  and  yearly 
increasing  area  of  low-lying  lands  going  to  waste,  and 
which  are  during  the  irrigating  season  stagnant  swamps 
breeding  disease.  The  frequency  of  typhoid  fever  and 
other  epidemics  in  the  fall  of  the  year,  is  doubtless  due 

*  The  Construction,  Maintenance  and  Operation  of  Large  Irrigation 
Canals  in  Transactions  of  the  Denver  Society  of  Civil  Engineers  and  Ar- 
chitects, Vol.  I. 


330  IRRIGATION    CANALS    AND 

to  this  cause,  so  that,  from  a  sanitary  point  of  view  at 
least,  drainage  must  be  speedily  undertaken." 

To  avoid  this  defective  irrigation,  some  means  should 
be  adopted  in  irrigation  districts,  to  prevent  the  use  of 
the  natural  drainage  channels,  for  any  purpose  what- 
ever, but  that  of  conveying  away  the  drainage  water 
that  reaches  them. 

A  good  effect  will  be  produced  by  restoring  to  their 
natural  state  such  drainage  outlets  as  have  been  con- 
verted into  irrigation  channels,  and,  if  required,  their 
carrying  capacity  can  be  increased  by  widening  and 
deepening  them  and  taking  out  the  sharp  bends.  An 
annual  clearance  of  debris,  brush  and  weeds  will  have  a 
good  effect  in  keeping  up  their  discharging  capacity. 

A  great  deal  has  been  written,  usually  by  mere  theo- 
rists, on  subsoil  drainage  in  connection  with  irrigation. 

In  an  able  paper  by  Mr.  H.  Scougall,  C.  E.,*  he 
states: — 

"  Now,  to  prevent  the  appearance  of  alkali  on  our 
lands,  water  must  be  used  sparingly  for  irrigation  pur- 
poses, and  not  a  drop  more  than  is  actually  necessary  to 
promote  the  growth  of  our  crops  should  be  poured  011 
the  land." 

This  is  quite  right  and  to  the  point.   Again  he  states: — 

"  No  good  system  of  irrigation  should  be  without 
drainage;  that  is,  drains  some  18  or  36- inches  below  the 
surface  which  will  carry  off  all  surplus  water." 

Whilst  it  is  a  fact  that  no  perfect  system  of  irrigation 
should  be  without  subsoil  drainage,  still  it  is  a  hard 
fact,  that  110  country  in  the  world  requiring  irrigation, 
can  at  the  present  moment  pay  for  such  a  system  as  is 
indicated  by  Mr.  Scougall  and  at  the  same  time  pay  for 
an  irrigation  system.  Doubtless,  exceptionally  small  areas 

*  The  Construction  of  Canals  for  Irrigation  Purposes  read  before  the 
Polytecthnic  Society  of  Utah,  March,  1891. 


OTHER    IRRIGATION    WORKS.  331 

can  be  pointed  out,  having  the  two  systems  in  opera- 
tion, but  what  we  refer  to  is  a  combined  system  covering 
a  large  area  such  as  is  commanded  by  the  Agra  Canal 
in  India,  or  the  Galloway  Canal  in  California. 

To  show  the  immense  magnitude  of  such  work  if  ap- 
plied to  the  irrigation  districts  of  India,  the  following 
extracts  are  taken  from  the  Statistical  Review  of  the 
Irrigation  Works  of  India,  1887-88:— 

At  the  end  of  the  financial  year,  1887-88,  there  were 
completed  in  India  5,520  miles  of  main  canals  and 
17,155  miles  of  distributaries,  and  these  works  irrigated 
over  10,000,000  acres.  This  includes  only  the  great 
works.  The  Minor  works  irrigated  2,000,000  acres  more. 
There  were,  therefore,  over  12,000,000  acres  of  land 
irrigated  in  1887-88.  The  subsoil  drainage  of  this 
area  of  land  could  not  be  carried  out,  to  a  successful 
completion,  by  any  country  in  the  world,  that  is,  as  a 
paying  investment. 

For  large  districts  the  subsoil  drainage  would  cost 
much  more  than  any  irrigation  system  by  open  earthen 
channels.  The  cost  at  present  prohibits  the  use  of  sub- 
soil drainage  on  an  extensive  scale. 

If  all  the  drainage  channels  are  improved  to  their 
outfall  into  some  river,  and  new  open  drainage  cuts  made 
where  required,  then  this  will,  as  a  rule,  prevent  surface 
flooding  and  super-saturation  of  the  soil,  and  this  is  as 
much  as  can  be  done  under  the  present  financial  condi- 
tion of  irrigated  countries. 


332  IRRIGATION    CANALS    AND 

Article  65.     Defective  Irrigation — Alkali — The  Effect  of 
Irrigation  on  Health. 

The  chief  objections  urged  against  irrigation  are  the 
unhealthfulness  that  follows  the  super-saturation  of  the 
soil,  and  the  injury  to  the  land  caused  by  alkali,  known 
in  india  as  "reh."  These  two  evils  can,  in  a  great 
measure,  be  avoided  by  using  only  just  sufficient  water 
to  mature  the  crop,  but  not  enough  to  saturate  the 
whole  sub-soil. 

The  returns  of  the  duty  of  water  in  America,  go  to 
prove  that,  as  a  rule,  too  much  water  is  used.  India, 
Egypt  and  America  are  suffering  from  alkali  in  the 
land,  and  the  evil  is  on  the  increase. 

Engineering  News  of  February  26th,  1887,  contains 
the  following  paragraph: — 

11  Professor  Hilgard,  of  the  State  University  of  Cali- 
fornia, warns  the  people  of  the  Pacific  Coast  that  land 
irrigation  may  be  overdone.  He  says  that  more  atten- 
tion must  be  paid  to  under-drainage,  and  sustains  his 
arguments  by  existing  conditions  in  the  irrigated  plains 
of  Fresno,  Tulare  and  Kern,  where  there  was  formerly 
no  moisture  within  thirty  or  forty  feet  of  the  surface, 
while  water  now  is  found  almost  anywhere  within  three 
to  five  feet.  The  roots  of  trees  and  vines  have  been 
forced  to  the  surface  and  the  alkali  accumulating  through 
centuries  is  also  brought  upward.  He  recommends  as 
a  remedy,  laws  providing  for  proper  location  and  con- 
struction of  the  ditches.7' 

Where  water  is  available  frequent  washing  of  the  sur- 
face of  alkali  land  will  do  much  to  reclaim  it.  The  land 
should  be  flooded  to  a  depth  of  a  few  inches,  and  left 
in  this  condition  for  a  few  days,  then  drawn  off,  and 
again  flooded  with  fresh  water,  and  this  operation 
should  be  repeated  until  the  surface  of  the  land  is 
cleared  of  alkali. 


OTHER    IRRIGATION    WORKS.  333 

Opinions  as  to  the  effect  of  irrigation  on  health  are 
somewhat  conflicting,  and  for  this  reason  we  give  below 
opinions  from  different  sources  on  this  subject. 

Dr.  H.  S.  Orine,  Member  of  the  State  Board  of  Health 
of  California,  states,  with  reference  to  the  influence  of 
Irrigation  on  Health*: — 

"  The  effect  of  the  irrigation  of  the  agricultural  lands, 
particularly  in  California,  upon  public  health  is  one  of 
growing  importance,  and  inasmuch  as  the  available 
evidence  bearing  upon  the  subject  is  somewhat  contra- 
dictory, it  is  necessary  to  note  the  conditions  of  locality, 
with  respect  to  soil,  temperature,  humidity  and  drain- 
age, wherever  irrigation  is  practiced. 

"  Although  irrigation  has  been  carried  on  in  Cali- 
fornia since  the  first  establishment  of  the  early  missions 
by  the  Franciscan  Fathers,  more  than  a  century  ago, 
very  little  progress  has  been  made  in  the  scientific 
application  of  the  system,  the  object  of  the  cultivator 
being  apparently  only  to  get  the  water  upon  his  land, 
without  regard  to  the  method  employed. 

The  application  of  the  water  used  in  irrigation  varies 
greatly  in  manner,  but  may  be  described  as  two  different 
methods,  viz:  first,  by  flooding  the  whole  surface  of  the 
land  from  open  ditches  (Zanjas);  and  second,  by  sub- 
irrigation,  that  is  a  conveyance  of  the  water  through 
pipes  beneath  the  surface  of  the  ground,  which  have 
openings  at  intervals,  protected  by  upright  pipes. 

So  far  as  the  effect  on  health  is  concerned  the  latter 
method  will  not  be  considered,  because  of  the  very  lim- 
ited extent  to  which  sub-irrigation  is  being  applied. 

In  the  case  of  the  application  of  water  by  flooding 
the  land  from  open  ditches,  the  various  reports  made  by 
impartial  authorities,  are,  in  some  respects,  conflicting. 

*  Appendix  to  the  Eighth  Biennial  Eeport  of  the  State  Board  of  Health, 
California. 


334  IRRIGATION    CANALS    AND 

For  instance,  in  Los  Angeles,  Ventura,  Santa  Barbara, 
San  Bernardino  and  San  Diego  counties,  where  irriga- 
tion has  been  carried  on  for  over  a  hundred  years,  the 
testimony  is  strong  to  the  point  that,  there  is  no  striking 
difference  in  the  amount  of  malarial  diseases,  whether 
irrigation  is  practised  or  not.  On  the  other  hand,  if 
we  consult  the  records  of  some  other  portions  of  Cali- 
fornia, we  find  an  increase  of  malarial  fevers  with  the 
increase  of  irrigation,  too  intimately  connected  to  be 
overlooked.  The  reasons  for  this  are  not  difficult  to  dis- 
cover. In  Los  Angeles  and  other  valleys  in  extreme 
Southern  California,  where  the  soil  is,  as  a  rule,  sandy 
or  gravelly  loam  of  unknown  depth,  the  water  in  irri- 
gation either  sinks  into  the  ground,  or,  if  there  is  much 
surface  slope,  immediately  drains  at,  or  near,  to  the  sur- 
face. In  such  sections  of  country  there  is  great  free- 
dom from  malarial  diseases.  Along  the  bottom  lands 
of  rivers  where  the  slope  is  insufficient  to  insure  good 
drainage,  or  where  the  soil  is  constantly  saturated,  the 
case  is  different.  Here  there  is  more  or  less  intermit- 
tent and  remittent  fever  during  the  warmer  season  of 
the  year.  In  the  case  of  swamp  or  overflowed  lands, 
especially  those  having  a  heavy  adobe  soil,  as  well  as 
those  which  remain  wet  and  boggy  from  the  winter 
rains,  and  are  in  summer  kept  in  a  saturated  condition 
by  artificial  means,  containing  also  an  excess  of  decom- 
posing vegetable  matter  and  many  stagnant  pools,  ma- 
larial diseases  of  the  most  pronounced  type  are  very 
prevalent.  In  such  localities  all  zymotic  diseases  are 
much  worse  in  summer  than  in  winter,  a  consequence 
which  naturally  results  from  the  high  tempt-rature  and 
increased  evaporation.  The  fact  that  the  people,  living 
in  these  low,  wet  adobe  sections  of  country,  are  depend- 
ent upon  impure  or  surface  water  for  drinking  arid  do- 
mestic purposes,  greatly  aggravates  the  difficulty.  In- 


OTHER    IRRIGATION    V.'ORKS.  335 

deed,  it  has  been  more  than  once  demonstrated  that 
people  living  in  a  "  fever  and  ague"  country  are  tol- 
erably exempt  from  the  fever  if  they  drink  only  pure 
water. 

In  referring  to  defective  irrigation  in  India,  the  En- 
gineer, London,  of  June  23,  1871,  has  the  following: — 

"It  is  notorious  that  wherever  irrigation  is  carried  on, 
cruel  malarious  diseases  as  surely  follow,  and  unless  Dr. 
CutlifiVs  report,  in  1869,  '  On  the  Sanitary  Condition  of 
the  lands  watered  by  the  Ganges  and  Jumna  Canals  ' 
very  greatly  errs,  it  is  very  questionable  whether  the 
aggregate  increased  mortality  in  a  number  of  years,  due 
to  irrigation,  does  not  even  exceed  what  that  of  a  pe- 
riodic famine  would  be. 

"There  are  very  extensive  portions  of  the  irrigated 
districts  where  subsoil  drainage  would  not  only  be  prac- 
ticable but  easy,  and  would  entirely  remedy  many  of 
the  existing  evils  distinctly  traceable  to  over  irrigation. 

"Nothing  beyond  an  extension  of  surface  drainage 
appears  even  yet  to  be  contemplated;  but  until  such 
works  are  regarded  as  merely  the  basis  of  subsoil  drain- 
age to  follow,  we  can  look  for  little  real  improvement  in 
the  system  of  agriculture  in  India." 

India  is  not  able  to  pay  now,  and  it  is  not  likely  that 
she  will  ever  be  able  to  pay,  fora  system  of  subsoil  drain- 
age. (See  Article  64.) 

On  the  subject  of  defective  irrigation,  we  have  more 
recent  information,  which  is  herewith  given  in  the  tes- 
timony of  Dr.  W.  W.  Hunter,  who  has  had  long  expe- 
rience in  India: — * 

"  Even  irrigation  itself  occasionally  displaced  a  popu- 
lation, and,  in  several  parts  of  India,  created  a  safeguard 
against  dearth  only  at  the  cost  of  desolating  the  villages 
by  malaria." 


Life  of  Lord  Mayo,  page  326,  Vol.  2. 


336  IRRIGATION    CANALS    AND 

We  have  additional  information  on  the  same  subject 
relative  to  Europe,  given  by  Mr.  G.  J.  Burke,  M.  Inst. 
C.  E.,*  who  had  a  large  experience  on  Irrigation  Works 
in  India:  He  was  of  the  opinion  that: — 

"  Drainage  and  irrigation  ought  to  go  together;  but 
how  many  engineers  had  seen  both  drainage  and  irri- 
gation properly  carried  out  at  the  same  time?  He  cer- 
tainly never  had.  He  had  seen  many  of  the  irrigated 
districts  in  Europe,  and  nearly  all  in  India,  and  the 
result  of  his  experience  was,  that  in  the  irrigating  sea- 
son, when  the  canals  were  full,  the  low-lying  lands 
became  swamps,  generating  disease  and  pestilence;  and 
he  had  110  doubt  that  a  good  deal  of  unhealthiness,  in 
countries  where  canal-irrigation  was  extensively  prac- 
tised, was  owing  to  the  neglect  of  drainage  to  carry  off 
the  surplus  water." 

Article  66.     Cost  of  Irrigation  per  acre  in  different 
countries. 

In  America,  as  a  rule,  the  land  and  water  go  together, 
and  the  only  expense  the  landowner  is  subject  to  is,  that 
of  maintenance  of  the  Canal. 

In  India,  on  the  contrary,  the  Government  owns  all 
the  great  canals  and  sells  the  water  to  the  cultivators. 

In  the  Statistical  Review  of  the  Irrigation  of  India, 
1887-88,  it  is  stated  that  the  rates  which  are  charged  for 
the  use  of  water  for  irrigation  vary  very  largely  in  dif- 
ferent parts  of  India  and  for  different  crops.  In  some 
cases  a  charge  is  made  for  a  single  watering,  and  in 
others  a  special  rate  is  taken  for  water  used  during  certain 
months,  but  generally  the  charge  is  an  average  rate  for 
irrigating  the  crop  to  maturity.  Excluding  very  excep- 

*Transactions   of  the   Institution  of   Civil    Engineers.     Vol.  LXXIII, 
1883. 


OTHER    IRRIGATION    WORKS. 


337 


tional  cases,  it  may  be  said  that  this  rate  varies  from 
forty  cents  an  acre  for  rice  crops  in  some  parts  of  Ben- 
gal and  Sind,  up  to  eight  dollars,  which  is  not  an  extreme 
rate  in  Bombay  for  sugar  cane  crops.  The  average  rate 
is  less  than  $1.20  an  acre.  (The  rupee  is  here  assumed 
as  equal  to  forty  cents.) 

In  the  Punjab  Revenue  Report  on  Irrigation  for  1889- 
90,  it  is  stated  that  the  average  water  rate  for  this  year, 
for  the  Western  Jumna  Canal  was  about  one  dollar  per 
acre. 

TABLE  21.     Giving  cost  of  irrigation  per  acre  in  different  countries. 


CANAL  OR  LOCALITY. 

COUNTRY. 

Rate  per 
acre  in 
dollars. 

AUTHORITY. 

Ganges  Canal 

India. 

$1  12 

F.  C  Danvers,  C  E     Trans  ICE    vol  33 

Eastern  Jumna  Canal.  .  . 
Western  Jumna  Canal.  .  . 
Baree  Doab  Canal  
India  (Rice)  
Madras  
North  West  Provinces  .  . 
Soonkasela  Canal  . 

India...  . 
India...  . 
India...  . 
India...  . 
India...  . 
India...  . 
India. 

1  16 
1  20 
1  17 
2  50 
3  00 
1  25 
3  00 

F.  C.  Danvers,  C.  E.    Trans.  I.  C.  E.,  vol.  33.' 
F.  C.  Danvers,  C.  E.    Trans.  I.  C.  E.,  vol.  33. 
F.  C.  Danvers,  C.  E.    Trans.  I.  C.  E.,  vol.  33. 
G.  J.  Burke,  C.  E.    Trans.  I.  C.  E.,  vol.  73. 
J.  B.  Morse,  C.  E.    Trans.  I.  C.  E.,  vol.  73 
J.  B.  Morse,  C.  E.    Trans.  I.  C.  E..  vol.  73. 
J.  H  Latham.  C  E     Trans  ICE    vol  34 

Ceylon  
Lower  Fgypt  
Alpines  Canal  

Ceylon.  . 
Egypt..  . 
France.  . 

50 
5  00 

$2  to  §3 

J.  B.  Morse,  C.  E.    Trans.  I.  C.  E.,  vol.  73. 
Gen.  Scott  Moncrieff—  19th  century—  Feb..  1885. 
George  Wilson,  C.  E.    Trans.  I.  C  E.,  vol  101 

Canal  from  Rhone  
Marseilles  Canal  
Verdon  Canal  

France.  . 
France.  . 
France.  . 

10.00 
6  50 
5  50 

Engineering,  29  June,  1877. 
George  Wilson,  C.  E.    Trans.  I.  C.  E.,  vol.  51 
George  Wilson,  C.  E.    Trans.  I  C  E  ,  vol  51 

Henares  Canal  
Esla  Canal  
Colorado  
Truckee  Valley,  Nevada.. 

Spain..  . 
Spain  
America  . 
America  . 

7  25 
5  75 

f  1  50  to  $3 
500 

George  Wilson,  C.  E.    Trans.  I.  C.  E.,  vol.  51. 
George  Wilson,  C.  E.    Trans.  I.  C.  E.,  vol.  51. 
R.  J.  Hinton—  Irrigation  in  the  United  States. 
Quoted  by  A.  D.  Foote,  C.  E. 

22 


338  IRRIGATION    CANALS    AND 

Article  67.     Annual  earning  of  a  cubic  foot  of  water  per 

second. 

The  following  extract  is  taken  from  a  work  by  the 
Honorable  Alfred  Deakin,  M.  P.,  of  Victoria.* 

"  At  Los  Angeles,  California,  water  is  sold  by  what  is 
called  a  "  head,"  which  under  their  loose  measurement, 
varies  from  two  cubic  feet  to  four  cubic  feet  per  second, 
at  $2  per  day  or  $1.50  per  night  in  summer  within  the 
city,  twice  that  price  outside  of  its  boundaries,  and  half 
the  price  in  winter.  At  Orange,  Southern  California, 
and  its  neighboring  settlements,  the  price  for  a  flow  of 
about  two  cubic  feet  per  second  is  12.50  for  twenty-four 
hours  or  $1.50  per  day  and  $1  per  night,  and  in  winter 
$1.50  for  twenty-four  hours.  At  Riverside  the  cost  is 
about  $1.90  per  day  or  $1.25  per  night,  for  a  cubic  foot 
per  second,  or  $3  for  the  twenty-four  hours.  These 
prices  varying  indefinitely  as  the  conditions  of  sale  vary, 
furnish  but  an  insecure  basis  for  any  generalization. 
Possibly  a  better  idea  of  the  importance  of  water,  than 
can  be  derived  from  any  list  of  purchases  and  rentals  in 
particular  places,  may  be  obtained  by  a  glance  at  its  cap- 
ital value.  It  has  been  calculated  that  the  flow  of  a 
cubic  foot  per  second  for  the  irrigating  season  of  all 
future  years  is  worth  from  $75  to  $125  per  acre  in  grain 
or  grazing  country,  to  $150  in  fruit  lands.  This  is  the 
price  paid  to  apply  such  a  stream  to  a  special  piece  of 
land  for  as  long  as  the  farmer  may  think  necessary,  the 
knowledge  that  an  excess  of  water  will  ruin  his  crop 
being  the  only  limit.  But  if  a  flow  of  a  cubic  foot  per 
second  were  brought  in  perpetuity  without  any  limit  to 
the  acreage  to  which  it  might  be  applied,  or  the  time  or 
circumstances  of  applying  it,  the  capital  value  of  such 
a  stream  in  Southern  California  to-day  would  be  at  least 
$40,000. 


*  Irrigation  in  Western  America,  Egypt  and  Italy. 


OTHER    IRRIGATION    WORKS. 


339 


The  following  table  is  compiled  from  various  sources: 

TABLE  22.     Showing  the  annual  earning  of  a  cubic  foot  per  second  in 
different  countries. 


NAME  OP  CANAL. 

Annual  earning 
of  a  cubi  :  foot 
per  second. 

AUTHORITIES. 

Ganges,  1866-67... 
Gauges,  1867-68.  .  . 
Ganges,  1868-69... 

Eastern  Jumna.  1866-67  .  .  . 
Eastern  Jumna,  1867-68... 

Eastern  Jumna,  1868-69.  .  . 
Western  Jumna  

£187 
195 
262 

261 
260 

326 
249 
164 
220 
295 
80 
75 
11000 
1875 
33 

Russel  Aitken.  C.  E.    Trans.  I.  C.  E.,  1871-2. 
Russel  Aitken,  C.  E.    Trans.  I.  C.  E.,  1871-2. 
Russel  Aitken,   C.  E.    Trans.  I.  C.   E.,   1871-2 
(year  of  drought). 
Russel  Aitken,  C.   E.    Trans.  I.   C.  E.,  1871  2 
(year  of  drought). 
Russel  Aitken,   C.  E.    Trans.  I.   C.  E.,  1871-2 
(year  of  drought). 
(Year  of  drought.) 
F.  C.  Danvers,  C.  E.  (year  of  drought). 
F.  C  Danvers,  C.  E.  (year  of  drought). 
Col.  W  H.  Greathead.    Trans.  I.  C.  E.,  vol.  35. 
Col.  W  H.  Greathead.    Trans.  I.  C.  E.,  vol.  35. 
Colonel  Baird  Smith. 
Colonel  Baird  Smith. 
George  Higgin,  C.  E.,  in  Trans.  I.  C.  E.,  vol.  27. 
George  Higgin,  C.  E.,  in  Trans.  I.  C.  E.,  vol.  27. 
H.  M.Wilson,  C.  E.,  in  Trans.  Am.  Soc.  C.  E.,1890. 

Ganges,  187071... 
Eastern  J  umna,  1870-71  .  .  . 
Piedmont 

Lombardy  

Henares,  Spain  

(Janals  in  Colorado  

Article  68.     Cost  of  Canals  per  Acre  Irrigated  and  per 
cubic  foot  per  second. 

The  following  table  is  taken  from  the  most  reliable 
sources  available,  but  no  doubt  there  are  errors  in  it  as 
the  account  of  cost  varies  by  different  authorities.  It 
is  merely  given  to  show  approximately  the  cost  of  ir- 
rigation canal  work  in  different  countries.  It  is  almost 
impossible  to  make  anything  like  an  accurate  comparison 
of  the  cost  of  works  in  different  countries,  there  are  so 
many  different  matters  entering  into  the  subject.  For 
example,  the  Ganges  Canal  is  estimated  to  have  cost 
$2,487,  per  cubic  foot  per  second,  whilst  the  Orissa  canals 
are  stated  to  have  cost  only  $1,000.  The  former  canal, 
however,  has  a  greater  number  per  mile  of  expensive 
works,  such  as  bridges,  falls,  regulators,  level  crossings, 
superpassages,  etc.  The  Orissa  system  of  canals  is 
situated  in  a  deltaic  country,  which  has  a  slope  some- 
what approaching  to  that  of  the  canals,  and,  as  a  ne- 
cessary consequence,  very  much  fewer  heavy  works  are 
required  than  on  the  Ganges  Canal  which  cross  the  drain- 
age of  the  lower  Himalayas. 


340 


IRRIGATION    CANALS    AND 


Again,  the  Henares  Canal,  in  Spain,  is  stated  to  have 
cost,  per  cubic  foot  per  second,  more  than  twelve  times 
as  much  as  the  Mussel  Slough  Canal  in  California,  but 
then  the  works  of  the  former  are  infinitely  superior  to 
the  latter.  It  is  very  likely  that  in  the  end  the  Henares 
Canal  will  be  the  cheaper  of  the  two,  as  its  annual  re- 
pairs will  cost  less,  and  the  works  being  permanent,  there 
will  be  no  renewals  of  bridges,  aqueducts,  etc. 

Table  23  is  compiled  from  a  table  given  by  Mr.  Ed- 
ward Bates  Dorsey,  M.  Am.  Soc.  E.  C.,*  and  from  other 
sources  of  information. 

TABLE  23.     Giving  the  cost  of  canals  per  acre  irrigated,  and  also  the 
cost  per  cubic  foot  per  second  of  discharge. 


NAME  OF  CANAL. 

COUNTRY. 

COST  OF  WORKS. 

Per  acre 
Irrigated. 

Per  cubic 
foot  per 
second  for 
water  used 
per  year. 

Western  Jumna  

India  .... 
India.  .  .  . 
India.  .  .  . 
India  
India  .... 
India.  .  .  . 
India  .... 
India.  .  .  . 
India  .... 
India  .... 
Colorado 
Colorado 
Colorado 
Colorado 
California 
California 
California 
California 
California 
California 
Idaho  .  .  . 
France.  .  . 
France..  . 
France.  .  . 
Spain..  .  . 

$10  88 
6  11 
26  50 
36  80 
28  80 
35  00 
32  00 
29  00 
39  00 
15  00 

10  83 

59  33 
6  25 
9  63 
52  75 
7  30 
7  18 
2  16 

35  67 
81  25 
46  66 

$1765 
2487 
1990 
2330 
2170 
1965 
2600 
1000 
280 
125 
549 
287 
1025 

549 

1507 
584 
277 
189 
4305 
2830 
15330 
7500 

Eastern  Jumna 

Sutlej  or  Sirhind  

Ganges  (with  navigation) 

Ganges  (without  navigation,  ^  deducted)  .... 
Baree  Doab   

Sone  

Bellary  Low  Level. 

Tomba^anoor 

The  Orissa  system  

Fort  Morgan  .  . 

Del  Norte. 

High  Level  .    ...                

Uncompahgre  

Cajon  .    .  .          

Seventy-six  .        

Santa  Clara  Valley  Irrigation  Co  

Riverside  

Mussel  Slouch 

King's  River  North  Side    . 

Idaho  Mining  &  Irrigation  Co.  (estimated).. 
Marseilles..                             

Carpentaras     

Verdon  

Henares 

Irrigation  in  Transactions  of  the  American  Society  of  Civil  Engineers.    Vol.  XVI,  1887. 


OTHER    IRRIGATION    WORKS.  341 

Article   69.     Measurement   of  Water. — Modules. — 

Meters. 

It  is  not  likely  that  the  greatest  duty  of  water  will  be 
reached  until  it  is  sold  by  measure.  It  will  then-4>6  to 
the  interest  of  the  user  of  water  to  economize  it  to  the 
fullest  extent. 

The  machines  used  to  measure  water  in  irrigation 
canals  are  generally  known  as  modules,  or  meters. 
The  principal  objects  to  be  sought  in  a  module  are: — 

1.  That    it   should  deliver    a    constant    quantity    of 
water  with  a  varying  depth  or  head  of  water  in  the  sup- 
ply channel. 

2.  That  it  should  expend  very  little  head  in  deliver- 
ing the  constant  quantity. 

3.  That  it  should  be  so  free  from  friction  as  not  to 
be  easily  deranged,  and  that  sand  or  silt   in  the  water 
would  not  affect  its  working. 

4.  That  it  should  be  cheap,  and  so  simple  in  con- 
struction  that    any   ordinary   mechanic    accustomed  to 
that  line  of  work  should  be  able  to  make  or  repair  one'. 

It  is  of  great  importance  that  there  -should  be  no 
intricate  or  concealed  machinery,  not  only  from  its 
liability  to  derangement,  but  because  there  is  then  so 
much  more  liability  to  an  alteration  in  the  discharge, 
without  its  being  noticed  by  the  official  in  charge.  It 
is  also  of  importance  to  have,  if  possible,  such  a  measure 
as  can  be  easily  inspected  by  those  using  the  water,  in 
order  that  each  man  may,  if  he  pleases,  satisfy  himself 
that  the  proper  quantity  of  water  is  flowing  into  his 
channel. 

Mr.  A.  D.  Foote,  M.  Am.  Soc.  C.  E.,  has  invented  a 
water  meter  which  goes  very  far  to  satisfy  all  the  above 
conditions.  Professor  L.  G.  Carpenter  gives  the  follow- 
ing description  of  this  water-meter.* 

*Oii  the  measurement  and  division  of  water. 


342 


IRRIGATION    CANALS    AND 


"  In  Figure  199,  A  is  the  main  ditch  with  a  gate  D,  forc- 
ing a  portion  of  the  water  into  box  B.  This  has  a  board 
on  the  side  towards  the  main  ditch,  with  its  upper  edge 
at  such  a  height  as  to  give  the  required  pressure  at  the 
orifice.  Then  if  the  water  be  forced  through  B,  the 
amount  in  excess  of  this  pressure  will  spill  back  into 
the  ditch.  If  the  box  B  is  made  long  enough,  and  the 
spill-board  be  sharp  edged,  nearly  all  the  excess  will 
spill  back  into  the  ditch  G,  thus  leaving  a  constant  head 
at  the  orifice." 


Fig.  199.    View  of  Water  Meter,  or  Module,  by  A.  D.  Foote,  C.  E. 

Mr.  Foote  thus  describes  this  meter: — * 

"  For  months  it  has  done  its  work  in  a  very  satisfac- 
tory manner,  seldom  clogging  and  never  varying  in  its 
delivery  to  an  appreciable  amount. 

"  The  whole  value  of  the  meter  depends  upon  the  long 


*A  Water-Meter  for  Irrigation  in  Transactions    of  the  American  Society 
of  Civil  Engineers,  Vol.  XVI— 1887. 


OTHER    IRRIGATION    WORKS.  343 

weir,  perhaps  better  described  as  an  excess  or  returning 
weir,  which  returns  all  excess  of  water  in  the  box  back 
to  the  ditch,  and  thus  keeps  the  pressure  at  the  delivery 
orifice  practically  uniform. 

l(  I  am  w7ell  aware  that  the  measurement  is  not  abso- 
lutely accurate  or  uniform;  but  if  it  is  remembered  that 
the  variation  in  delivery  is  only  as  the  square  root  of 
the  variation  in  head,  and  that,  owing  to  the  long  ex- 
cess weir  the  variation  in  head  is  only  a  small  portion 
of  the  variation  in  the  delivery  ditch,  it  will  be  seen 
that  actual  delivery  through  the  orifice  is  very  nearly 
uniform. 

"  There  need  be  but  an  inch  or  two  loss  of  grade  in  the 
ditch,  as  but  very  little  more  water  should  be  stopped 
than  is  delivered  through  the  orifice.  The  gate  or  other 
obstruction  in  the  ditch  should  back  the  water  suf- 
ficiently to  keep  the  excess  weir  clear,  and  at  the  same 
time  keep,  say,  a  quarter  of  an  inch  of  water  on  its  crest, 
and  the  surface  of  the  water  in  the  box  should  then  be 
exactly  four  inches  above  the  center  of  the  delivering 
orifice. 

11  The  principle  of  the  long  excess  weir  can  be  used  for 
delivering  water  through  an  open  notch  or  weir,  but  it  is 
more  accurate  with  a  pressure  or  head,  and  the  greater 
the  head  the  greater  the  accuracy,  as  will  readily  be 
seen . 

' '  Any  one  using  the  meter  will  naturally  adapt  it  to 
their  own  circumstances  and  desires.  It  is  cheaply  con- 
structed and  easily  placed  in  position,  costing  from  four 
to  six  dollars;  quickly  adjusted,  as  the  gates  do  not  have 
to  be  precisely  set;  needs  no  oversight  or  supervision  (if 
properly  locked  as  they  should  be)  until  a  change  in 
volume  is  desired;  will  deliver  a  large  or  small  quantity, 
which  is  a  great  convenience,  as  the  irrigator  usually 
wants  a  small  stream  continuously  and  a  large  stream  on 


344 


IRRIGATION    CANALS    AND 


irrigating  day;  is  riot  likely  to  clog,  as  floating  leaves 
and  grass  pass  over  the  excess  weir.  Half-sunken  leaves 
may  catch  in  the  orifice,  but  as  it  is  to  the  farmer's  in- 
terest to  keep  that  clear,  he  will  probably  attend  to  it. 

"  To  me,  however,  the  greatest  merit  the  method  pos- 
sesses (excepting  its  accuracy)  is  that  the  irrigator  him- 
self, with  his  pocket-rule,  can,  at  any  time,  demonstrate 
to  his  entire  satisfaction  that  he  is  getting  the  full 
amount  of  water  he  is  paying  for." 

Whilst  Mr.  Foote  believes  that  the  main  ditch  need 
not  lose  more  than  a  few  inches  fall,  that  is  from  A  to  C, 
Mr.  "VV.  H.  Graves,  C.  E.,  who  has  introduced  the  meter 
on  large  canals,  prefers  at  least  a  foot. 

The  module  adopted  011  the  Henares  and  Esla  canals, 
in  Spain, *  is  illustrated  in  Figures  200,  201,  202  and 
203. 

MODULE  IN  USE  ON  HENARES  CANAL 


F1G.200    n~ 


FIG.201 


CROSS  SECTION 


PLAN., 


"The  water  is  measured  by  being  discharged  over  a 
knife-edged  iron  weir,  shown  at  E,  Figure  201.  The 
water  flows  from  the  main  canal  into  the  distributary  A, 


irrigation  in  Spain,  by  Geogre  Higgin,  M.  Inst.  C.  E.,  in  Transactions 
of  the  Institution  of  Civil  Engineers.     Vol.  XXVII,  1867-68. 


OTHER    IRRIGATION    WORKS.  345 

Figure  202,  from  which  place  it  is  admitted  into  the 
chamber  (7,  by  a  sluice  working  in  the*  division  wall  B. 
From  G  the  water  passes  into  the  second  chamber  I), 
where  the  weir  is  fixed  at  E.  The  communication,  be- 
tween the  two  chambers,  G  and  D,  is  made  by  narrow 
slits,  and  the  water  arrives  at  the  weir  without  any  per- 
ceptible velocity,  and  perfectly  still.  The  weirs  vary 
from  3.28  feet  to  6.56  feet  in  breadth,  according  to  the 
quantity  of  water  required  to  be  passed  over.  On  the 
wall  of  the  outer  chamber  is  fixed  a  scale,  with  its  zero 
point  at  the  level  of  the  weir  edge,  and  by  means  of  this 
scale,  any  person  can  satisfy  himself  that  the  proper 
dotation  of  water  is  flowing  into  the  distribution  chan- 
nel. By  managing  the  sluice  the  guard  can  regulate 
to  a  nicety  the  height  of  water  to  be  passed  over  the 
weir.  This  module  has  several  good  points.  The  sys- 
tem of  measurement  is  that  which  possesses  the  most 
fixed  rules  in  hydraulics,  and  gives  the  most  constant 
results;  it  is  simple,  and  almost  incapable  of  derange- 
ment; it  will  serve  equally  well  for  turbid  waters  as  for. 
clear  ones;  it  can  take  off  the  waters  with  the  least  pos- 
sible loss  of  head — a  most  important  point  in  countries 
having  a  slight  surface  grade,  where  the  loss  of  a  few 
feet  of  headway  would  prevent  the  irrigation  of  many 
thousand  acres.  The  canal  official  can  see  at  a  glance 
whether  the  proper  amount  of  water  is  passing  into  the 
channel,  and  the  irrigators  can  satisfy  themselves  on  the 
same  point.  The  only  reasonable  objection  to  this  mo- 
dule is,  that  any  sudden  variation  in  the  head  of  water 
in  the  canal  will  affect  the  discharge,  which  will  con- 
tinue to  be  greater  or  less  than  it  ought  to  be,  according 
to  circumstances,  until  the  official  comes  round  again. 
This  is  undoubtedly  true,  *  *  *  but  in  most  well- 
regulated  canals  there  is  never  likely  to  be  any  serious 
variation  in  the  head  of  water  in  twenty-four  hours. 


346  IRRIGATION    CANALS    AND 

There  is,  or  should  be,  a  man  in  charge  of  the  head- 
works,  whose  special  duty  it  is  to  see  that  a  constant 
body  of  water  is  admitted  into  the  canal.  If  the  river 
is  flooded,  he  must  close  the  gates;  if  it  diminishes  he 
must  open  them.  The  water  taken  off  from  the  Henares 
and  Esla  canals, for  the  different  water-courses  is  a  fixed 
quantity,  and  that  passed  on  to  the  lower  portion  is, 
therefore,  likewise  variable.  The  only  cause  of  a  sud- 
den change  of  head  would  be  in  the  case  of  a  sudden  and 
heavy  fall  of  rain;  but  to  provide  against  this  at  every  one 
or  two  miles,  there  is  a  waste  weir, 'or  escape,  which 
would  immediately  carry  off  the  surplus  waters;  and 
even  if  a  little  more  was  discharged  through  the  module 
for  a  short  time,  no  inconvenience  would  result  from 
this." 


OTHER    IRRIGATION    WORKS.  347 

REPORT  ON  THE  PROPOSED  WORKS 

OF  THE 

TULARE    IRRIGATION"    DISTRICT,   CALIFORNIA, 

BY  P.  J.  FLYNN,   CIVIL  AND  HYDRAULIC  ENGINEER,    MAY,    1890. 


To  the  Honorable,  the  President  and  Board   of  Directors  of 

the  Tidare  Irrigation  District : 

GENTLEMEN: — In  accordance  with  your  instructions,  1 
have  investigated  several  routes,  in  order  to  select  the 
best  line,  for  a  canal  to  convey  500  cubic  feet  of  water 
per  second,  or  25,000  miner's  inches,  under  a  four  inch 
head,  from  the  Kaweah  River  to  the  site  of  your  pro- 
posed reservoir.  I  have  also,  in  this  report,  according 
to  your  instructions,  given  explanations  with  reference 
to  objections  made  to  certain  parts  of  the  works. 

I  herewith  submit  for  your  consideration  plans  and 
profiles  and  also  detailed  estimates  of  the  cost  of  these 
lines.  I  also  submit  tabular  statements  giving  details 
as  to  dimensions,  grades,  etc.,  of  each  line.  (Only  one 
of  these  tables  referring  to  Middle  Level  Canal,  No.  1, 
is  given  in  this  pamphlet.) 

ESTIMATES. 

The  estimated  cost  of  each  line  is  as  follows: 

High  Level  Canal $  744,456 

Middle  Level  Canal,  No.  1 659,273 

Middle  Level  Canal,  No.  2 664,94!) 

Middle  Level  Canal,  No.  3 669,389 

Low  Level  Canal 695,983 

Each  estimate  includes  the  cost  of  head  works  on  the 
Kaweah  River,  canal  line  to  reservoir,  including  tunnels, 
dam  and  outlet  works  at  reservoir,  canal  through  the 


348  IRRIGATION    CANALS    AND 

plains  from  the  reservoir  to  the  district  and  the  compen- 
sation to  be  paid  for  land  for  the  reservoir  and  canal 
.lines.  To  the  total  cost  of  the  above  twenty  per  cent, 
has  been  added,  that  is,  ten,  per  cent,  for  loss  on  sale  of 
bonds,  and  ten  per  cent,  for  contingencies.  This  twenty 
per  cent,  is  included  in  the  estimates  given  above. 

I  recommend  the  adoption  of  the  line  designated 
Middle  Level  Canal,  No.  1,  for  the  following  reasons: 

1.  It  is  the  cheapest  line. 

2.  With  the  exception  of  the  High  Level  Canal  there 
will  be  less  loss  of  water  by  percolation  than  on  the  other 
lines. 

3.  Also  with  the  exception  of  the  High  Level  Canal, 
the  cost  of  annual  repairs  will  be  less.     Briefly  stated, 
the  works  on  this  line  include  head  works  on  the  Kaweah 
River,  thence  one  mile  in  length  of  canal  to  a  flume  100 
feet  long  at  Horse  Creek,  thence  a  canal  2.75  miles  long 
to  a  tunnel  700  feet  long.      After   this   tunnel   comes  a 
canal  2,400  feet  in  length,  then  follows  another   tunnel 
1,100  feet  long  and  thence  4.59  miles  of  canal   to  reser- 
voir.    The  total  length  of  this  canal  is  9.15  miles.     No 
water  is  drawn  from  the  canal  between  the  river  and  the 
reservoir.     At  the  reservoir  there  is   a  large  dam  and 
outlet  works,  and  from  the  reservoir  a  canal  twenty-five 
miles  long  brings  the  water  to  and   through   the   Tulare 
District.     The  district  has  an  area  of  about  40,000  acres. 

PRICES. 

The  prices  for  work  are  fixed  as  near  the  current  rate 
of  labor  and  materials  as  could  be  ascertained. 

BORINGS  AND   TRIAL    PITS. 

In  order  to  make  an  accurate  estimate  borings  were 
taken,  with  a  light  steel  rod,  at  every  hundred  feet 
where  the  rock  was  cohered  with  earth.  This  work  was 
done  at  slight  expense  as  the  ground  at  the  time  was 


OTHER    IRRIGATION    WORKS.  349 

thoroughly  saturated  with  water.      A  few  trial  pits  were 
also  sunk. 

SIDE  SLOPES. 

The  side  slopes  in  cuttings  vary  with  the  nature_of  Jbhe 
material  cut  through.  In  fill  the  top  of  the  banks  is  6 
feet  in  width  and  1J  feet  above  the  surface  of  the  water. 
For  one  mile  from  the  head  works  the  side  slopes,  both 
inside  and  outside  the  canal,  are  2  horizontal  to  1  ver- 
tical. With  this  exception  the  banks  in  fill,  when  not 
protected  by  dry  rubble,  have  slope  sides  of  1J  to  1  on 
the  inside  of  the  canal,  and  2  to  1  on  the  outside.  I 
give  a  short  description  of  the  different  lines  reported  on. 

HIGH  LEVEL  CANAL. 

The  head  of  this  canal  is  on  the  left  bank  of  the  Ka- 
weah  River  in  Section  33,  T.  17  S.,  R.  28  E.  From  this 
point  this  canal  runs  via  A,  B,  C,  D,  E,  X,  F,  G,  M,  S, 
(see  map)  to  reservoir  at  S.  The  head  of  the  canal  for 
about  200  feet  is  through  granite,  and  for  the  next  5,000 
feet  to  Horse  Creek  at  B,  it  is  through  bowlders,  gravel 
and  sand.  For  about  3,000  feet  from  the  Kaweah  river 
this  line  is  in  cut  and  the  balance  is  in  fill,  about  500 
feet  in  13  feet  fill.  This  is  the  largest  fill  on  any  of  the 
lines. 

Horse  Creek  is  passed  by  a  flume  100  feet  long.  After 
this  for  500  feet  the  line  runs  along  a  bold  rocky  bluff, 
the  method  of  passing  which  is  described  under  the 
heading,  side-hill  work.  From  this  point  to  D  via  B,  C, 
D  (see  map),  7,400  feet  in  length,  the  line  has  frequent 
sharp  curves  and  runs  in  steep  side-hill  ground.  The 
channel  is  fourteen  feet  wide  at  bottom,  with  a  depth  of 
water  of  seven  feet,  and  with  side  slopes  of  J  horizontal 
to  1  vertical.  This  part  of  the  line  has  been  kept  as 
much  as  possible  in  five  feet  cut  to  prevent  loss  of  water 
by  percolation  and  breaches.  The  material  cut  through 


IRRIGATION    CANALS    AND 


is  sandy  loam,  usually  covering,  for  a  few  feet  in.  depth, 
decomposed  granite  or  solid  granite.  Solid  granite 
shows  at  the  surface  at  several  places,  and  for  about  half 
a  mile  after  leaving  Horse  Creek  Carlo  11,  there  are  large 
granite  bowlders  scattered  over  the  surface  of  the 
ground,  some  of  them  measuring  as  much  as  several 
cubic  yards.  In  order  to  avoid  the  steep  side-hill 


ground  from  C  to  V  via  C,  H,  I,  T,  K,  V  (see  map),  the 
line  C,  D,  E,  having  a  tunnel  D,  E,  7,500  feet  long,  was 
investigated.  By  this  tunnel  the  line  passes  through 
the  range  of  hills  that  run  parallel  to,  and  on  the  south 


OTHER    IRRIGATION    WORKS.  351 

side  of  the  Kaweah  River.  This  tunnel  is  in  granite. 
In  cross-section  it  has  a  level  bed  10  feet  3  inches  wide, 
with  vertical  sides  7  feet  high  and  a  segmental  top.  Its 
grade  is  1  in  300.  From  E  this  canal  runs  via  E,  X,  F, 
G,  M,  S,  for  3.7  miles  to  the  reservoir.  This  part  of  the 
line  is  on  fairly  level  ground,  through  sandy  loam,  and 
no  difficulty  is  met  with.  This  part  of  the  canal  has  a 
bed  width  of  thirty-three  feet,  a  depth  of  water  of  six 
feet,  the  side  slopes  next  to  the  water  1|-  to  1,  and  the 
outer  slope  2  to  1.  The  top  of  the  bank  is  six  feet  wide 
and  1|  feet  above  the  surface  of  the  water  in  the  canal. 
Its  grade  is  1  in  7,000,  and  its  mean  velocity  two  feet 
per  second.  The  total  length  of  this  line  is  7.58  miles. 

MIDDLE    LEVEL    CANAL    NO    1. 

This  canal,  which  is  the  line  recommended  for  adop- 
tion, is  the  same  as  the  High  Level  Canal  from  the  head 
works  on  the  Kaweah  river  at  A  (see  map)  to  C,  that  is 
for  about  2.5  miles.  From  C  to  V,  via  C,  H,  I,  T,  K,  V, 
it  runs  in  a  tortuous  course,  on  rough,  steep,  side-hill 
ground,  through  sandy  loam,  rotten  granite  and  solid 
granite.  Large  granite  bowlders  are  scattered  over  the 
surface  of  this  route.  It  will  be  necessary  not  only  to 
clear  the  line  of  these  bowlders,  but  also  to  clear  the  hill 
side  above  the  canal  line  of  all  large  bowlders  that  are 
likely,  during  rainy  weather,  to  roll  down  and  fall  into 
the  canal.  From  0  to  I  for  7,800  feet  the  canal  has  a 
bed  width  of  14  feet,  depth  of  water  of  7  feet,  side  slopes 
of  J  to  1,  and  a  grade  of  1  in  1000  or  5.28  feet  per  mile. 

At  I,  this  line  goes  by  a  tunnel  700  feet  long  in 
granite,  under  the  pass  near  Mr.  Marx's  house,  and  it 
emerges  from  this  tunnel  011  the  south  side  of  the  range 
of  hills  that  run  parallel  to,  and  south  of  the  Kaweah 
River.  The  lower  end  of  the  tunnel  is  situated  at  the 
head  of  Lime  Kiln  canon.  This  canon  joins  at  its  lower 


352  IRRIGATION    CANALS    AND 

end  with  the  plain  that  stretches  from  the  Lime  Kiln  to 
the  pass  M,  S  (see  map),  that  leads  to  the  reservoir. 
From  I,  this  line  runs  along  bold,  rocky  side-hill  ground 
for  2,400  feet  to  the  beginning  of  a  tunnel  in  granite 
1,100  feet  long.  The  method  of  passing  this  place  is  the 
same  as  that  adopted  in  passing  the  rocky  bluff  near 
Horse  Creek,  and  is  explained  under  the  heading  Side- 
Hill  Work.  From  the  beginning  of  the  700.  foot  tunnel 
to  the  lower  end  of  the  1,100  foot  tunnel,  the  line  runs 
through  granite.  Through  this  length  of  4,200  feet  the 
channel  has  the  same  dimensions  and  grade,  that  is,  in 
cross-section,  bottom  level  and  9  feet  in  width,  sides 
vertical  and  7  feet  high  to  surface  of  water.  The  grade 
for  the  tunnels  and  canal  for  this  length  of  4,200  feet  is 
1  in  200,  or  26.4  feet  per  mile.  The  velocity  in  this 
part  of  the  line  is  very  high,  8.15  feet  per  second,  but 
the  channel  is  well  able  to  bear  this  velocity,  as  it  is 
composed  of  granite  and  rubble  masonry,  the  latter 
having  a  coat  of  hard  plaster  composed  of  Portland 
cement  and  sand.  From  the  lower  end  of  the  1,100  foot 
tunnel  this  line  falls  22.6  feet  in  1,100  feet  by  13  vertical 
drops,  and  horizontal  reaches  to  K,  and  the  cross-sec- 
tional dimensions  are  the  same  as  the  last  section,  hav- 
ing a  bed  width  of  9  feet.  From  K  the  line  runs  for 
4,700  feet  to  V,  along  the  steep,  side-hill  ground,  through 
sandy  loam  and  rock.  The  channel  here  has  a  bed 
width  of  14  feet  with  sides  as  heretofore  described. 
From  V  this  line  runs  to  X,  and  thence  for  18,400  feet 
to  the  reservoir  via  V,  X,  F,  G,  M,  S,  and  from  X  to 
reservoir  it  is  the  same,  in  every  respect,  as  the  High 
Level  Canal.  At  V  the  depth  of  the  canal  changes  from 
7  to  6  feet,  and  the  surface  of  the  water  in  the  channel 
is  assumed  to  drop  one  foot  near  this  place.  From 
Horse  Creek  to  V  for  4.68  miles  the  canal  has  a  high 
velocity  sufficient  to  wash  away  loams  and  similar  soils. 


OTHER    IRRIGATION    WORKS. 


353 


Where  the  canal  channel,  14  feet  in  width,  passes 
through  these  materials  the  bed  and  banks  have  a  lining 
of  dry  rubble  in  order  to  prevent  erosion.  The  supe- 
riority of  this  line  over  the  Middle  Level  Canals,  Eos.  2 
and  3,  lies  in  its  smaller  cross-section  and  higher  grade 
from  K  to  V,  and  also  in  following  the  line  of  the  High 
Level  Canal  from  X  to  S.  The  depth  of  cutting  through 
the  pass  from  M  to  S  is  less  on  this  line  than  on  lines 
Nos.  2  and  3.  There  are  two  tunnels  on  this  line,  one 
of  700  and  the  other  of  1,100  feet  in  length.  The  indi- 
cations are  that  these  tunnels  are  in  solid  granite  and 
will  not  need  timbering  or  lining.  The  length  of  this 
line  is  9.15  miles. 

The  following  table  gives  the  dimensions  and  grades 
of  the  different  sections  of  the  Middle  Level  Canal,  No. 
1,  from  the  headworks  to  the  reservoir.  The  velocities 
are  computed  by  Kutter's  formula  with  n  =  .025.  The 
required  discharge  is  500  cubic  feet  per  second. 


• 

o 

"i 

8 

^; 

5-d 

, 

1 

a 

h 

a 

•S 

i 

$ 

jjSy 

n 

1-1 

I 

^ 

«^  « 

s 

2 

O    02 

i 

| 

d 

1 

0"- 

"GO 

53 

d 

O    *M 

i 

55 

1 

1 

2 

11 

Is 

5200 

2600 

2.03 

54. 

3.5 

1  to  2 

213.5 

2.49 

532-(i) 

100 

200 

26.4 

16. 

4. 

Vertical. 

64. 

8. 

513-(2) 

400 

200 

26.4 

9. 

7. 

Vertical. 

63. 

8.15 

513 

14200 

1000 

5.28 

14. 

7. 

i  to  1 

110.25 

4.65 

513 

700 

200 

26.4 

9. 

7. 

Vertical. 

63. 

8.15 

513-(3) 

2400 

200 

26.4 

9. 

7. 

Vertical. 

63. 

8.15 

513 

1100 

200 

26.4 

9. 

7. 

Vertical. 

63. 

8.15 

513 

1100 

9. 

7. 

Vertical. 

63. 

8.15 

513-(4) 

4700 

1000 

5.28 

14. 

I  to  1 

110.25 

4.65 

j  i  tj     \-s:  / 

r.i.r 

14400 

7000 

0.754 

33. 

6. 

H  to  1 

252. 

2. 

504-(5) 

4000 



20. 

7. 

1  to  1 

189. 

2.55 

500-(6) 

(1.)  This  section  begins  at  head  works. 

(2.)  Flume,  drop  of  0.5  feet. 

(3.)  Tunnel,  drop  at  tunnel  mouth  0.5  feet. 

(4.)  Level  reaches  and  vertical  drops. 

(5.)  Bed  continuous,  drop  1  foot  in  surface  water. 

(6.)  Level  reaches  and  vertical  drops. 
23 


354  IRRIGATION    CANALS    AND 

MIDDLE  LEVEL  CANAL,   NO.    2. 

This  canal  is  the  same,  in  every  respect,  as  Middle 
Level  Canal  No.  1,  from  the  head  works  at  A  to  K  (see 
map).  At  K  it  drops  four  feet  lower  than  Canal  No.  1, 
in  order  to  avoid  bad  ground  from  K  to  V.  From  K  to 
V  it  is  in  a  slope  of  1  in  7,000,  whereas  Canal  No.  1  has 
in  this  distance  a  slope  of  1  in  1,000.  From  V  this  line 
runs  to  the  reservoir  via  V,  G,  M,  S,  through  moderately 
level  ground.  This  part  of  the  line  is  in  sandy  loam 
and  there  is  no  difficulty  in  it.  There  are  two  tunnels 
on  this  line,  having  a  total  length  of  1,800  feet.  The 
length  of  this  line  is  nine  miles. 

MIDDLE  LEVEL  CANAL    NO.  3. 

This  canal  is  the  same,  in  every  respect,  as  Middle 
Level  Canal  No.  2,  from  the  head  works  at  A  to  the  res- 
ervoir at  S  (see  map),  with  the  exception  of  that  part 
from  I  to  K.  From  I  this  canal  runs  to  K  via  I,  R,  K, 
all  in  open  cutting. 

This  part  is  7,000  feet  in  length.  It  is  very  tortuous 
and  runs  on  steep  side-hill  ground,  through  sandy  loam 
and  rock.  Large  granite  bowlders  are  scattered  over  the 
surface  and  embedded  in  the  sandy  loam  that  covers  the 
bed  rock.  From  the  lower  end  of  the  700  foot  tunnel  at 
I,  the  line  falls  forty-three  feet  in  1,100  feet  by  fourteen 
vertical  drops  and  level  reaches.  Of  all  the  lines  .this 
has  the  shortest  length  of  tunnel,  700  feet.  From  the 
last  drop  below  I  it  runs  in  a  channel  of  the  same  di- 
mensions and  grade  that  Middle  Level  Canal  No.  2  has 
from  K  to  S,  and  it  joins  with  this  channel  on  the  same 
level  at  K.  It  has  the  greatest  length  of  any  of  the 
lines,  of  difficult,  broken,  side-hill  ground.  The  length 
of  this  line  is  9.38  miles. 


OTHER  IRRIGATION  WORKS.  355 

LOW  LEVEL  CANAL. 

The  headworks  of  this  canal  are  situated  on  the  left 
bank  of  the  Kaweah  River  in  Section  36,  T.  17  S.,  R.  27 
E.  The  river  is  here  over  500  feet  wide  and  it  is  divided 
into  two  channels.  The  great  body  of  the  water  flows 
in  the  channel  near  the  left  bank,  and  the  river  has  a 
decided  set  towards  this  bank.  There  is,  however, 
always  danger  in  such  a  wide  river  bed  that  the  main 
channel,  after  a  heavy  flood,  might  change  to  the  right 
bank.  In  such  a  case  it  would  be  very  expensive  work 
to  excavate  a  channel  from  the  right  branch  to  the  head 
works  of  this  canal.  The  head  works  of  Middle  Level 
Canal  No.  1  are  not  exposed  to  this  danger  as  explained 
further  on.  At  the  side  of  the  head  works  of  the  Low 
Level  Canal  the  left  branch  of  the  river  is  about  150 
wide  on  the  surface  of  the  water,  and  its  low  water 
depth  about  four  feet.  The  site  for  the  head  works  is  in 
solid  granite.  A  dam  in  the  river,  at  this  place,  would 
be  a  costly  work  as,  to  be  effective,  it  should  reach  from 
bank  to  bank. 

From  the  head  works  at  N  this  line  runs  via  N,  0,  P, 
L,  M,  S,  to  the  reservoir  at  S.  From  the  head  works  at 
N  the  line  runs  across  the  flat  above  the  left  bank  of  the 
river  to  the  base  of  the  hill  at  0.  This  line  is  1,850 
feet  in  length,  through  sandy  loam  and  hard-pan.  This 
part  has  a  bed  width  of  thirty-one  feet,  five  feet  in  depth 
of  water,  side  slopes  of  J  to  1  and  a  grade  of  1  in  2,500. 
From  O  this  line  runs  through  the  hill  in  a  tunnel  to  P 
for  2,850  feet  in  limestone.  From  P  the  line  runs 
through  the  plain  east  of  the  Wachumna  Hill,  thus 
avoiding  all  side-hill  work,  to  a  tunnel  under  the  pass, 
M,  S.  The  canal  through  the  plain  has  a  bottom  width 
of  thirty  feet,  a  depth  of  seven  feet  and  side  slopes  of  1 
to  1  with  a  grade  of  1  in  8,000. 

After  passing  through  the  tunnel  3, 300  feet  in  length, 


356  IRRIGATION    CANALS    AND 

the  line  runs  for  2,000  feet  more  to  the  reservoir  at  S, 
through  sandy  loam,  hard-pan  and  granite.  There  are 
two  tunnels  on  this  line  of  a  total  length  of  6,350  feet. 
The  tunnels  have  in  cross-section  a  level  bed  10  feet  3 
inches  in  width,  vertical  sides  with  a  depth  of  water 
seven  feet  and  a  segmental  roof.  The  grade  is  1  in  300. 
This  line  is  the  shortest  of  the  five  routes.  Its  length 
is  5.59  miles. 

TUNNELS. 

Under  certain  conditions  a  tunnel,  when  in  sound 
rock,  is  preferable  to  an  open  channel  for  conveying 
water.  The  conditions  are  that  no  water  is  required  to 
be  drawn  off  this  part  of  the  line,  and  that  a  heavy 
grade  can  be  given.  By  sound  rock  is  meant  rock  not 
subject  to  percolation,  to  any  appreciable  extent,  that 
will  stand  the  high  velocity  without  injury  by  erosion, 
and  also  that  will  not  require  lining  for  its  sides  or  arch- 
ing for  its  roof.  When,  in  addition,  a  steep  grade  can 
be  obtained,  a  high  velocity  can  be  given  to  the  water, 
and  the  cross-sectional  area  and  consequent  expense  re- 
duced. 

In  such  a  tunnel  the  loss  of  water  by  evaporation  and 
percolation  and  the  expense  of  maintenance  is  at  a 
minimum.  It  has  several  advantages  over  the  open 
channel  in  steep,  side-hill  ground.  Its  sides  and  bed  are 
impervious  to  water  and  it  is  covered  from  the  sunlight. 
It  shortens  the  line,  there  is  no  compensation  to  be  paid 
for  land,  and  it  does  not  interfere  with  or  cross  the 
drainage  of  the  country  on  the  surface.  Should  it  be 
required  at  any  future  time  to  increase  the  carrying 
capacity  of  the  canal,  the  discharge  of  the  tunnel  can 
be  increased,  without,  however,  increasing  its  dimen- 
sions. 

All  that  will  be  necessary  is  to  fill  all  the  hollows  be- 
tween the  projecting  ends  of  the  rocky  bed  and  sides 


OTHER    IRRIGATION    \VQRKS.  357 

with  good  cement  concrete,  and  after  this  to  give  a  coat 
of  good  plaster  to  the  surfaces  .in  contact  with  the  water 
and  make  them  smooth.  Although  the  section  will  be 
diminished,  still  the  velocity  and  consequent  xlis_charge 
will  be  doubled. 

Let  us  assume  the  loss  of  water  in  a  certain  length  of 
open  channel  at  six  per  cent,  of  the  total  flow.  If,  by 
adopting  a  tunnel  line,  the  loss  of  water  is  only  one  per 
cent.,  it  is  evident  that  it  would  pay  to  expend  the  value 
of  five  per  cent,  of  the  water  on  the  tunnel  line  above 
that  on  the  open  channel. 

Another  argument  in  favor  of  the  tunnel  is,  that  the 
amount  saved  yearly  in  maintenance  capitalized  could 
be  expended  on  the  tunnel  over  that  upon  the  open 
channel  in  order  to  give  a  fair  comparison  with  the  lat- 
ter. The  above  are  good  reasons  in  favor  of  the  High 
Level  Canal.  But,  on  the  other  hand,  there  are  two 
very  weighty  objections  to  this  route.  The  principal 
one  is  the  time  the  tunnel  would  take  in  construction. 

Under  favorable  circumstances,  and  with  granite  of 
medium  hardness,  this  tunnel  could  be  constructed  in. 
two  years;  but,  should  circumstances  turn  out  unfavor- 
able, and  very  hard  rock  as  well  as  water  be  encoun- 
tered, the  time  might  be  increased  to  four  years  and  the 
cost  of  driving  also  very  much  enhanced.  The  estimated 
cost  of  the  High  Level  Canal  is  $85,000  more  than  that 
of  the  Middle  Level  Canal,  No.  1.  If  that  were  the  only 
difference  and  after  taking  everything  into  considera- 
tion, then  in  my  opinion  the  High  Level  Canal  would 
be  the  best  of  the  five  lines,  but  on  account  of  the  uncer- 
tainty as  to  time  and  cost,  I  recommend  the  next  best 
line,  the  Middle  Level  Canal,  No.  1. 


358  IRRIGATION    CANALS    AND 

HEADWORKS    OF    MIDDLE     LEVEL    CANAL,    NO.     1. 

The  headworks  of  this  canal  are  situated  on  the  left 
bank  of  the  Kaweah  River,  in  Section  36,  T.  17  S.,  R. 
27  E.  At  this  site  the  Kaweah  River  is  well  adapted 
for  the  headworks  of  an  irrigation  canal,  in  fact,  it  would 
be  extremely  difficult  to  find  in  any  locality  a  more  fa- 
vorable location  for  such  a  work.  It  is  in  a  single 
channel,  in  a  well-defined,  permanent,  rocky  bed,  free 
from  sand,  silt,  gravel  and  bowlders.  The  depth  of  dig- 
ging at  the  head  is  only  about  eleven  feet  in  rock 
for  about  200  feet  in  length,  and  for  a  mile  from 
the  head  the  greatest  depth  of  digging  is  only  sixteen 
feet,  and  this  in  gravel  or  bowlders.  At  low  water  the 
greatest  width  of  the  river  at  this  place  is  about  150  feet, 
and  the  greatest  depth  about  four  feet.  At  high  water 
its  greatest  surface  width  is  probably  not  more  than  300 
feet.  At  about  500  feet  below  this  point  there  is  a  sudden 
fall  in  the  rocky  bed  of  the  river,  and  below  this  fall  the 
channel  widens  considerably,  to  800  feet  in  some  places; 
and  its  bed  is  covered  with  debris  composed  of  bowlders, 
gravel,  sand  and  silt.  At  low  stages  of  the  river,  in  the 
irrigating  season,  when  water  for  irrigation  is  most 
needed,  a  large  percentage  of  it  is  lost  by  percolation 
through  this  porous  bed.  If,  at  some  future  time,  in 
order  to  economize  water  and  reduce  expenses,  all  canals 
and  ditches  on  the  left  bank  of  the  Kaweah  River,  from 
Wachumna  Hill,  to  the  mouth  of  Cross  Creek,  should 
combine  and  take  out  the  water  from  the  river  in  one 
canal,  then  this  is  the  proper  location  for  the  headworks. 
With  a  good  permanent  dam  across  the  river  immedi- 
ately below  the  headworks,  every  cubic  foot  of  water 
coming  down  the  Kaweah  River  can  be  intercepted  at 
this  point  and  diverted  into  the  canal.  In  seasons  of 
great  drought,  when  every  cubic  foot  of  water  counts  for 
so  much,  it  is  of  the  utmost  importance  to  be  able  to 


OTHER    IRRIGATION    WORKS.  359 

utilize  the  water  that  now  runs  to  waste  in  the  porous 
river  bed.  The  canal  can  get  its  supply  without  a  dam 
in  the  river,  but  to  be  able  to  intercept  all  the  flow  in  the 
low  stages  of  the  river,  a  dam  would  be  necessary.  In 
order  to  prevent  the  silting  up  of  the  river  bed  above  the 
dam  to  its  crest,  and  the  choking  of  the  canal  head  by 
debris,  under-sluices  would  be  required.  If  the  above- 
mentioned  combination  of  ditch  owners  should  find  the 
building  of  such  a  dam  necessary,  then,  by  opening 
these  under-sluices  in  said  dam  when  required,  the  cur- 
rent will  carry  away  any  debris  deposited  opposite  the 
head  gates  and  keep  the  latter  clear. 

For  the  reasons  above  given  the  place  selected  for  the 
location  of  the  headworks  has  advantages  over  every 
other  place  that  I  have  seen  on  the  river.  These  ad- 
vantages are: — 

1.  Its  elevation   above  the  reservoir  is  sufficient  to 
give  a  steep  grade  to  the  canal  through  the  bad,  rocky 
ground,  and  thus  diminish  its  cross-section  and  expense. 

2.  The  river  is  in  a  single,  narrow  channel,  in  a  per^ 
maiient  bed  free  from  debris. 

3.  The  foundation  for  the    headworks   of   the  most 
stable  and  permanent  kind,  a  bed  of  solid  granite. 

4.  The  face  line   of  the  head  gates  can  be  located  on 
the  bank  of,  and  parallel  to  the  direction  of  the  current 
in  the  river,  and  by  this  means  it  can  be  kept  clear  of 
the  debris. 

5.  With  a  dam  across  the  river,  and  regulating  shut- 
ters at  the  head  of  canal,  there  will  be  a  command  of  the 
wrater  for  irrigation,  and  the  water  that  at  low  stages  of 
the  river  is  now  lost  in  the  bed  below  can  be  intercepted 
and  utilized.      By  closing  the  regulating  shutters  at  any 
time  the  supply  can  be  cut  off  from  .the  canal  and  its  bed 
laid  dry. 

6.  On  account  of  the  advantages  of  site   above  ex- 


360  IRRIGATION    CANALS    AND 

plained  permanent   head  works   can   be   constructed  at 
moderate  expense. 

RESERVOIR. 

The  reservoir  has  an  area,  when  full,  of  657  acres,  and 
it  contains  635,340,000  cubic  feet  of  water.  Its  water- 
shed has  an  area,  including  the  reservoir,  of  twenty 
square  miles.  It  has  an  earthen  dam  56  feet  high  at  the 
deepest  part.  Its  greatest  depth  of  water  is  50  feet,  and 
its  average  depth  22.2  feet.  The  dam  contains,  includ- 
ing puddle  and  rip-rap,  923,000  cubic  yards  of  material. 
Its  length  is  3,800  feet.  Its  top  is  16  feet  wide  and  6 
feet  above  the  level  of  crest  of  waste  weir  that  is  above 
the  surface  of  a  full  reservoir.  At  the  deepest  part  the 
dam  is  296  feet  wide  at  the  base.  Its  outer  slope  is  2 
horizontal  to  1  vertical,  and  its  inner  slope  facing  the 
water  3  to  1.  This  slope  is  to  be  faced  with  rip-rap. 
Under  the  center  of  the  dam,  and  for  its  whole  length, 
a  trench  is  to  be  sunk  to,  and  into  the  impervious 
clayey  loam,  and  afterwards  filled  with  puddle  to  about 
two  feet  above  the  surface  of  the  ground.  The  dam  will 
be  constructed  in  thin  layers  of  selected  clayey  loam 
well  consolidated.  An  ample  waste  weir  with  its  crest 
6  feet  below  the  top  of  the  dam  will  be  made  at  each  end 
of  the  dam,  and  it  will  be  arranged  also  so  that  the  out- 
let can  be  used  as  an  additional  waste  channel.  The 
outlet  will  be  through  a  tunnel  in  solid  rock  and  through 
the  spur  of  the  hill  at  the  south  end  of  the  dam.  The 
outlet  will  be  entirely  unconnected  with  the  dam,  which 
will  have  no  pipe  or  culvert  running  through  it.  The 
tower  or  chamber  connected  with  the  outlet  tunnel  will 
be  of  ample  dimensions  and  of  good  masonry. 

The  specifications  will  enter  into  more  details  about 
materials  and  mode  of  construction. 

The  dimensions  given  for  the  dam  are  those  adopted 


OTHER    IRRIGATION    WORKS.  361 

in  the  best  practice  throughout  the  world.  Theory  has 
little  to  do  with  the  design  of  an.  earthen  dam.  Ex- 
perience in  different  parts  of  the  world  has  shown  that 
writh  good  materials* and  careful  construction  a  dam  of 
the  above  dimensions  can  be  made  perfectly  ¥afe. 
Statements  have  been  made  that  there  is  110  necessity 
for  a  reservoir,  that  all  that  is  required  is  a  canal  from 
the  Kaweah  River  to  the  district,  that  there  has  hereto- 
fore been  ample  water  in  the  river  for  all  the  require- 
ments of  irrigation,  and  that  it,  therefore,  follows  that 
there  will  be  an  ample  supply  in  the  future. 

In  a  work  entitled  "  Physical  Data  and  Statistics  of 
California,"  published  by  the  State  Engineering  De- 
partment of  California,  there  are  tables  giving  the  flow 
of  the  Kaweah  River  at  Wachumna  Hill  for  six  years, 
from  1878  to  1884  inclusive.  The  drainage  area  of  the 
Kaweah  River  at  this  place  is  619  square  miles.  From 
these  tables  I  have  compiled  the  table  1  at  the  end  of 
this  report. 

For  those  more  accustomed  to  compute  the  flow  of 
water  by  miner's  inches  than  by  cubic  feet  per  second, 
I  give  the  equivalent  of  the  average  flow  in  that  unit  of 
measurement.  Fifty  of  these  inches  are  equivalent  to 
one  cubic  foot  per  second.  The  miner's  inch  used  is 
that  under  a  mean  head  of  four  inches. 

From  an  inspection  of  these  tables  it  will  be  evident 
that  the  expectation  of  ample  supply  in  a  very  dry  year, 
such,  for  instance,  as  1879,  is  not  well  founded. 

There  are  over  twenty  canals  and  ditches  drawing 
their  water  from  the  Kaw^eah  River  that  will  have  a 
prior  right  to  the  use  of  the  wTater,  and  to  which  they  are 
legally  entitled,  before  the  Tulare  Irrigation  District 
can  take  its  supply  from  that  river.  I  here  give  the 
names  of  some  of  these  canals.  They  are  Wachumna 
Canal,  People's  Consolidated,  Kaweah  Canal,  Farmers' 


362  IRRIGATION    CANALS    AND 

Ditch,  Evans'  Ditch,  Tulare  Canal,  Packwood,  Mill 
Creek,  Outside  Creek,  Cameron  Creek,  Lower  Cross 
Creek,  Ketchum  Ditch,  Hayes  Ditch,  Hambletoii  Ditch, 
Meherton  Ditch.  In  addition  to  the  ahove  there  are 
some  small  ditches  not  mentioned  in  this  list. 

The  table  shows  that  the  average  flow  of  the  river  in 
May,  1879,  was  only  774  feet.  This  is  the  month  in 
which  water  is  most  urgently  required  for  irrigation. 
The  only  safe  rule  by  which  to  arrive  at  the  available 
supply  in  a  year  of  drought  is,  to  take  the  least  flow  of 
the  river  when  water  is  most  in  demand.  The  canals 
and  ditches  mentioned  above  are  entitled  to  more  than 
774  cubic  feet  per  second.  It  is  very  likely  that  all  the 
canals  have  never  drawn  the  full  supply  to  which  they 
are  entitled  at  the  same  time  during  the  period  of  least 
supply.  The  time,  however,  is  sure  to  come  when  they 
will  do  so.  As  the  country  is  thickly  settled  the  de- 
mand for  water  will  increase  until  every  available  cubic 
foot  that  can  be  drawn  from  the  river  will  be  utilized  on 
the  land. 

Under  these  circumstances,  in  a  very  dry  year  it  is 
evident  that  there  will  not  be  sufficient  water  to  save 
the  crops  that  are  depending  for  their  supply  on  the 
canal  alone.  In  such  a  deplorable  state  of  affairs  the 
loss  to  the  district  in  a  year  of  great  drought  would  be 
more  than  the  total  cost  of  the  reservoir.  The  reservoir 
is  intended  to  insure  a  supply  during  the  period  of  the 
low  stage  of  the  river,  and  to  prevent  a  water  famine  on 
the  irrigable  lands  of  the  Tulare  Irrigation  District. 

The  canal  alone  no  doubt  will  bring  a  supply  during 
years  of  average  or  more  than  average  rainfall,  but  it  is 
sure  to  fail  when  most  required  in  seasons  of  great 
drought,  for  the  sufficient  reason  that  there  will  be  no 
water  supply. 

During  this  year  there  is  an  abundance  of  water  avail- 


OTHER    IRRIGATION    WORKS.  363 

able,  but  it  is  well  to  remember  that  we  are  after  hav- 
ing a  most  unusual  wet  winter,  and  it  is  of  still  more 
importance  to  remember  that  extraordinary  seasons  of 
drought  happen  periodically,  and  that  in  only  one  such 
season  the  use  of  the  storage  water  from  the  reservoir 
will  more  than  repay  the  expenditure  incurred  on  the 
dam.  Without  a  reservoir  in  such  a  year  the  canal  will 
be  a  dry  channel  unable  to  supply  the  perishing  crops 
with  water. 

In  the  months  between  irrigating  seasons,  when  there 
is  not  such  a  large  quantity  drawn  from  the  river  for 
irrigation,  the  water  that  now  runs  to  waste,  during  that 
period,  can  be  taken  to  fill  the  reservoir,  and  there  will 
thus  be  a  storage  reserve  to  be  used  only  when  it  is  ur- 
gently required  in  April  and  May.  In.  the  meantime, 
after  the  reservoir  is  full,  any  water  that  may  be  drawn 
from  the  river  can  be  allowed  to  flow  down  to  the  dis- 
trict and  be  used  for  irrigation.  For  instance:  Let  the 
reservoir  be  filled  at  the  end  of  the  irrigating  season, 
when  there  is  always  an  abundant  supply  of  water  in 
the  river  from  the  melting  snow.  Now,  from  this  pe- 
riod until  the  following  irrigating  season  in  April,  the 
supply  obtained  from  the  river  flows  to  and  out  of  the 
reservoir,  keeping  it  full.  In  case,  however,  that  the 
supply  from  the  river  should  at  any  time  in  a  dry  year 
fail,  there  will  still  be  a  full  reservoir  stored  for  use. 

In  average  years,  however,  the  reservoir  can  be  filled 
several  times  from  freshets  and  melting  snow,  and  by 
this  means  at  the  periods  of  irrigation  there  will  be  a 
larger  supply  available  at  certain  intervals  than  could 
be  obtained  from  the  river  by  the  canal  alone. 

The  above  facts  prove  that  to  have,  in  all  seasons,  an 
effective  system  of  irrigation  works  for  this  district,  a 
storage  reservoir  is  essential. 

Statements  have  been  made  that,  after   completion,  a 


364  IRRIGATION    CANALS    AND 

full  reservoir  would  not  be  capable  of  irrigating  one 
section,  that  is,  640  acres  of  land.  I  now  proceed  to 
prove  that  these  statements  very  much  exaggerate  the 
probable  loss  from  evaporation  and  percolation.  The 
quantity  of  water  required  to  irrigate  land  varies  very 
much.  The  number  of  acres  that  a  cubic  foot  per  second, 
or  fifty  miner's  inches  will  irrigate  is  known  as 

THE    DUTY    OP    WATER. 

This  varies  from  50  in  wheat  lands,  in  some  parts  of 
America,  to  1,600  in  fruit  land  in  Southern  California. 
When  this  high  duty  is  reached  the  water  is  conducted 
in  pipes,  and  it  is  used  with  economy. 

In  Elche,  in  Spain,  where  water  is  very  scarce,  a  cubic 
foot  per  second  irrigates  1,000  acres  of  land. 

General  Scott  MoncriefT,  R.  E.,  gives  the  duty  that 
can  be  got  out  of  one  cubic  foot  of  water  per  second  in 
Northern  India,  at  250  acres,  and  he  states  that  there  is 
frequently  fifty  days  between  each  irrigation. 

J.  S.  Beresford,  C.  E.,  states  that  five  inches  in  depth 
is  a  safe  allowance  for  one  watering  in  Northern  India. 
I  have  heard  an  experienced  irrigator  in  this  district, 
Tulare,  state  that  he  gave  over  six  feet  in  depth,  at  one 
watering,  to  a  piece  of  land  having  a  sandy  soil.  He 
had  an  unlimited  supply  of  water  and  the  quantity 
used  he  measured  from  the  supply  channel. 

Prof.  George  Davidson  in  his  Report  on  Irrigation, 
states  that: — 

"  The  amount  of  water  required  for  a  crop  of  wheat, 
barley,  maize,  etc.,  is  almost  identical  with  the  amount 
deduced  from  observations  in  the  great  valley  of  Cali- 
fornia, where  a  rainfall  of  10|  inches,  fairly  distributed, 
will  insure  a  crop/' 

"  The  capacity  of  a  canal  may,  therefore,  be  fairly 
estimated  by  assuming  that  12  inches  of  water  over  the 


OTHER    IRRIGATION    WORKS.  365 

surface  of  the  irrigable  land  will,  if  properly  applied, 
be  amply  sufficient  for  the  maturing  of  one  grain  crop; 
and  hence,  knowing  the  capacity  of  a  canal,  we  can  de- 
termine the  area  its  water  will  irrigate." 

In  one  of  his  lectures  before  the  Academy  of  Sciences 
at  San  Francisco,  Prof.  Davidson  says  on  the  same  sub- 
ject:— 

"  In  estimating  the  total  acres  that  can  be  irrigated 
from  a  given  supply,  allowance  must  be  made  for  the 
amount  lying  fallow,  woodland,  marsh,  roads,  streams, 
towns,  etc.  In  India,  the  average  under  cultivation 
each  season  is  only  one-third  of  any  given  area;  in  this 
country  we  might  safely  estimate  it  at  two-thirds  of  any 
irrigation  district." 

Experienced  irrigators  state  that  in  this  district,  as  a 
rule,  one  watering  some  time  in  May  will  save  the  crops, 
vines  and  fruit  trees,  and  that  fruit  trees  and  vines  can, 
with  careful  cultivation,  tide  over  one  dry  season,  with 
less  than  an  average  depth  of  six  inches  over  the  land. 
From  the  instances  given  it  will  be  seen  that  there  is  a 
wide  diversity  in  the  quantity  of  water  used  per  acre  to 
irrigate  land. 

The  reservoir,  when  full  to  the  level  or  waste  weir, 
will  contain  635,340,000  cubic  feet,  equivalent  to  4,752,- 
660,870  U.  S.  standard  gallons  of  water.  If  we  reduce 
this  quantity  by  thirty-six  per  cent,  for  evaporation  and 
percolation,  up  to  the  point  of  delivery  to  the  irrigators, 
we  have  left  for  purposes  of  irrigation  406, 617, 600  cubic 
feet.  This  is  the  quantity  that,  after  the  loss  by  evapo- 
ration and  seepage,  would  be  given  to  the  irrigators  for 
use  on  their  land  in  a  very  dry  year  in  April  or  May. 
This  quantity  is  sufficient  to  cover  11,200  acres  to  a 
depth  of  ten  inches  or  18,600  acres  to  a  depth  of  six 
inches. 

It  is  the  opinion  of  irrigators   well   informed   on  the 


366  IRRIGATION    CANALS    AND 

requirements  of  this  district,  that  this  quantity  of  water, 
used  with  economy,  would  be  sufficient  to  save  the  crops, 
fruit  trees  arid  vines,  and  tide  over  a  very  dry  year  in 
this  district. 

Doubtless,  during  the  first  few  years  after  the  opening 
of  the  canal  the  loss  of  water  will  be  more  than  thirty- 
six  per  cent.,  but  as  explained  under  the  heading  Evap- 
oration and  Percolation,  the  loss  from  seepage  will  de- 
crease with  the  age  of  the  canal  and  also  as  the  sub-soil 
gets  saturated  with  water.  The  Fresno  District  is  a  no- 
table instance  of  the  saturation  of  sub-soil.  A  small 
percentage  of  the  quantity  of  water  used  at  first  to  irri- 
gate a  certain  area  is  now  sufficient  to  insure  a  crop. 

I  am  informed  that  the  distribution  channels  that  I 
constructed  in  1877,  to  irrigate  the  twenty  acre  lots  of 
the  Central  California  Colony  at  Fresno,  have  since 
been  leveled  and  filled  up,  as  the  sub-soil  is  so  saturated 
with  water  that  very  little  flooding  is  now  required. 
There  is  a  deeper  porous  sub-soil  in  this  district  and, 
therefore,  it  is  not  likely  that  its  saturation  will  be  to 
the  same  extent  as  that  of  Fresno,  but  it  will  probably 
be  sufficient  to  diminish  the  quantity  of  water  now  re- 
quired to  irrigate  a  certain  area  in  this  district.  I  am 
informed  that  already  there  is  a  sensible  rise  in  the  sub- 
soil water,  in  and  around  Tulare,  which  is  attributed  to 
the  seepage  from  the  irrigation  channels  in  the  district. 

The  storage  capacity  of  one  full  reservoir,  at  a  time 
when  there  is  no  additional  supply  flowing  into  it  from 
the  Kaweah  River,  would  supply  a  canal  having  a  dis- 
charge of  500  cubic  feet  per  second  or  25,000  miner's 
inches  for  fifteen  days,  and,  when  there  is  no  outflow 
from  the  reservoir,  it  would  take  an  equal  length  of  time 
for  the  supply  canal  from  the  river  to  fill  it. 

In  the  period  of  greatest  demand  for  irrigation,  in 
years  of  ordinary  rainfall,  there  will  be  a  supply  from 


OTHER    IRRIGATION    WORKS.  307 

the  river,  flowing  into  the  reservoir  to  add  to  its  greatest 
storage  reserve.  This  supply  from  the  river  will  be  a 
material  addition  to  the  irrigating  capacity  of  the  reser- 
voir. 

As  an  instance  let  us  assume  that  during  the  pefToch 
of  irrigation  500  cubic  feet  per  second  are  drawn  from  a 
full  reservoir,  while  it  is,  at  the  same  time,  receivin;;- 
200  feet  per  second  in  excess  of  all  losses,  including  evap- 
oration and  percolation.  In  this  instance  the  reservoir 
and  canal  combined  will  give  a  supply  for  irrigation  of 
500  cubic  feet  per  second  for  twenty-four  and  one-half 
davs  and  will,  during  this  time,  cover  24,297  acres  to  a 
depth  of  one  foot. 

Without  the  reservoir  the  200  cubic  feet  per  second 
supplied  by  the  canal  would  cover  two-fifths  of  that  area, 
equal  to  9,719  acres. 

Without  the  additional  200  cubic  feet  per  second  by 
the  canal,  the  reservoir  alone  would  give  a  supply  of  500 
feet  per  second  for  fifteen  days,  and  would  cover  14,585 
acres  to  a  depth  of  one  foot.  I  append  a  table  showing 
the  great  increase  of  the  irrigable  capacity  of  the  reser- 
voir supplemented  by  a  supply  from  the  river. 

The  first  column  of  the  table  gives  the  number  of 
cubic  feet  per  second  supplied  by  the  canal  from  the 
river  to  the  reservoir. 

The  second  column  gives  the  number  of  days  supply 
for  irrigation  at  the  rate  of  500  cubic  feet  per  second, 
that  the  full  reservoir  of  635,340,000  cubic  feet  can  give 
when  supplemented  by  the  quantity  in  column  one. 

The  third  column  gives  the  number  of  acres  that  can 
be  covered  to  a  depth  of  one  foot  by  500  cubic  feet  per 
second,  in  the  number  of  days  given  in  second  column. 

The  fourth  column  gives  the  number  of  acres  that  the 
canal  supply  in  the  first  column,  but  without  the  reser- 


368 


IRRIGATION    CANALS    AND 


voir,  can  cover  to  a  depth  of  one  foot  in  the  number  of 
days  given  in  the  second  column. 


Canal  from  Kaweah 
River,  cubic  feet  per 
second. 

Reservoir  and  Canal 
gives  a  supply  of  5(iO 
cubic  feet  per  second 
for  days 

Reservoir  and  Canal 
cover  to  a  depth  of 
one  foot  acres 

Canal  alone  without  res- 
ervoir cover  to  a  depth 
of  one  foot  acres 

15. 

14,585 

50 

16.3 

16,202 

1,616 

100 

18.4 

18,235 

3,650 

150 

21. 

20,833 

6,248 

200 

24.5 

24,297 

9,719 

250 

29.4 

29,  157 

14,570 

2f5 

30. 

29,759 

15,174 

300 

36.8 

36,483 

21,897 

350 

49. 

48,595 

34,016 

400 

73.5 

72,899 

58,314 

450 

147. 

145,792 

131,206 

Aii  inspection  of  this  table  will  show  the  necessity  for 
a  reservoir  in  a  dry  year.  With  a  supply  of  100  cubic 
feet  per  second,  5,000  miner's  inches,  the  canal  alone, 
in  18.4  days  will  cover  3,650  acres  to  a  depth  of  one  foot, 
whilst  the  reservoir,  plus  this  supply,  will  irrigate  18,- 
248  acres  to  the  same  depth  in  the  same  time.  In  the 
former  case  there  would  be  blighted  crops  over  a  large 
area,  and  in  the  latter,  on  the  contrary,  there  would  be 
sufficient  water,  if  used  economically,  to  save  the  crops 
throughout  the  district. 


LOSS  FROM  EVAPORATION  AND  SEEPAGE. 

There  is  a  popular  belief  that  the  loss  of  water  from 
the  surfaces  of  rivers,  canals  and  reservoirs  is  much 
greater  than  is  actually  the  case. 

The  records  of  evaporation  at  Kingsburg  bridge, 
Tulare  county,  published  by  the  State  Engineering  de- 
partment of  California,  are  given  in  the  tables  at  the 
end  of  this  report.  From  Table  12  it  will  be  seen  that 
the  mean  annual  evaporation  at  Kingsburg  bridge  for 
the  four  years  from  1881  to  1885  is  3.85  feet  in  depth, 


OTHER    IRRIGATION    WORKS.  369 

when  the  pan  is  in  the  river,  which  is  equal  to  an  aver- 
age depth  of  one-eighth  of  an  inch  per  day  for  a  whole 
year.  For  the  same  period  the  evaporation,  when  the 
pan  was  in  air,  was  4.96  feet  in  depth,  that  is,  equal  to 
a  mean,  daily  depth  of  evaporation  throughout  theTyuar, 
of  less  than  three-sixteenths  of  an  inch  per  day. 

The  greatest  evaporation  is  in  the  month  of  August, 
when  it  is  more  than  one-sixth  of  the  evaporation  for 
the  whole  year.  The  average  for  this  month  is  one- 
third  of  an  inch  per  day. 

During  the  months  when  the  largest  quantity  of 
water  is  used  for  irrigation  in  this  district,  the  table 
shows  that  the  mean  evaporation  is:- — 

For  March  one-twelfth  of  an  inch  per  day. 

For  April  one-twelfth  of  an  inch  per  day. 

For  May  one-fifth  of  an.  inch  per  day. 

To  some  people  these  depths  of  evaporation  may  ap- 
pear very  small.  Let  us,  therefore,  examine  the  result 
of  observations  in  other  countries: — 

Colonel  Baird  Smith,  in  his  work  on  Italian  Irriga- 
tion, states  that  in  the  north  of  Italy  and  center  of 
France,  the  daily  evaporation  varies  from  one-twelfth  to 
one-ninth  of  an  inch  per  day;  while  in  the  south,  and 
under  the  influence  of  hot  winds,  it  increases  to  between 
one-sixth  and  one-fifth  of  an  inch  per  day. 

In  July,  1867,  the  evaporation  in  Madrid,  according 
to  the  returns  of  the  Royal  Observatory,  was  13J  inches 
in  depth,  or  less  than  half  an  inch  per  day;  and  in  May  of 
the  same  year  it  was  only  one-quarter  of  an  inch  per 
day.  July  was  the  hottest  month  in  1867,  and  it  was 
estimated  that  during  this  month  the  total  evaporation 
of  the  Henares  Canal,  carrying  105  cubic  feet  per 
second,  or  5,250  miner's  inches,  amounted  to  only  three- 
fourths  of  one  per  cent,  of  the  total  flow. 

W.  W.  Culcheth,  C.  E.,  states  as  the  result  of  his  in- 
24 


370  IRRIGATION    CANALS    AND 

vestigation  on  the  Ganges  Canal,  in  Northern  India, 
that  for  evaporation,  one-quarter  of  an  inch  per  day 
over  the  wetted  surface  may  be  taken  as  the  average  loss 
from  a  canal. 

Dr.  Murray  Thompson's  experiments  in  the  hot 
season  in  Northern  India,  with  a  decidedly  hot  wind 
blowing,  gave  an  average  result  of  half  an  inch  in  depth 
evaporated  in  twenty-four  hours. 

M.  Lemairesse's  observations  at  Pondicherry,  in 
French  India,  give  a  daily  evaporation  of  from  three- 
tenths  to  half  an  inch  in  depth  per  day. 

Trautwiiie  made  observations  in  the  Tropics  and  he 
found  the  evaporation  from  ponds  of  pure  water  to  be  at 
the  rate  of  one-eighth  of  an  inch  per  day,  but  he  ob- 
serves that  the  air  in  that  region  is  highly  charged  with 
moisture. 

The  above  quoted  observations,  although  they  do  not 
prove  the  accuracy  of  the  Kingsburg  experiments,  still 
they  give  results,  in  warm  climates,  so  close  to  each 
other  that,  for  all  practical  purposes,  the  latter  experi- 
ments may  be  accepted  as  correct. 

Let  us  now  investigate  the  loss  of  water  from  the 
reservoir  by  evaporation: — 

Let  us  assume  that  the  reservoir  is  full  on  the  31st  of 
July,  and  that  it  receives  no  water  from  the  river  from 
this  time  until  it  is  drawn  upon  for  watei  for  irrigation 
on  April  1st,  of  the  following  year.  Allow  twenty  days 
for  the  reservoir  to  become  empty  and  the  surface  ex- 
posed to  evaporation  during  this  time  is  equal  to  the 
surface  at  full  supply  for  half  the  time,  or  ten  days. 
From  Table  12  we  find  the  average  evaporation  for  four 
years  to  be  as  follows: — 


OTHP:R  IRRIGATION  WORKS.  371 

August 0.861  feet  in  depth 

September 0.615 

October 0.289 

November 0.174 

December 0.104 

January •  •  0.081 

February 0.091 

March,  one-third  of 0.075 


2.290 

This  shows  a  total  depth  evaporated  during  this  time 
equal  to  2.29  feet,  but  the  average  depth  of  the  reservoir 
at  full  supply  level  is  22.2  feet,  and  therefore  the  evapo- 
ration is,  in  round  numbers,  10  per  cent,  of  the  full 
reservoir. 

To  this  will  have  to  be  added  evaporation  of  twenty 
days  in  April  in  the  main  canal  and  small  ditches,  dur- 
ing the  time  that  the  reservoir  is  being  emptied. 

If  we  take  the  length  of  the  main  canal  at  40  miles 
and  the  width  of  water  surface  at  66  feet,  we  have  an 
area  of  320  acres,  and  if  we  allow  the  same  area  for  the 
smaller  ditches,  we  have  640  acres  for  twenty  days  in 
April,  or  in  round  numbers,  the  same  area  as  the  reser- 
voir, 657  acres.  The  evaporation,  Table  12,  is  given  as 
0.286  feet  in  depth  for  the  whole  month  of  April.  As 
the  water  from  the  reservoir  will  pass  over  the  heated, 
dry  bed  of  the  canal,  let  us  allow  the  evaporation  for  the 
twenty  days  in  April  to  be  as  much  as  that  of  the  whole 
month,  or  0.286  feet  in  depth.  This  depth  on  657  acres 
is  equal  to  1.3  per  cent,  of  the  mean  depth  of  the  reser- 
voir. This  shows  that  the  evaporation  from  reservoir 
and  channels  below  reservoir  is  less  in  volume  than  12 
per  cent,  of  the  full  reservoir. 

The  observations  made  last  year  at  the  Merced  reser- 
voir are  in  support  of  these  deductions,  the  evaporation 
having  been  found  less  than  that  given  in  Table  12. 

There  is  usually  more  loss  of  water  from  seepage  in 
earthen  channels  than  from  evaporation. 


372  IRRIGATION    CANALS    AND 

In  every  new  canal,  through  sandy  loam,  the  loss  by 
absorption  at  first  is  very  serious.  Gradually  the  ground 
gets  saturated,  and  at  the  same  time  the  interstices  of 
the  porous  material  of  the  bed  and  banks  get  filled  up 
with  particles  of  clay,  which  diminish  the  percolation. 
The  bed  of  a  canal  acts  as  an  elongated  filter.  It  is  well 
known  that  the  sand  of  a  water-works  filter-bed,  if  it  is 
not  periodically  washed,  or  replaced  with  clean  sand,  the 
interstices  between  its  particles  get  filled  with  silt 
and  the  filter  ceases  to  act,  or  acts  so  slowly  as  to  be 
practically  useless.  The  same  thing  takes  place  in.  a 
canal,  but  at  a  slower  rate  than  in  a  filter-bed.  There  is 
less  deposit  in  a  canal,  as  the  greater  part  of  the  finer 
particles  of  silt  do  not  subside  until  the  water  reaches 
the  land  to  be  irrigated. 

At  first,  after  the  completion  of  the  canal,  probably 
not  more  than  25  per  cent,  of  the  irrigable  land  of  the 
district  will  require  water.  Gradually,  as  time  goes  on, 
small  fruit  farms  will  increase  in  number,  and  with  them 
the  area  of  land  requiring  water.  At  the  same  time  the 
percentage  of  loss  by  percolation  will  decrease,  and  a 
larger  quantity  of  water  will  be  available  than  at  the  first 
opening  of  the  canal. 

The  loss  by  percolation  will  be  most  serions  in  the 
sandy  reaches  of  the  canal.  These  sections  can  be  taken 
in  hand  and  puddled,  one  at  a  time,  during  the  annual 
repairs,  and  the  puddling  thus  spread  over  several  years 
and  charged  to  the  working  expenses.  The  puddling 
can  be  done  at  a  time  when  the  canal  is  not  used  ior  irri- 
gation purposes. 

Ribera  estimated  the  total  loss  from  evaporation  and 
percolation  in  the  Isabella  Canal,  in  Spain,  a  masonry- 
lined  channel,  at  two  per  cent. 

In  the  Ganges  Canal,  in  India,  the  largest  irrigation 
canal  in  the  world,  with  a  discharge  of  5,000  cubic  feet 


OTHER    IRRIGATION    WORKS.  373 

per  second,  or  250,000  miner's  inches,  the  loss  in  1873- 
74,  from  all  causes,  including  evaporation,  seepage  and 
waste,  was  69  per  cent.  The  length  of  main  and  branch 
canals  of  all  sizes  was,  however,  at  this  time,_overji,000 
miles  long.  The  length  of  main  canal  alone  was  648 
miles.  It  is  admitted  that  water  was  very  wastefully 
used,  and  this,  together  with  the  great  length  of  the 
channels,  accounts  for  the  extraordinary  loss. 

P.  O'Meara,  C.  E.,  in  writing  on  the  results  of  irriga- 
tion in  this  country,  attributes  the  principal  loss  of  water 
to  evaporation,  and  he  states  that: — 

"  The  question  of  evaporation  was  so  important  that 
it  was  doubtful  if  any  loss  of  irrigating  power  occurred 
in  Colorado,  other  than  that  which  was  due  to  it.'7 

Walter  H.  Graves,  C.  E.,  in  a  paper  read  before  the 
Society  of  Engineers,  in  Denver,  Colorado,  in  1886, 
states: — 

"The  factor  of  seepage  is  a  variable  one,  depending 
mostly  upon  the  nature  of  the  soil,  and  gradually  grows 
less  through  a  long  term  of  years.  Evaporation  is  very 
nearly  a  constant  quantity.  *  *  *  In  calculating  the 
loss  from  these  sources  in  the  older  canals,  about  twelve 
per  cent,  should  be  deducted  from  the  carrying  capacity. 
Observation  and  experiment  by  the  writer  in  various 
parts  of  Colorado,  tend  to  show  that  evaporation  ranges 
from  .088  to  .16  of  an  inch  per  day,  during  the  irriga- 


ting season. 


From  what  has  been  written,  it  will  be  seen  that  the 
loss  from  evaporation  and  seepage  combined  varies  from 
twelve  per  cent,  in  Colorado  to  sixty-nine  per  cent,  in 
India.  As  a  fair  average,  therefore,  thirty-six  per  cent, 
is  allowed  for  the  loss  of  water  from  these  causes,  in 
computing  the  capacity  for  irrigation  of  the  reservoir 
and  canal  of  the  Tulare  Irrigation  District. 


374  IRRIGATION    CANALS    AND 

EARTHEN    DAMS. 

Several  objections,  not  founded  on  facts,  have  been 
urged  against  the  reservoir,  and  it  has  been  stated  that 
an  earthen  dam  cannot  be  built  to  impound  water  at  a 
depth  of  fifty  feet.  This  is  a  mistake.  Facts  prove  the 
contrary.  There  is  no  good  reason  to  doubt  that  what 
has  been  well  done  before  in  thousands  of  cases,  in  put- 
ting a  large  quantity  of  good  clayey  loam  together  to 
retain  water,  can  be  done  again. 

There  are  thousands  of  earthen  |dams  in  different 
parts  of  the  world,  impounding  water  to  a  depth  of  50  feet 
or  more,  that  are  in  use  to-day,  and  that  possess  as  much 
stability  as  the  modern  brick  houses  in  which  are  living 
millions  of  people.  Properly  constructed,  on  a  good 
foundation,  and  with  a  waste  weir  large  enough  to  carry 
off  the  greatest  rainfall,  an  earthen,  dam  can  be  con- 
structed to  have  as  much  stability,  and  as  long  a  life,  as 
any  iron  railroad  bridge  in  the  country. 

An  ample  waste  weir  is  the  safety-valve  of  a  reservoir. 

If,  by  any  means,  the  waste  weir  is  contracted  so  as  to 
diminish  its  discharging  capacity  below  its  requirement 
for  the  maximum  rainfall,  then  the  dam  is  in  danger. 
There  would  be  as  much  sense  in  bolting  down  the 
safety  valve  of  a  steam  engine,  as  in  obstructing  a  waste 
weir  of  a  reservoir,  and  still  we  read  that  the  latter  has 
been  done  and  caused  frightful  loss  of  life. 

The  top  of  the  dam  must  also  be  kept  to  the  level  of  its 
original  height  above  the  crest  of  the  waste  weir.  Al- 
lowing the  top  of  the  dam  to  settle  below  its  intended 
height  is  just  as  bad  as  raising  the  waste  weir  an  equal 
distance.  In  the  construction  of  the  dam  provision 
must  be  made  for  settlement  by  adding  a  certain  percent- 
age to  its  height. 

It  is  as  essential  to  keep  a  dam,  its  waste  weir  and 
outlet  in  repair,  as  it  is  to  keep  a  house  or  bridge  in  the 


OTHER    IRRIGATION    WORKS.  375 

same  condition.  Some  people  assert  that  if  a  dam  is 
built  it  should  be  of  masonry,  as,  in  their  opinion,  this 
is  the  only  material  that  can  safely  resist  the  pressure 
and  erosion  of  the  water. 

A  masonry  or  concrete  dam  requires  to  ba  founded  on 
the  solid  rock.  Clay  or  impervious  clayey  loam  is  not 
a  suitable  foundation  for  it.  This  is  the  reason  why,  in 
so  many  instances,  the  underground  work  on  a  masonry 
dam  has  cost  more  than  that  above  ground,  as  it  has  to 
be  taken  down  to  bed  rock.  A  masonry  dam  founded 
011  clay,  or  other  compressible  material,  is  likely  to 
settle  and  crack,  and  thereby  cause  serious  trouble  and 
expense,  or  its  total  destruction.  On  the  other  hand, 
while  an  earthen  dam  can,  with  safety,  be  founded  on 
solid  rock,  still,  its  best  foundation  is  in  good  clay, 
clayey  loam,  hard-pan  or  other  similar  material  imper- 
vious to  water.  The  reservoir  dam  proposed  has  for  the 
greater  part  of  its  length  a  good  foundation,  at  little 
depth,  in  clayey  loam  or  hard-pan,  and  for  this  reason 
an  earthen  dam  has  been  selected  as  being  the  most 
suitable  for  the  location. 

During  the  last  few  years  railroad  bridges  have  broken 
down  under  passenger  trains,  causing  fearful  loss  of 
life,  and  Buddenseick  buildings  have  tumbled  down 
either  during  erection  or  soon  after  completion.  These 
accidents  have  not  prevented  people  from  traveling  by 
rail  or  living  in  brick  houses. 

Experience  has  proved  that  an  earthen  dam  can  be 
constructed  so  as  to  be  as  safe  and  stable  as  any  bridge 
or  building  in  the  world.  In  this  State,  the  Merced  darn 
and  the  dams  of  the  Spring  Valley  Water  Company  of 
San  Francisco,  are  examples  of  safe  construction.  Some 
of  them  are  in  use  for  over  twenty  years. 

India  can  show  thousands  of  dams  that  have  been  in 
use  for  over  a  century,  and  that  are  perfectly  safe  now. 


376  IRRIGATION    CANALS    AND 

In  the  Presidency  of  Madras,  the  official  records  show 
that  there  are  over  43,000  reservoirs  in  use  at  the  present 
time.  In  an  official  return  issued  by  the  Irrigation  De- 
partment of  Bombay,  on  the  1st  of  September,  1877, 
there  is  a  list  of  seventeen  dams,  either  completed  or  in 
progress  of  construction,  the  lowest  of  which  is  41  feet 
and  the  highest  101  feet  high,  and  this  is  the  work  of 
only  a  few  years.  This  shows  that  the  Indian  engineers 
have,  from  long  experience,  the  fullest  confidence  in  the 
stability  of  their  earthen  dams.  Is  it  to  be  credited 
that  the  progressive  American  of  the  present  time  is 
not  able  to  construct  an  earthen  dam  as  well  as  the 
natives  of  India  of  the  last  century? 

As  pertinent  to  this  subject  an  extract  is  given  from 
a  paper  by  the  writer,  published  in  the  Transactions  of 
the  Technical  Society  of  the  Pacific  Coast  for  June, 
1885,  on  the 

SHRINKAGE    OF    EARTHWORK. 

"Embankments  in  India  are  often  constructed  by 
basket  work,  the  material  being  carried  in  saucer  shaped 
wicker  baskets,  containing  less  than  a  cubic  foot.  In 
the  construction  of  embankments  to  retain  water,  this 
basket  work  is  done  in  thin  layers  of  less  than  nine 
inches  in  depth,  the  earth  being  roughly  leveled  up  as 
it  is  deposited  from  the  baskets,  and  then  well  punned 
with  wooden  or  cast-iron  rammers,  weighing  about 
twelve  pounds.  In  addition,  the  constant  tramping  of 
the  men,  women  and  children  employed  in  carrying 
the  baskets,  so  consolidates  the  bank  as  to  make  it  im- 
pervious to  water.  The  layers  of  earth  are  sometimes 
watered.  Embankments  constructed  in  this  manner 
shrink  or  settle  very  little  after  they  are  finished.  They 
are,  in  fact,  an  approach  to  puddle  work,  though  not 
nearly  so  expensive.  The  writer  has  constructed  many 


OTHER    IRRIGATION    WORKS.  377 

embankments  with  a  grading  machine,  tipping  from 
wagons  from  grade,  wheel-barrows,  hand-cars,  carts, 
scrapers  and  punned  basket  work,  and  of  all  these  he 
believes  that  punned  basket  work  settles  the  least,  and 
is  the  best  suited  for  hydraulic  work,  and  the  next  best 
work  to  it  for  a  similar  purpose  is  that  done  by  scrapers. 

11  Thousands  of  embankments,  and  some  of  them 
counted  among  the  largest  and  oldest  dams  in  the  world, 
have  been  constructed  in  India,  by  basket  work,  with- 
out any  puddle  wall  or  puddle  lining;  and  some  of  them, 
that  have  been  looked  after  and  kept  in  repair,  are  as 
good,  if  not  better,  at  the  present  day  than  when  they 
were  originally  constructed,  hundreds  of  years  since. 
This  kind  of  work  is  done  much  cheaper  there  than 
earthwork  in  this  country. 

"  The  writer  has  constructed  embankments  in  the 
Punjab,  the  lead  being  from  100  to  200  feet,  for  three 
rupees  per  thousand  cubic  feet,  that  is,  at  the  rate  of 
four  cents  per  cubic  yard." 

The  numerous  reservoirs  for  the  water  supply  of  cities 
all  over  the  United  States  are  proof  that  earthen  dams 
in  large  numbers,  and  of  a  greater  height  than  50  feet, 
have  been  constructed  during  the  last  forty  years  in 
America. 

These  dams  are  as  safe  as  the  ordinary  railroad  struc- 
tures, and  many  of  them  are  located  in  the  midst  of  a 
dense  population. 

The  failure  of  earthen  dams  in.  the  United  States  is 
mainly  due  to  the  cupidity  of  companies  or  corrupt  con- 
tractors. Another  cause  of  failure  is  the  too  common 
belief  that  any  ordinary  laborer,  that  any  man  who  has 
used  a  scraper  on  a  county  road,  is  fitted  to  superintend 
the  construction  of  an  earthen  reservoir  dam.  Materials 
that  would  in  some  instance  be  suitable  for  a  county 
road  or  a  railroad  embankment,  would  be  likely  to  cause 


378  IRRIGATION    CANALS    AND 

destruction  to  a  reservoir  dam,  and  even  with  proper 
materials  more  care  lias  to  be  taken  in  constructing  the 
latter  than  the  former,  and  also  a  different  method  of 
raising  the  embankment  has  to  be  adopted. 

It  is  safe  to  assert  that  over  fifty  per  cent,  of  all  the  dams 
in  the  world,  constructed  as  part  of  the  works  for  the 
water  supply  of  cities  are  built  of  earth. 

Long  experience  has  shown  the  dimensions  required 
for  dams.  With  these  dimensions,  good  material  prop- 
erly put  together,  a  tower  and  outlet  pipe  through  a 
tunnel  in  solid  rock,  the  face  of  the  dam  covered  with 
rip-rap,  and  an  ample  waste  weir,  an  earthen  dam  can 
be  made  as  safe  as  any  structure  on  the  best  constructed 
railroads. 

Some  anxiety  has  been  expressed  about  danger  to  the 
dam  from  gophers,  but  it  appears  that  they  do  110  sensible 
damage  to  the  Merced  or  Spring  Valley  dams  of  this 
State  already  referred  to. 

CANAL  ON  STEEP  SIDE  HILL  GROUND. 

In  the  description  of  the  different  lines  already  given, 
frequent  mention  is  made  of  steep  side-hill  work.  Fol- 
lowing the  lines  of  the  canal  on  the  map  from  Horse 
Creek  by  the  distinguishing  letters,  B,  C,  H,  I,T,  K,V,  and 
also  the  loop,  I,  R,  K,  almost  all  the  work  for  this  distance 
is  on  steep  side-hill  ground,  the  slope  in  some  instances 
being  as  high  as  twenty-six  degrees,  that  is,  a  slope  of 
two  horizontal  to  one  vertical.  The  material  is  sandy 
loam,  hard-pan,  disintegrated  rock  and  solid  granite. 
The  depth  of  the  rock  from  the  surface  varies  consider- 
ably. Sandy  loam  is  usually  a  surface  covering  of  the 
other  materials,  and  varies  in  depth  from  a  few  inches 
to  six  feet  and  more.  It  is  much  more  difficult  to  carry 
a  canal  discharging  500  cubic  feet  of  water  per  second, 
or  25,000  miner's  inches,  along  such  ground  than  it  is 
to  carry  a  railroad  or  county  road. 


OTHER    IRRIGATION    WORKS.  379 

Hydraulic  miners,  who  have  had  to  construct  ditches 
and  keep  them  in  repair,  know  the  great  difficulty  and 
expense  of  keeping  a  ditch  to  convey  twenty-five  cubic 
feet  of  water,  or  1,250  miner's  inches,  in  repair.^  How 
much  more  difficult,  then,  must  it  be,  to  convey  twenty 
times  that  quantity  in  one  ditch,  that  is  500  cubic  feet 
of  water  per  second.  Other  things  being  equal,  the  less 
the  cross-sectional  area  of  the  channel,  the  less  will  be 
its  cost,  and  the  less  the  annual  expense  for  repairs, 
when  the  velocity  is  kept  within  the  limiting  resistance 
of  the  materials  of  which  the  channel  is  composed,  that 
is,  when  it  is  not  so  great  as  to  abrade  the  bed  and  banks. 

These  considerations  led  to  the  adoption  of  the  cross- 
section  having  a  bottom  width  equal  to  twice  the  depth, 
for  the  steep,  side-hill  work,  with  the  exception  of  the 
crossing  of  the  bluff  at  Horse  Creek,  and  that  part  of 
the  line  between  the  700  and  1,100  feet  tunnels.  The 
dimensions  are,  bed  width  14  feet,  depth  of  water  7 
feet,  side  slopes  {  to  1.  With  a  grade  of  1  in  1;000,  that 
is,  5  feet  3  inches  per  mile,  the  velocity  in  this  channel, 
according  to  Kutter's  formula  with  TI=  .025,  is  4.65  feet 
per  second,  and  the  discharge  500  cubic  feet  per  second. 
The  levels  through  the  hills  admit  of  the  grade  given 
without  adding  materially  to  the  length  of  the  tunnels, 
and  the  material  cut  through  is,  on  the  whole,  suitable 
for  a  high  velocity.  When  the  material  cut  through  is 
sandy  loam,  or  other  materials  that  the  high  velocity  of 
4.65  feet  per  second  in  this  canal  would  wash  away,  pro- 
tection is  afforded  the  banks  by  a  facing  of  dry  rubble 
masonry,  and  the  bed  will  be  protected  with  stone  pav- 
ing. Rock  is  in  abundance  all  along  the  hillsides  for 
this  work. 

It  has  been  stated  that  this  channel  will  not  discharge 
500  cubic  feet  per  second,  and  that  a  more  suitable  one 
would  be  a  section  with  a  bed  of  50  feet,  a  depth  of 


380  IRRIGATION    CANALS    AND 

water  3|-  feet,  with  side  slopes  of  2  to  1.  The  latter  sec- 
tion, with  a  slope  of  two  feet  per  mile  will,  according  to 
Kutter's  formula  with  n=  .025,  give  a  velocity  of  2.5 
feet  per  second  and  a  discharge  of  500  cubic  feet  per 
second.  The  small  section  will  discharge  just  as  much 
as  this  large  one,  and  its  cost  will  be  much  less.  The 
principal  objection  to  the  large  section  is  its  expense. 

Fig.  205. 


<X  6  cd 
a.  6  cm 


Figure  205  is  a  diagram  drawn  to  a  scale  of  thirty  feet 
to  the  inch,  showing  the  two  channels  on  side-hill 
ground.  The  slope  of  the  ground  is  fourteen  degrees. 
This  is  about  an  average  slope  on  the  bad  ground.  The 
cross-section  a,  /,  g,  k,  adopted  for  the  steep  side-hill 
ground  in  this  report  has  an  area  in  round  numbers,  of 
151  square  feet,  and  the  cross-section  of  a,  6,  c,  d,  with  a 
bed  50  feet  wide,  and  side  slopes  of  2  to  1  has  an  area  of 
1,218  square  feet,  that  is,  in  the  latter,  about  eight  times 
as  much  material  will  have  to  be  moved  as  in  the  former 
section.  If,  again,  the  slope  c,  m,  be  made  i  to  1,  then 
the  area  a,  b,  c,  m,  is  equal  to  634  square  feet,  that  is 
more  than  four  times  as  much  as  the  section  adopted. 

The  large  section  is  not,  under  any  circumstances,  the 
right  one  for  steep  side-hill  ground,  although  it  is,  in 
some  cases,  suitable  for  a  canal  in.  the  plains.  An  in- 


OTHER    IRRIGATION    WORKS.  381 

spection  of  the  cross-sections  in  Figure  205,  will  make 
this  very  evident. 

In  Figure  205,  the  cutting  is  made  of  such  a  depth  that 
the  water  is  all  in  soil,  that  is,  that  the  depth  of  cutting 
is  made  equal  to  the  depth  of  water  in  the  channeT  ~  If, 
however,  the  canal,  instead  of  being  in  cutting  is  in 
embankment  equal  to  or  less  than  3->  feet,  and  the  sur- 
face of  the  water  in  the  small  channel,  be  at  the  same 
level  as  in  the  larger  one,  the  advantage  is  still  in  favor 
of  the  smaller  section.  Where  it  can  be  done  with  ad- 
vantage the  intention  is  to  keep  the  adopted  section  a, 
/,  g,  h,  in  about  five  feet  depth  of  cutting,  at  the  point, 
/,  that  is,  that  the  vertical  depth  of  the  bed  at /will  be 
five  feet  below  the  surface  of  the  ground  at  a.  As  the 
depth  of  water  in  this  section  is  7  feet  there  will  be  2 
feet  in  depth  of  water  in  embankment.  The  top  of  the 
bank  will  be  6  feet  wide  and  will  be  1J  feet  above  the 
\vater,  and  its  outer  slope  in  earth  2  to  1,  that  is,  for 
every  two  feet  horizontal  there  will  be  one  foot  vertical. 

If  necessary,  the  cross-section  will  be  varied  to  suit 
the  ground,  keeping  the  depth  of  water  seven  feet  in  all 
cases  in  side-hill  ground. 

As  a  rule,  the  best  but  most  expensive  plan,  for  a  canal 
in  loamy  soil  in  steep  side-hill,  is  to  put  the  section  in 
cut  equal  to  the  full  depth  of  the  water. 

In  passing  the  bold  rocky  point  at  Horse  Creek,  and 
also  in  that  portion  of  the  line  between  the  tunnels  I 
and  T,  the  rock  will  be  taken  out  in  the  shape  of  a 
right-angled  triangle,  as  shown  in  cross-section  at  a,  d,  c, 
Figure  206.  Then  a  wall  of  uncoursed  rubble  masonry  in 
liine  mortar  will  be  built  on  the  lower  side.  The  inner 
side  of  this  wall  will  have  a  coat  of  plaster  composed  of 
Portland  cement  and  sand. 

As  an  additional  precaution  to  prevent  percolation,  a 
groove  will  be  cut  in  the  rock  under  the  wall,  which 


382 


IRRIGATION    CANALS    AND 


groove  will  be  filled  with  concrete  and  this  concrete  will 
be  joined  with  and  form  part  of  the  rubble  wall.  The 
cross-section  of  the  channel  inside  the  rubble  wall  will 
be  nine  feet  on  a  level  bed,  with  vertical  sides.  The 
wall  will  be  eight  feet  high,  two  feet  wide  on  top  and 

Fig.  206. 


five  feet  on  the  bottom,  with  the  side  next  the  water 
vertical  and  the  outside  battered.  The  grade  of  this 
channel  will  be  1  in  200  or  26.4  per  mile.  The  cross- 
section  and  grade  of  this  channel,  from  its  bed  to  the 
surface  of  the  water,  will  be  the  same  as  that  of  the  tun- 
nels at  each  end  of  it. 

This  section  of  the  line  from  the  upper  end  of  the  700 
foot  tunnel  to  the  lower  end  of  the  1,100  foot  tunnel  will 
be  the  best  part  of  the  line.  There  will  be  less  loss  of 
water  by  evaporation  and  percolation,  less  expense  in 
annual  repairs,  and  less  danger  of  breaches  than  in  any 
other  part  of  the  line  through  the  hills  of  an  equal 
length. 

It  has  before  been  mentioned  that  the  discharge 
through  the  tunnels  can  be  doubled  by  giving  the  bot- 
tom and  sides  a  smooth  plastered  surface.  The  same 


OTHER    IRRIGATION    WORKS.  383 

thing  can  be  done  in  the  channel  2,400  feet  in  length, 
between  the  two  tunnels  which  has  the  same  sectional 
area  as  the  latter.  This  is  a  fact  well  known  to 
hydraulic  engineers,  that  the  new  and  improved^formulse 
give  an  increased  discharge  in  proportion  to  the  smooth- 
ness of  the  material  over  which  the  water  flows.  This 
fact  was  not  taken  into  account  in  the  old  formulae, 
which  are  now  known  not  to  give  the  true  discharge 
under  all  conditions  of  channel. 

Materials  for  building  the  rubble  will  cost  very  little. 
After  the  excavation  there  will  be  sufficient  rock  for  the 
work  at  hand;  the  bed  of  the  Kaweah  River,  a  short 
distance  away,  will  supply  the  sand  required;  lime  is 
burned  within  half  a  mile  of  the  work,  and  water  is  in 
abundance  in  Mr.  Pogue's  ditch.  In  the  remainder  of 
side-hill  ground  from  Horse  Creek  to  V,  a  similar  sec- 
tion, 16  feet  wide  on  bottom,  can,  110  doubt,  be  adopted 
in  several  places,  but  this  can  be  ascertained  only  after 
the  surface  covering  of  sandy  loam  is  removed.  This 
part  of  the  line  has  a  grade  of  1  in  1000,  or  5.28  feet  per 
mile. 

A  level  bed  16  feet  in  width,  with  vertical  sides,  hold- 
ing seven  feet  in  depth  of  water  with  this  grade,  will, 
according  to  Kutter's  formula,  with  n  =  .025,  give  a 
velocity  of  4.53  feet  per  second,  and  a  discharge  of  507 
cubic  feet  per  second. 

RAINFALL. 

An  inspection  of  the  rainfall  of  Tulare  given  in  tables* 
will  show  that,  during  the  ten  years  from  1874  to  1884, 
three  years  had  total  depth  of  rainfall  for  each  year  of 
less  than  four  inches,  three  years  of  less  than  seven 
inches,  three  years  of  less  than  ten  .inches,  and  one  year 

*  Tables  not  given  in  this  Report. 


384  IRRIGATION    CANALS    AND 

of  11.65  inches,  which  was  the  maximum  during  this 
period. 

This  plainly  shows  the  necessity  for  irrigation,  in  this 
district  and  nothing  further  will  be  said  011  this  subject. 

A  rainfall  of  10  to  12  inches  properly  distributed  will 
mature  a  crop  in  this  district. 

The  catchment  basin  of  the  reservoir,  including  the 
area  of  the  latter,  is  20  square  miles.  The  reservoir  is  a 
little  more  than  one  square  mile  in  area. 

In  order  to  show  the  height  which  a  large  rainfall 
would  raise  the  reservoir,  let  us  assume  that  the  reser- 
voir is  full  to  the  level  of  waste  weir,  and  that  no  water 
can  flow  out  of  it  through  the  waste  weir  or  otherwise. 
In  this  state  of  affairs  let  the  canal  flow  500  cubic  feet 
per  second  for  one  hour,  whilst  at  the  same  time  an  ex- 
traordinary rainfall  of  three  inches  per  hour  takes  place, 
of  which  50  per  cent,  reaches  the  reservoir.  At  the  end 
of  one  hour  the  reservoir  would  have  risen  2  feet  7 
inches,  leaving  the  top  of  the  dam  3  feet  5  inches  above 
the  surface  of  the  water. 

This  is  a  state  of  the  reservoir  not  possible  under  any 
circumstances.  The  waste  weirs  will  be  always  open 
and  discharging  to  the  capacity  of  the  depth  of  water  on 
them.  A  very  heavy  rainfall  usually  lasts  but  a  short 
time,  and  the  large  capacity  of  the  reservoir  prevents  a 
dangerous  elevation  of  its  surface  during  heavy  rains. 

The  total  length  of  the  waste  weirs  at  each  end  of  the 
dam  must  be  made  of  sufficient  capacity  to  carry  off  the 
flood  water  (computed  by  Dicken's  formula),  in  addition 
to  500  cubic  feet  per  second  from  the  Kaweah  River. 
A  sufficient  length  of  waste  weir  will  be  given  so  that 
the  depth  of  water  on  its  crest  will  not  be  greater  than 
three  feet.  This  would  leave  the  top  of  the  dam  three 
feet  above  the  surface  of  flood  water. 


OTIIKR    IRRIGATION    WORKS.  385 

PREVENTION    OP    WASTE    OF    WATER. 

Two  methods  have  been  adopted  to  prevent  waste  of 
water.  One  by  measurement  and  the  second  by  making 
the  irrigators  raise  all  the  water  they  use  from  Uie_su.p- 
ply  canals.  There  are  two  methods  used  in  India,  in 
supplying  water,  known  as  flush  and  lift.  In  flush 
irrigation  the  water  flows  by  gravitation  on  to  the  land 
to  be  irrigated.  In.  lift  irrigation  the  water  reaches  the 
land  at  such  a  low  level  that  it  cannot  flow  over  the  sur- 
face of  the  land  to  be  irrigated.  This  requires  power  of 
some  kind,  usually  manual  labor,  to  raise  the  water 
sufficiently  to  enable  it  to  flow  over  the  land.  So  great 
was  the  loss  from  waste  in  India  some  years  since,  that 
it  was  seriously  proposed  to  supply  all  the  water  at  such 
a  level,  that  it  should  be  lifted  some  height,  however 
small,  before  it  could  be  used.  It  would  then  be  to  the 
interest  of  the  irrigators  to  prevent  waste.  In  this 
country  the  best  method  to  prevent  waste  is  by 

MEASUREMENT    OF    WATER. 

A  meter  for  measuring  water  for  irrigation  purposes 
must  be  cheap  and  simple  in  construction  and  must 
cause  little  loss  of  head.  No  machine  has  yet  been  in- 
vented that  fulfills  all  these  conditions.  The  great  dif- 
ficulty is  the  fluctuation  of  the  level  of  the  water  in  the 
main  canal. 

It  is  believed,  however,  that  a  machine  can  be  de- 
vised to  fulfill  these  conditions  that  will  give  a  close 
approximation  to  the  quantity  of  water  used.  When 
the  same  method  of  measurement  is  used  toward  all 
the  irrigators  they  will  be  treated  on  perfect  equality 
and  no  one  will  have  good  reason  to  complain  of  in- 
justice more  than  another. 
25 


386  IRRIGATION    CANALS    AND 

DRAINAGE. 

As  a  rule  the  drainage  of  irrigated  land  will  take  care 
of  itself,  if  the  natural  drainage  channels  are  left  free  and 
unobstructed.  These  channels  should  not  be  used  as 
drainage  channels  and  also  for  purposes  of  irrigation. 
Nature,  the  best  engineer,  located  them  to  convey  water 
from  the  land.  They  cannot,  with  advantage,  be  used 
for  irrigation  and  drainage,  and  when  so  used  the  worst 
results  invariably  follow. 

If  the  sub-soil  and  surface  water  cannot  escape  freely 
by  the  natural  channels,  super-saturation  follows  and 
the  ground  becomes  water-logged. 

We  have  not  to  go  far  to  see  the  evil  effect  of  too 
much  irrigation  with  defective  drainage.  A  dense 
growth  of  weeds  on  the  land  and  enervating  malaria  are 
the  sure  followers  of  bad  drainage. 

To  avoid  this,  stringent  rules  should  be  enforced  to 
prevent  the  use  of  the  natural  drainage  channels  for 
any  purpose  whatever,  but  that  of  conveying  away  the 
drainage  water  that  reaches  them. 

EMPLOYMENT  OF  LOCAL  LABOR. 

A  great  deal  of  the  work,  including  all  the  earthwork, 
could  be  done  by  petty  contract  or  day  labor,  and,  in  this 
way,  employment  could  be  given,  after  the  harvest  is 
over,  to  a  large  number  of  the  residents  of  the  district, 
who  would  be  willing  to  do  the  work. 

In  what  I  have  above  written,  I  have  covered  all  the 
points  contained  in  your  instructions  to  me.  In  con- 
clusion I  have  to  acknowledge  the  assistance,  which  as 
Directors  of  Tulare  Irrigation  District,  individually  and 
collectively,  you  have  at  all  times  given  me. 
Respectfully  presented, 

P.  J.  FLYNN. 


INDEX. 


Page 

Abbot  (see  Humphrej^s). 
Abraidiug  Power  of  Water. .  .43-51 

62-65 
Absorption  (see  Percolation). 

Abyssinia 63 

Acequia 153 

Afflux  on  Weir 101,   110 

Africa,  Lakes  of  Central 63 

Alginet  Syphon,  Spain 182 

Alkali  (reh) 19,  68,  328,  329 

330,  332,  336 
American  and  Indian  Irrigation 

Canals  Compared 2-5 

American  Irrigation 279 

American  Society  of  Civil  En- 
gineers, Transactions  of.  .61,   128 
172,   197,  245,  322,  340,  342 

Anderson,  G.   G 2,  329 

Anicut  (see  also  Weirs). 81,  87,     95 
108,   109,   115 

Atella,  Spain 182 

Apron... 87,   96,   106,  108,    109,   114 
117,   120,   121,   123,   193 
Aquatic  Plants  (see  weeds). 
Aqueducts.... 46,   79,   150-164,    175    ! 
228,  241,  252    j 

Ashlar.  105,  108,   110,   115,   119,   120    j 
Ashti  Tank,  or  Keservoir.  .324,  325 

Asphalt 174,  294,  295 

Astronomer  Boyal,  English ...     49 
Asufnuggur  Falls  ....  192,   193,   194 

Atbara  Kiver 63 

Aymard,    M 182 

Back-water 96,    98,  260 

Baker,  Sir  B 57,  326 

Bakersfield 88 

Banks  (see  Embankments). 
Banks,  Dimensions  of  Canal..  26-29 
Bar...  86,   111,  273 


Page 

Barota 37 

Barrage  (see  also.  Weirs) .  81,  96,     98 

99,   101,    102,  270 

Barrage  of  the  Nile  .81,  82,  83,  95,  197 

Bars  of  Grating,  Plan  of 209 

Barton,  Stephen 234 

Bayou  La  Fourche 40 

Bayou  Plaquemine 32 

Bazin 41,  42,   185,  258 

Beas  Kiver 150,   151 

Bench  Marks 254,  244,  257 

Bends  in  Canals 28 

Bengal  Revenue  Report 105 

Beresford,  J.  S 290,  326,  364 

Berm 27,     28 

Berthoud,  Captain  Edward  L.  18,     28 

Betwa  Weir 119 

Beton  (see  Concrete). 

Bhim  Tal  Dam 119 

Binnie,  A.  B -318 

Blackwell,  T.  E 50 

Blocks,  Foundation. 77,  78,  79,   105 
111,   112,   113,   114,   115 

Boats  on  Canals 104,  241 

Bombay   Presidency  Irrigation 

Beport 274 

Boom 153 

Borings 348,  349 

Bowlders... 46,  51,  87,  88,  96,   150 
163,   186,  215,  217,  218,  351 

Boyd,  Mr.... 322 

Branch  Canals 221 

Breast  Wall 177 

Bridge....  84,  86,  98,  99,   127,   149 
152,   169,   185,    191,   193,  241 

Bridge  Foot 85,  89,   101,    146 

' '  Bridge  of  Blessings  " 98 

Browne,  Major  J 62 

Brownlow,  Major. 37,   111,   187,  257 
Brunei  ..  .147 


388 


INDEX. 


Page 

Buffon,  Nadault  de 324 

Buriya  Torrent 177 

Burke,  G.  J 336 

Cairo,  in  Egypt 198,  270 

California  Irrigationist 265 

Canals,  A  List  of  Irrigation .  29,     30 

31 

Canals  divided  into  Two  Classes. 1,  2 

Canal,  Agra..  14,  30,   106,   177,  228 

324,  331 

Canal,  Alpines 31 

Canal,  Arizona 31 

Canal,  Aries 35 

Canal,  Arrah 33 

Canal,  BareeDoab..  12,   14,  30,     35 

39,    150,    193,    195,    197,  202-205 

215,  217,   300 

Canal,  Bear  Kiver,  Utah 90,   157 

159 

Canal,  Beruegardo 242 

Canal,  Boise  Kiver 229 

Canal,  Buxar 33 

Canal,  Calloway.31,  88,  89,  214,  331 

Canal,  Cajon 340 

Canal,  Carpentaras 31 

Canal,  Cauvery 312 

Canal,  Cavour..25,  30,  35,  87,    121 
122,   125,   129,   152,   179 
Canal,  Central  Irrigation,   Dis- 
trict Calif ornia ...  25,  28,  31,   175 
176  177 

Canal,  Cigliano 30,  268,  269 

Canal,  Citizens,  Colorado 31 

Canal,  Crappone 31,  35,  269 

Canal,  Del  Norte 31,  35,   128 

Canal,  Delta,  Main,  Egypt 30 

Canal,  Eagle  Rock  and  Willow 

Creek 31 

Canal,  Elche 293 

Canal,  Empire 31 

Canal,  Esla 299,  344-346 

Canal,  Forez 293 

Canal,  Fort  Morgan 31 

Canal,  Ganges,  Lower.  .30,  110,  151 


Page 

Canal,  Ganges,  Upper..  12,  26,  29 
30,  38,  40,  82,  95,  112,  120,  125 
127,  130,  158,  159,  161,  166,  167 
170,  185-187,  192,  193,  198,  199 
228,  249,  251.  286,  290,  292,  304 

Canal,  Genii 293 

317,  325,  335,  339 
Canal,  Grand  River,  Colorado..     17 
31,   153 
Canal,  Hansi  Branch,   Western 

Jumna  Canal 39 

Canal,  Henares.27,  30,  87,  119,   120 

134,  163,  270,   298,   317,  340,  344 

345,  346 

Canal,  High  Line,  Colorado. .  .     31 
232,  323 

Canal,  Ibrahimia 30 

Canal,  Idaho  Canal  Co.'s. .  .31,   128 
Canal,  Idaho  Mining  &  Irriga- 
tion Co.'s 31 

Canal,  Isabella  II, 30,  244,  324 

Canal,  Istres 35 

Canal,  Ivrea 30,  268 

Canal,  Jucar,  The  Royal 50,   182 

Canal,  Jumna,  Eastern. .  .  1,  30,     37 
112,  188,  249,  258,  286,  302 

Canal,  Jumna 36,   335 

Canal,  Jumna,  Western.  14,  30,     39 
286,  328 
Canal,  Kotluh,  branch  of  Sutlej 

Canal 224,  225 

Canal,  Kurnool 312 

Canal,  Larimer 31 

Canal,  Lorca 293 

Canal,  Lozoya,  Spain 182 

Canal,  Marseilles.  .31,  230,269,  234 
300,    324 

Canal,  Martesaua..  .30,  35,  228,  229 
259,  323 

Canal,  Mazzafargarh 286 

Canal,  Merced, 31,  88,  232 

Canal,  Midnapore 139 

Canal,  Mijares 182 

Canal,  Mussel  Slough,  Califor- 
nia.. .   340 


INDEX. 


389 


Page 

Canal,  Muzza 30,  228,  229 

Canal,  Nagar  (flood) 30 

Canal,  Naviglio  Grande. 35,  228,  274 
Canal,  North  Poudre. .  .31,  153,   157 

Canal,  ttira 27,  293 

Canal,  Ojhar  Tarnbat 325 

Canal,  Orissa 340 

Canal,  Ourcq 31 

Canal,  Palkhed 274,  325 

Canal,  Phyllis 31 

Canal,  Platte,  High  Line..  154,   155 

Canal,  Quinto  Sella 25 

Canal,  Eotto 30,  268,  269 

Canal,  New,  from  Khone, . .  .299  324 

Canal,  Sahel 30 

Canal,  San  Joaquin  and  King's 

Kiver 31 

Canal,  Santa  Clara 340 

Canal,  Seventy-six 31 

Canal,  Sirsawiah 30 

Canal,  Sone.  ...  14,  30,  33,  103,  222 
228,  256,  257,  286 

Canal,  Sooiikasela 30 

Canal,  St.  Julian 31 

Canal,  Subk 30 

Canal,  Sukkur 210-212 

Canal,  Sutlej  or  Sirhind 11,     14 

29,  30,  172,  177,  225,  242,  243 

Canal,  Grand,  of  Ticino 30 

Canal,  Turlock,  California.  .31,    197 

Canal,  Tomtaganoor 340 

Canal,  Uncompahgre.  .31,   152.  531 

215 
Canal,  Verdon,  France. .  . .  179,  234 

270 

Canal,  Wutchumna 231 

Canterbury    Plains,     New    Ze- 

land 197,  323 

Carlet,  Spain 182 

Syphon  (see  Inverted  Syphon). 

Carpenter,  Prof.  L.  G 341 

Catch  water  Drain 28,  67,   240 

Cautley,  SirProby.36,  95,  185,   186 

187,  192,  254 

Cavour  Canal,  Weir 87 


Cement,  Hydraulic 115,   121 

Central  California  Colony 366 

Chains 84,  134,   146 

Chailly 51 

Chains,    Formula  for  Finding 

Tension  on 137 

Channeling 36 

Channels,  Economical 69,     73 

Channels,  Deep  and  Narrow.. .     73 
Channel,   Maximum  Discharg- 
ing   12,     14 

Checks  or  Drops  (see  Falls)... . 
Checks  for  Flooding.  .281,  282,  283 

Check-making 265 

1  Chivasso  Bridge,  Italy 121 

Chukkee  Torrent 150 

Cistern,  Depth  of,  below  Fall..    198 

Clamped,  Cut  Stones 116 

Clearance  of  Silt  from  Canals..      19 

21,  24,  25,  33,  35,  52,  55,  257,  258 

273,  274,  330 

Coast  Range  of  Mountains,  Cal- 
ifornia    176 

Coffer  Dams 115 

Colorado,    Faulty  Designs  and  . 

Construction  of  Canals  in. .  .     34 
Colorado,  Irrigation  in.. .  .279,  282, 

283 

Colmatage 65-68 

Compartments  by  Checks.  .281,  282 

Colusa 175 

Concrete   .77,  79,  110,  112,  114,   115 

119-123,   159,    176,   179,    237,  262 

294,  375,  385 

Construction 262 

Corbett,  Major 289 

Cost  of  Canals  per  acre  Irrigated 
and  per  Cubic  Foot  per  Sec- 
ond  295,  339  340 

Cost  of  Irrigation  per  acre  in 

Different  Countries. 272,  336,  337 
Cost  of  Pumping  and  of  Water. 

270-272 

Cotton,  Sir  A 242 

Crest  of  Fall,  Raising 199 


390 


INDEX. 


Page 

Crest  of  Weir 103,  104,  105,   107 

108,   112,   115,   124,   125,  360,   374 

384 

Crevasses 87 

Cribs 88,  90,  92,   186 

Crofton,  Major.... 26,  161,  186,   193 
224,  242 

Cross-section  of  Channels. .  13,      19 
27,  28,  69,  70,  256,  261,  380,  382 
Cross-section  on  Steep  Hill  side 

13,  380 
Crown  of  Weir  (see  Crest  of  Weir) 

Culcheth,  W.  W 317 

Culverts 149,  150,   177 

Cunningham,  Major  Allen.  137,  318 

Curbs,  Well 78,   114 

Curtain  Walls 33,  111,   114 

Curves 28,  244 

Cuttings 68,  70,  241 

Cylinders 77,   159 

Darns,  Bowlder 66,     82 

Dams,  Earthen,  for  Reservoirs.  374 
375,  376 

Dam  in  Eiver,  Location  of.  .86,  90 
Dams,  Masonry,  for  Reservoirs  375 
Dams,  Reservoir.. 360-364,  374-376 
Dams  in  Rivers.  .  .9,  83,  84,  85,  230 
358-360 
Dams,  Submerged.  .2,  237,  262,  265 

Dam,  Temporary 87,     88 

Damietta,  branch  of  the  Nile. .     97 
98,  99,  101,  102 

Danube 64 

D'Arcy 147,   185 

Daubisson Ill 

Davenport,  W.  H 231 

Davidson,  Prof.  G 87,  300,  364 

Deakin,  The  Hon.  Alfred.. 268,  270 

279,  308,  338 

Defective  Irrigation. .  .  .33,  332-336 

Dehri 33 

Delhi 106,  108 

Delta. .     .  .6,  7,  10,  59,  98,  270,  339 


Page 

Delta  of  the  Nile 6,     98 

Denver   Society    of    Civil   En- 
gineers  2,  3,  18,  274,  287,  290 

316,  321,  329,  373 

Deodar  Wood 205 

Deola 37 

Depositing  Basins. .  .46,  52,  56,     58 
229-232 

Depth  to  bed,  width  of  Canal ..  12-17 

241 

Development  of  Water. .  .2,  234-2.38 
Deyrah  Dhoon  Water  Courses .     45 

229 

Dhunowree  Dam 112 

Dhunowree  Level  Crossing.  166,   167 

170 

Diamond  Drills 237 

Dickens,  Col.  C.  H.. . .  105,  254,  257 

Dimensions  of  Canals 12-17 

Distributaries..  .19,  29,  36,67,   184 

197,  245,   246-262,    277,  281,  282 

291,  292 

Ditching 264 

Diversion,  Weirs  (see  Weirs). 
Dora  Baltea  Aqueduct  in  Italy.  152 

153 

Dora  Baltea  River 60 

Dorsy,  E.  B 61,  322,  340 

Dove-tail  Joints 91 

Dowlaiswaram  Branch  of  God- 

avery  Anicut 115,   116 

Drainage.. 7,  26,  28,  29,  67,  68,  275 
277,  327-331,  386 

Drainage  Area  of  Rivers. . .  .64,   150 
Drainage,  Main,  in  London...     50 

Dredger,  Canal. .    : 263,  265-268 

Dredging 33,52,     55 

Drift  Bolts 90 

Drifts,  Tunnel 237 

Drop,  Big,  Grand  River  Canal, 

Colorado 153 

Drop  Gate 84,  134,  169,  226 

Drops  (see  Falls) 

Drop  Wall  (see  Curtain  Wall). 


INDEX. 


391 


Page 

Drought 113 

Dubuat's  Formula... 36,  41,  43,   185 

Dupuit 147 

Dutac,  Messrs 66 

Durance  Eiver,  Silt  in.. 59,  6<fc     63 

230 

Duty  of  Water. .  .  .11,  251,  286,  289 

to  293,  295,  298,  301,  302,  304,  313 

341,  364,  365 

Dwyer's  Formula  for  Mean  Ve- 
locity       15 

Dyas,  Col.  J.  H. . .  .39,  40,  200,  205 

Earning,    Annual,    of   a   Cubic 
Foot  of  Water  per  second . . .    338 

339 

Earthwork,  Shrinkage  of. .  .75,     76 
376-378 

Eaton,  Fred 294 

Egypt..  56,  57,  63,  82,  98,  99,  326 
Egypt,  Lower...  .2,  97,  98,   99,   103 

Elche,  in  Spain 364 

Embankments,  Breaches  iii.69,  253 
260,  274 

Embankments,  Kiver.  ..66,  68,     69 

•    70,  75,  97,  98,   106,   107,   113,  150 

152,   157,   159,   160,   161,   190,   191 

219,  241,  376 

Engineer  (London) 335 

Engineering 143,   148 

Engineering  News 228,  312,  332 

Epinal 65,     66 

Equalizing,  Cuttings  and  Em- 
bankments   68-72 

Erosion  of  Bed  and  Banks 13 

36-40,  43-47,  80,  82,  83,  117,   121 

165,    183,    188-191,  195,  199,  228 

273,  274,  379 

Escapes 29,   121,   124,   149,   175 

177,  221,  226-229 

Evaporation. 277,  288-291,  302,  310 
316-320,  321,  366,  368-373 
Excavation  to  Balance  Embank- 
ment . .  10 


Page 

Eytelwein's  Formula  for  Open 
Channels 172 

Fahey,  C.  E 80 

Failure  of  Dams rrrrn   377 

Falls... 25,    33,  34,  36,  37,  46,     87 

109,    120,    149,    184,   185,   189-215 
241,  255,  256,  273 

Fall,  Timber 191,   196,  214 

Fall,  Vertical 87,   109,   119,   192 

195,   197,  202,  209 

Famine 335 

Farmington 61 

Fascines 88 

Fernow,  B.  E 306 

Fertilizing  Silt 21,  56-62 

Figari  Bey 270,  271 

Filtration  (see  Percolation). 
Flanks  of  Dam. . .  .84,  95,   101,   113 
116.  117,    124 
Flash  Boards.. 89,  92,   176,   192,  214 

Floats,  Gauging 325 

Flood,  Discharge  of  River 151 

Floods  in  Eivers  . .  .95,  98,  99,   101 

105,   106,   110-113,   124 

Flooding,  Irrigation  by.  .  .279,   283 

333 
Flooding,  Size  of  Compartments 

for 279 

Flooring,  Masonry . .  83,  84,  95,     96 
101,  109,   114-116 

Flooring,  Plank 80 

Flumes  (see  Aqueducts). 

Flush  Irrigation 285,  286,  358 

Flynn,  P.  J 347 

Foote,  A.  D..61,  229,  292,  341-344 

Forestry  and  Irrigation 278 

304-307 

Forrest,  E.  E.46,  249,  251,  292,  304 
Foundations 77-79,    82,  85,     90 

99,    101,    102,    105,   106,   109,   111 
112,   113,   114,   116,   120 

Fouracres,  C 138,   139,   142 

Fouracres'  Excavator 105,   140 


392 


INDEX. 


Page 

Franciscan  Fathers 333 

French  Profile  for  Dams 119 

French  Weirs 135 

Fresno 366 

Furrow  Irrigation.  ..  .279,  283,  285 

286,  287,  288 

Fyfe,  Colonel 318 

Ganges  Kiver 64,  110 

Ganguillet  (see  Kutter) 44 

Garonne,  Silt  on  River 63 

Gates,  Sliding 80,  84,  95,  96 

128-146 

Gauging  Canal 325 

Gauges  on  Canals 277 

Gauge,  Water 197 

Geelong  Dam 119 

Ghooua  Falls 37 

Girders 159 

Godavery  Kiver 63 

Godavery  Anicut.87,  109,  115,  116 

147 

Godavery  Headworks 135 

Godavery  River,  Delta 59 

Gordon,  George 59 

Gordon,  E 185 

Gophers 378 

Grade  of  a  Canal,  Adjusting 

the 20-26,  33,  34 

Grade,  Sub,  of  Canal 28,  29 

Grade.  Initial,  Reduced 24 

Grade,  Too  Great 36,  183-189 

Grade,  Adding  to,  at  Head  of 

Distributaries 25 

Grade,  Reducing. 25 

Grade  or  Slope  of  Bed  of  Canal.  20 

21 

Grade,  Uniform 25 

Graves,  Walter  H....  3,  17,  60,  274 
287,  316,  321,  344 

Greaves,  C 323 

Grunsky,  C.  E 176 

Gratings  for  Falls 202,  209 

Gulch  Bridge 154 

Gwynne's  Pnnips 115 


Page 

Haine  River,  Slope  of 32 

Hartley,  Sir  Charles 63 

Heads  of  Branch  Canals. .  .221-226 

Head  of  Canal. 9,   10,   108,    121,   122 

125,  241 

Head  of  Water 338 

Head  or  Waterway 259 

Headworks  of  Canal 73,  79-82 

95,  98,  103,  134,  140,  275,  276 
358-360 

Health  of  Country. . .  .69,  327,  328 
332-336 

Henares  Canal  Sluices 133 

Higgin,  G 344 

Hilgard,  Professor 332 

Himalya  Rivers 105 

Hiuton,  Col.  R.  J 262,  294 

Horary  Rotation.. 251,  302-304,  324 

Horse-power 269,  270,  271 

Humidity,  mean,  of  Different 

Countries 315 

Humphreys  and  Abbot 40,  185 

Hunter,  Dr.  W.  W 335 

Hurdwar 26,  319 

Hurron  Creek  syphon 177,  180 

Hyderabad,  Evaporation  in  the 

Deccan 318 

Hyraulic  Buffers  or  Rams 139 

Hydraulic  Miners 379 

Ice  Gorges 86 

Idaho 61 

Inclination  of  Canal  (see  grade) 

Indus,   River 2,  34,  59,  63,     81 

Infiltration  (see  percolation).. . 

Inlet 128,   175,  176,  219-220 

Institution  of  Civil  Engineers, 
Proceedings  of. 49,  52-56,  59,  62 
80,  85,  94,  103,  137,  144  153,  186 
187,  195,  197,  222,  249,  279,  304 
305,  313,  317,  318,  323,  326,  328 
336,  344 

Inundation  Canal 34,     52 

Inverted  Syphons  (see  syphons) 
Irrigation  Age. .  .    159 


INDEX. 


393 


Page 
Irrigation  Channels,  Old  Kiver 

Beds  as 6 

Irrigation  Canals,  Works  of . . .  77 

Irrigation,  From  Kiver 7 

Irrigation,  Improved  System, 

Egypt 57,  103 

Irrigation,  Stoppage  of 69 

Irrigation,  Limit 10 

Jackson,  L.  D'A 43 

Jaolee  Falls 39 

Jeffreys,  Major  W 110,  111 

Jumna  River 102,  106 

Kali  Nudee  Aqueduct 151 

Kaweah  River,  California. 231,  347 

361,  366,  383 

Kern  County,  California,   Irri- 
gation System 280 

Kern  River 88 

Kern  River  Dam 83,  214 

Kilgour,  Mr 59 

Kiiigsbridge,    Tulare    County, 

California,  Evaporation  at ...  316 

Kistna  River,  Delta 59,  63 

Kunkur 110,   112,  175 

Kurrachee 106,  213 

Kutter 43,  200,  202,  210 

Kutter's  Formula.. 21,  45,   172,  379 

Lago  Maggiore 124 

Lahore 224 

Lang,  Major  A.M....  105,   110,   115 

La  Gosse 66 

Laterals  (see  Distributaries). 

Latham,  Baldwin 51 

Latham,  J.  H 60 

Le  Conte,  Professor  J 48 

Leakage  (see  Percolation). 

Lamairesse,  M 319 

Leslie,  Sir  John 51 

Levees,  River 87 

Level  Crossing.  . .  134,  151,   164-170 

220 
Lift  Irrigation 285,  286 


Page 

Lifting  Sluice 144 

Limestone  Country 59 

Linant  Pasha 320 

Locks 1,   33,  53,    101,   104,    117 

125,   170,  241,~24^T  277 
Login,  T..14,  26,  49,   186,   187,   195 

197 

Loire,  River 49 

Lozoya  Dam,  Spain 119 

MacLean,  L.  F 222 

Madhapore 224 

Madras 95,   108 

Madras  Presidency 60,     82 

Madras,  System  of  Weirs. .  106,   109 

Madrid  Evaporation 317 

Mahanuddy  River 63 

Mahanuddy  Headworks.  . .  135,   137 

Mahewah  Valley Ill 

Mahmoodhoor   Rajbuha    (Dis- 
tributary)      38 

Maintenance  and  Operation  of 

Irrigation  Canals 253,  257 

273-278,  336 

Majaiiar  Torrent 163 

Malad  River,  Corinne  Branch, 

Iron  Flume '.  157,   159 

Malad    River.     West     Branch, 

High  Flume 156 

Manure  ....56,  58,  59,  61,  62,     64 

Marcite  Cultivation 298 

Masonry 78,  83,   102,   105,   106 

120,  375 

Masonry  Channels 14,     45 

Measurement   of  Water,    Mod- 
ules, Meters 341-346,   385 

Mediterranean 98 

Medley,  Colonel  J.  G 46 

Merced  Dam 375,  378 

Methods  of  Irrigation..  . . .  .279-289 

Midnapore,  Rainfall  in 59 

Mills..  ; 269 

Mississippi 40,     64 

Mississippi,  Slope  of   32 

Miner's  Inch  of  Water. .          , .  361 


394 


INDEX. 


Moncrieff,  Gen'l  Sir  C.  C.  .  .37, 
65,    99,    101,    182,    187,   301, 

Morin 

Morton,  Lieut.  W.  S   261, 

Moors  of  Spain v 

Moselle  Kiver 65, 

Mougul,  M ,    

Movable  Dams.  . .  104,   105,   128 

Mud  Sills   

Mulching 

Muskurra  Eiver 37, 

Myapore  Dam. S3,  95, 

Myapore  Kegulating  Bridge .  . . 


Myers 


Page 
60 

320 
364 
43 
262 

182 
66 
99 

-146 
89 
288 
188 
96 
126 
127 
150 


Nagpore,  Evaporation  in 318 

Napoleon .  , 57 

Navigation  Canals.  1,  11,  12,35,     36 

103,  125,  170,  222,  240-243 

Narora  Weir. .  .87,  95,  108,  109,   110 

112 

Needle  Dams 132,  221-224,  226 

Neva,  Slope  of 32 

Neville's  Hydraulics 40,  44,   185 

Newarree  Bridge 39 

Newka,  Slope  of 32 

Night,  Use  of  Water  at 293 

Nile,  Blue 63 

Nile  Eiver. . .  .56,  57,  64,  98,  99,   101 

102 

Nile,  Silt  in 34,  62,  272 

Nira   Canal,    India,    Cross-sec- 
tion of 27 

North  Poudre  River,  Weir 90 

Nowgong  Dam   , 188 

Nyashahur  Bridge 37 

Off-take  of  Canal 54 

Ogee  Falls 46,  87,  120,  192,   195 

209 

Ohio,  Slope  of 32 

Okhla  Weir.. .  .   87,  95,  96,  102,   105 
106,  108,  112,  113,  114,   125 


O'Meara,  P. .  .94,  153,  157,  279,  313 

322 
Ontario  Land  Improvement  Co.  234 

Orissa 135 

Orissa  Canals,  Cost  of 339 

Orme,  Dr.  H.  S 333 

Outfall  into  Eiver   331 

Overfalls 167 

Panel , 90 

Paving 124,  379 

Peculiarities  of  American  En- 
gineering    89,  105,   153 

Penstock 153 

Percolation.. .  10,  58,  60,  63,  68,     69 

77,  94,  111,  112,  113,  120,  147,  148 

149,  152,   161,  276,  277,  282,  291 

302,  304,  321-326,  366,  368-373 

Periar  Eiver,  India 233 

Persia 305 

Pharaonic  System  of  Irrigation.    57 

Phoenix,  Arizona 87 

Phosphoric  Acid 57 

Piers  of  Bridges 86 

Piles   89,  115,   169 

Piling,  Sheet 89,  193,   199 

Piles,  Iron 159 

Pipes...  139,  147,  181,  182,  186,  220 

262 

Pipe  Inlet 128 

Pipe  Outlet, 253,  254 

Pipe  Irrigation    293-298,  333 

Pipe   Irrigation    System,     On- 
tario, California 296 

Plank  Gate    129 

Planking 87,     90 

Planks  on  Weir 85,  260,  261 

Plantations 278 

Planting  of  Trees 304 

Platform,  Masonry.96,  101,  102,   103 

Plaster 352 

Plow 264,  272,  283,  289 

Plunger 139 

Plum  Creek 153 

Pondicherry 319 


INDEX. 


395 


Pago 

Po,  Kiver 121 

Po,  River,  Silt  in 60,     63 

Portland  Cement 217 

Posts  on  Weir 85 

Potash,  Salts  of 57 

Powell,  Major 308 

Professional  Papers  on  Indian 
Engineering...  105,   110,   115,    137 
205,  209,  210,  215,  248,  280,   317 

319 

Prony    41 

Prise  or  Headworks    182 

Protecting  Banks    84,     87 

Public  Works  Department,  In- 
dia    105,  276 

Puddle,  Clay....  110,  111,   115,   152 
156,   175,  262,  323,  360,   374 

Pumping 2,   115,  270,  271,  272 

Punjab  Eivers 59 

Puttri  Torrent 170 

Rainfall.. 59,  64,  149,   172,  263,   290 
305,   308-315,   320,  374,   383,  384 
Rajhubas  (see  Distributaries).. 

Ranipore  Torrent 170,   171,   174 

Rankiiie 41,  239 

Rapids 51,    192,  215-218 

Ratchets 134 

Ravi  Bridge    49 

Ravi  River 150,  224 

Regimen  of  Rivers 83,  273 

Regulator... 79,  80,  85,  89,  95,     96 
101,   121,    124-137,   149,   165,   169 
184,   191,  221,  222,  227,  243,  259 
Regulating  Bridge  (see  Regula- 
tor). 

Reh  (see  Alkali). 
Relief  Gates  (see  Escapes). 

Revy,  Mr 42 

Repairs  to  Canals ..  69,  87,  273,  277 
(see  also  Clearance  of  Canals) . 

Reservoirs 58-60,   75,   81,  294 

304,    305,   318,  351,  360-364,  366 

374,  377,  384 

Reservoir  and  Canal   .        .  .  366-368 


Page 

Retaining  Walls 238-240 

Retrogression  of  Levels  ...  .36,    111 

114,    161,   183-189 

Revenue  from  Distributaries . .   259 

Rhine,  Silt  in  River ~~."  .77.  ~63 

Rhine,  Slope  of  River 32 

Ribera   324 

Rip  Rap 360,  378 

Ritso,  G.  F 197,  323 

Rivers,  Change  of  Course 6 

Rivers,  in  Flood.. 52,  55,  62,  68,  81 

84,  86 

Rivers,  North  Poudre 90 

Rivers,  Raising  Bed  of 66 

Rivers,  Sandy  Bed   79,  87 

Rivers,  Slope  of 32 

Rivers,  Water  for  Irrigation . .  58-60 
Roadway  on  Bank  of  Canal .  .26,  274 

Rock  Cutting 156,  382 

Roorkee   160,  318,   319 

Roorkee  Bridge 38,40 

Roorkee  Civil-  Engineering  Col- 
lege        159 

Roorkee  Gauge 38 

Roorkee  Treatise  on  Civil  En- 
gineering  46,85,  96,   169,  260 

277 

Rosetta,  branch  of  Nile.. 97,  98,  99 
101,   102 

Royal  Engineers 186 

Rubble 120,  381-383 

Rubble,  Dry 105,   106,   108 

Rubble,   Pitching 101,   109 

Rutmoo  River 167 

Sacramento  Valley 176 

Sainjon,  Chief  Engineer.    49 

Sakiyehs 271 

Solaiii  Aqueduct 38,  77,  153 

158-163 

Saluggia 268 

San     Antonia     Tunnel,      Cali- 
fornia     234 

San  Bernardino  Valley 235 

San  Gabriel . .  .  295 


396 


INDEX. 


Page 
Sand    Boxes    (see    Depositing 

Basins). 

Sand  Dams 79 

Sand,  Quick 237 

Sandstone 115 

Saone,  Slope  of 32 

Scougall,  H   330 

Scour.. 53,  56,  84,  86,  96,    108,   113 
117,    135,   136,   140 
Scouring   Sluices    (see    Under 

Sluices). 

Scraper,  Buck 265 

Scraper,   Iron 264 

Scraper,  V  Shape 264 

Sea,  Level,  Mean 106 

Season  for  Irrigation .  278,  315,  362 

Section,  Constant  Cross 25 

Seesooan  Superpassage 171,   173 

Seine  Kiver,  Weirs  on 135 

Seine  Kiver,  Slope  of 31 

Senate  Report  U.  S.  ..262,  281,  283 

Sesia  Torrent,  Italy. .  *. 179 

Sewers,  Storm 46 

Sewers,  Velocity  in 46,50,     51 

Shadoofs 271 

Shafts 182 

Shafts,  Tunnel 237,  263 

Shahpur  Inundation  Canal. . .  .   286 

Sheet  Piling 123 

Streeviguntum  Anicut.87,  108,   109 

Shoals 86 

Shrinkage  of  Earthwork 69,     72 

75,  374,  376 

Shutters  for  Weirs . .  54,  55,  56,     95 
104,   105,   128-146,  359 

Sidelong  Ground,  Canal  on 28 

73,  74,  352.  378-383 

Side  Slopes ....  17-20,  70,  257,  273 

349,  360 

Side  Slopes,  Protecting 341 

Sidhnai  Canal,  India 222,  224 

Sills 90,     96 

Silt  Carried  by  Kivers 62-65 

Silt  Fertilizing  (see  Fertilizing 

Silt). 


Page 

Silt 5,  9,  18,  25,  26,  29,  33-35 

37-39,    46-48,    52,    53,    57,  59-64 

66,  67,  80-83,   115,  117,   124,   126 

257,  260,   277 

Silting  up...  65-68,  81,  89,  93,    108 

112,   121,   124,   125,   189,   190,  226 
229,  257,  275 

Silting  Up,  To  Prevent 24,   104 

Silt,     On     Keeping     Irrigation 

Canals  Clean  of 52-56 

Silt      Traps     (see     Depositing 

Basins). 
Sind,  Inundation  Canals  in. 29,     81 

Sirdhana 40 

Skips 115 

Slabs,   Stone 79 

Sleeper  Planks 84,   130  169 

Sliding  Sluices 80,   134,    135 

Slime,  (see  Silt 101 

Slope    of    Bed   of    Canal    (see 

Grade). 

Slope,  Natural,  of  Materials .  20,     73 
Slope  of  Canal  Increases  from 

Head  to  Tail 21 

Stoney,  F.  M.  G 144 

Sluices 98,    105,   128-146,  281 

Sluices,  Head.. 25,  52,  53,  56,     89 

95,  96,  99,  104,   115,   117 

Sluices,  Under.. 53,  55,  77,  79,     80 

83,  95,  96,   103-106,  108-110,   114 
115,   117,   121,   124-127,   138 

Smith,  Colonel  Baird 116,   317 

Snow 26 

Sorgues  Kiver 60 

Spain 120 

Spoil  Banks  (see  Waste  Banks) . . 

28,  35,  268 
Spring  Valley  Water  Company's 

Dams,  California 375,  378 

Sprinkling  Irrigation  by    279 

Spurs 150 

Stand  Pipes,  for  Irrigation .  298,  333 
Stevenson,  Col.  C.  L.. 61,   285,   301 

Stony  Creek   175-178 

St.  Paul  Syphons   179,   181 


INDEX. 


397 


Page 

Stop-planks. 134 

Stonework 101 

Sub-soil  Drainage 330,  331,  332 

335 
Sub-surface  Irrigation  by  means 

of  Pipes 279,  333 

Sugar  Cane 60 

Superpassage..  ..151,  169-175,  220 

221 

Superintendence  of  Canal 276 

Super-saturation  of   Land  (see 

Water-logging). 

Suranah . 225 

Survey .241-252 

Swamps, 69,  327,  328,  334,  336 

Smeaton.    50 

Syphons,  Inverted 151,   175-183 

220,  252,  255 
Syphons,  Kock 181 

Tail  of  Apron 114,   116 

Tail  of  Canal 81,  249,   255 

Talus... 101,  103,  106,  107,  108,    109 

110,  112,   114 

Tambrapoorney  Kiver 108 

Tanjore    .. 58 

Tank  (see  Eeservoir) 
Technical  Society  of  the  Pacific 

Coast,  Transactions  of 75,   396 

Telephone  Service  on  Canals.  .  274 
Temperature  at  Eoorkee,  India.  318 
Temperature,  Mean,  of  different 

Countries    315 

Thames  Tunnel 147 

Thompson,  Dr.  Henry 317 

Ties 141 

Tiber,  Slope  of   32 

Timber,  Decay  of   277 

Timber  Falls  (see  Falls  Timber). 
Toghulpoor  Sand  Hill,  Ganges 

Canal 38,   188 

Tower  in  Eeservoir 360,  378 

Tow-paths       on      Navigation 

Canals 174,  242 

Training  of  Eivers 277 


Page 

Transporting  Power  of  Water. .  43 
-51,  62-65,  257 

Trask,  F.  E 234,  296 

Trautwine _  .  .  .  319 

Trenails ~  "91 

Trestle.... 89,  159 

Trial  Pits  69,348,349 

Tropics  319 

Tulare  Irrigation  District,  Ee- 

port  on  proposed  Works  of. .  347 
Tumbler  for  Eegulating  Distrib- 

taries,  Midnapore  Caiia  ....  139 
Tunnels 147,  154.  156,  169,  181 

182,  232-238,  267,  353-357,  360 
378,  382 

Tunnels  to  Develop  Water. .  .2,  232 
233,  234,  235,  236,  237,  238 

Tunnel  Lining 235-238 

Tuolumne  Eiver 117 

Turlock  Weir. 87,  117 

Umpfenbach 49 

Utah 61,     90 

Utah,  Irrigation  in , 285 

Valencia  in  Spain 299 

Velocity   Allowable  in  Certain 

Soils 14,    34,  35 

43-47,  81 

Velocity,   Bottom 41-44,  113 

Velocity,  High 35,  44-47 

Velocity,  Destructive 43-47,  215 

217,  218 
Velocity  too  Great  Better  than 

too  Small  34 

Velocity    Increases     with    In- 
crease of  Depth 47 

Velocity,  Low  mean 33,  34 

Velocity,  Maximum  mean 34 

Velocity,  Maximum  Surface..  .  37 

38,  41,  42 

Velocity,   Mean 29,  35,  37-43 

Velocities,   Mean,   Surface  and 

Bottom 41,   42,  207,  208 

Velocity,  Mean,  Uniform    21 


398 


INDEX. 


Page 

Velocity,  Minimum,  in  Canals 
in  America 34 

Velocity,  Minimum,  in  Canals 
in  Egypt. , 34 

Velocity,  Minimum,  in  Inunda- 
tion Canals  in  Sind 34 

Velocity,  Minimum,  in  Indian 
Canals 33 

Velocity,  Minimum,  in  Spanish 
Canals 34 

Vertical  Drop  of  Dam 120 

Vertical  Falls  (see  Falls  Verti- 
cal). 

Viga  Valley  Irrigation  Project, 
Madras 233 

Viuda  Kavine 182 

Vrynwy  Eeservoir  Dam 119 

Warping  (see  Colmatage) . 

Waste  Bank 28,  35,  69,  268 

Waste  Board 116 

Waste  Gates  (see  Escapes). 

Waste  Weir 360,  374,   378,  384 

Water,  Cost  of  and  of  Pump- 
ing   270 

Water  Cushion.... 87,  96,  109,   120 
137,   186,   197,   198 
Water,  Diverting  the,  from  the 

Eiver  to  the  Land   5-11 

Water,  Duty  of  (see  Duty  of 
Water). 

Water,  Economy  of 113 

Water,  Kinds  of 58 

Water  Logging  of  Lands...  69,  251 
275,  289,  291,  304,  327,  328,  33 1* 

366 

Water  Power  of  Irrigation  Ca- 
nals   ;268,  269,  270 

Water  Spring 60 

Water,  Waste  of,  to  Prevent. . .   385 


Page 
Waterings,  Number  and  Depth 

of 284,  298-302,  314,  324 

Water,  Quantity  of  Eequired 

for  Irrigation 11,  12 

Watershed.. 244,  245,  248,  260,  328 

Weeds.... 33,   38,  40,   189,  260,  273 

327,  330 

Weeping  Holes  163,  243 

Weirs.. 53,  77,  79,  80,  81-124,  125 

134,  147-149,  277 

Weirs,  Cross  Sections  of . .  82,  105 

106,  108,  115 
Weirs,  India,  by  Major  A.  M. 

Lang 115 

Weir,  Curved  on  Plan 119,  122 

Weir,  Oblique , 85 

Wells 2,  60,  62,  292 

Wells,  Artesian 2,  313 

Wells,  Foundation.. 77,  78,  79,  109 

111,  114,  115,  116 

Well  Water  , 58 

Wilson,  Allan 60,  305 

Wilson,  H.  M...172,  197,  245,  246 

Willcocks,  W....57,  103,  319,  328 

Windlasses 132,  134,  222 

Wing  Dam .  , 87 

Wing  Walls 109 

Wooden  Flumes  153 

Works  of  Irrigation  Canals 77 

Wrought  Iron  Syphon 179 

Wutchumna  Eeservoir 231,  232 

Wutchumna  Tunnel 231,  232 

Yarpoor  Falls 37 

Zero  of  Canal  for  Measurement     95 

243 

j   Zero  for  Levels 128,   132,  243 

Zanjas  or  Open  Ditches 333 


FLOW  OF 


IRRIGATION  CANALS, 

DITCHES,  FLUMES,  PIPES,   SEWERS, 
CONDUITS,  Etc. 


WITH 


TABLES 

Simplifying  and  Facilitating  the  Application  of  the  Formulae  of 
KUTTEE,  D'AKCY  AND  BAZIN, 


P.  J.  FLYNN,  C.  E. 

Member  of  the  American  Society  of  Civil  Engineers;  Member  of  the  Technical  Society  of  the 
Pacific  Coast;  Late  Executive  Engineer,  Public  Works  Department,  Punjab,  India; 

AUTHOR  OF 

"Hydraulic  Tables  based  on  Kutter's  Formula," 
"Flow  of  Water  in  Open  Channels,"  etc. 


[ALL  RIGHTS  RESERVED.] 


SAN  FRANCISCO,  CALIFORNIA. 


Entered  according  to  Act  of  Congress  in  the  year  1891, 

BY  P.  J.  FLYNN, 
In  the  office  of  the  Librarian  of  Congress,  at  Washington,  D.  C. 


SAN    FRANCISCO  : 

GEORGE  SPAULDING  &  Co., 
PRINTERS  AND  ELECTROTYPERS. 


TABLE  OF  CONTENTS. 


ARTICLE  1 — Introduction rrrr-r-^-      1 

Inaccuracy  of  old  formulas,  1;  Accuracy  of  the  formulas  of  Kutter, 
Bazin  and  D'Arcy,  1;  Major  Allen  Cunningham's  experiments 
on  the  Ganges  Canal,  2;  Kutter's  formula  found  to  be  correct,  3. 

ARTICLE  2 — The  Application  of  K niter's  Formula  simplified  and  facili- 
tated by  the  use  of  the  Tables  in  this  ivork 5 

Plan  of  Tables,  5;   Example  of  their  use,  6. 

ARTICLE  3 — Formulae,  for  Mean  Velocity  in  Open  Channels 0 

Nomenclature,  6;  Value  of  g,  7.  D'Aubisson's,  Taylor's,  Down- 
ing's,  Beardmore's,  Leslie's,  and  Poles'  formula  for  large  and 
rapid  rivers,  8;  Leslie's  for  small  streams,  8;  Stevenson  for 
streams  over  2,000  cubic  feet  per  minute,  8;  Stevenson  for 
streams  under  2,000  cubic  feet  per  minute,  8;  D'Aubisson,  8; 
Beardmore,  8;  Eytelwein,  8;  Eytelwein,  9.  Neville  straight 
rivers  with  velocity  up  to  1.5  feet  per  second,  9;  Neville  straight 
rivers  with  velocities  above  1.5  feet  per  second,  9;  Neville,  9; 
Dwyer,  9.  Dupuit,  9;  Young,  9;  Dubuat,  9;  Girard,  9;  De 
Prony,  9;  De  Prony  with  Eytelwein's  co-efficient,  9;  Weisbach, 
10;  St.  Veuant,  10;  Ellet,  10;  Provis,  10;  Hagen,  10;  Schlicht- 
ing's  Hagen,  10;  Fanning,  10;  Humphreys  and  Abbot,  10; 
Gauchler,  10.  Table  1 — Giving  the  values  of  the  co-efficients 
to  be  employed  in  Gauchler's  formula  for  canal  and  rivers,  11; 
Molesworth,  11.  Table  .2— Giving  the  value  of  the  co-efficients 
in  Molesworth's  formula  for  canals  and  rivers,  11;  Bazin,  11; 
Brandreth's  modification  of  Bazin,  12;  Kutter,  12.  Formulas 
for  Use  in  the  Application  of  Tables,  13. 

ARTICLE  4 — Remarks  on  the  Formulae, 13 

Old  formulas  have  constant  co-efficients,  13;  Gauchler,  Bazki, 
Molesworth,  Kutter,  13;  value  of  c  in  Kutter  varies  with  n,  s, 
and  r,  13.  Table  3 — Values  of  c  for  earthen  channels  by  Kut 
ter's  formula,  14. 

ARTICLE  5 — Bazin's  Formula  for  Channels  in  Earth 15 

Bazin's  formula  correct  for  small  channels  in  earth,  15;  Brandreth's 
modification  of  Bazin,  16. 

ARTICLE  6 — Comparing  Kutter's  and  Bazin's  Formulce. 10 

Table  4 — Giving  the  Velocity  and  Discharge  of  earthen  channels 
according  to  the  formulas  of  Bazin  and  also  Kutter,  17. 

ARTICLE  7 —  Value  of  n 18 

Table  5 — Giving  value  of  n  for  different  channels,  19.  Table  6 — 
Showing  the  effect  of  the  co-efficient  of  roughness  n  on  the 
velocity  in  channels,  23. 


IV  TABLE    OF    CONTENTS. 

Page 

ARTICLE  8 — Side  Slopes 24 

In  large  channels  change  in  side  slopes  makes  little  change  in 
velocity,  24.  Table  7 — Showing  the  velocity  and  discharge  of 
channels  having  different  side  slopes,  n  =  .025,  26. 

AKTICLE  9 — Open  Channels  having  the  same  velocity 27 

ARTICLE  10 — Open  Equivalent  Discharging  Channels 28 

ARTICLE  1 1 — Interpolating 28 

ARTICLE  12 — Preliminary    Work 29 

Fig.  1— Trapezoidal  Channels,  30;  Fig.  2 — Rectangular  Channel, 
30;  Fig.  3— V-Flume. 

ARTICLE  13 — Explanation  and  Use  of  the  Tables 30 

Example  1 — To  find  the  mean  velocity  and  discharge  of  a  canal 31 

Example  2 — Given  the  discharge,  bottom  width  and  depth,  to  find 

the  grade  of  channel 34 

Example  3 — Given  the  discharge,  bottom  width  and  grade  of  canal, 

to  find  the  depth 36 

Example  4 — Given  the  hydraulic  mean  depth  and  mean  velocity  of  a 

channel,  to  find  the  slope  or  grade 37 

Example  5 — Given  the  discharge  velocity  and  grade  of  a  channel,  to 

find  the  bed  width  and  depth 38 

Example  6 — Gauging  a  stream  to  find  its  velocity  and  discharge,  and 

the  number  of  acres  it  is  capable  of  irrigating 40 

Example  7 — Given  the  dimensions  of  a  canal  in  earth,  to  find  the 

width  of  a  masonry  channel  having  the  same  discharge,  the  two 

channels  having  the  same  depth  and  grade 42 

Example  8 — Increased  discharge  of  an  earthen  channel  by  clearing  it 

of  grass  and  weeds 43 

Example  9 — Increase  of  discharge  by  improving  in  smoothness  the 

masonry  surface  of  a  channel 44 

Example  10 — To  find  the  velocity  and  discharge  of  a  channel  having 

bed  width,  depth  and  side  slopes  not  given  in  the  tables 45 

Example  11 — Given  the  discharge,  grade  and  ratio  of  bed  width  to 

depth,  to  find  bed  width  and  depth 46 

Example  12 — Diminution  of  discharge  of  channel  by  grass  and  weeds  47 
Example  13 — Given  discharge,  velocity  and  ratio  of  bed  width  to 

depth,  to  find  slope  or  grade 48 

Example  14 — Given  the  bed  width,  depth  and  grade  of  a  channel  not 

given  in  the  tables,  to  find  the  velocity  and  discharge 49 

Example  15 — To  find  the  value  of  c  and  n  in  an  open  channel 41 

Example  16 — To  find  the  velocity  and  discharge  of  a  brick  aqueduct 

by  Bazin's  formula,  the  dimensions  and  grades  having  been  given  52 
Example  17 — Increase  of  discharge  of  a  channel  in  rock-cutting  by 

plastering  its  surface 52 


TABLE    OF    CONTENTS. 


FLUMES.  Example  IS  —  To  find  the  velocity  and  discharge  of  a  rect- 

angular flume  ................................................  54 

Example  19  —  To  find  the  velocity  and  discharge  of  a  V-flume  ........     55 

Example  20  —  Given  bed  width,  depth  and  discharge  of  a  flume,  to 

find  its  grade  or  slope  ................................  7.  .T-TT—  56 

Table  8  —  Channels  having  a  trapezoidal  section  with  side  slopes  of  1 
to  1.  Values  of  the  factors  a  =  area  in  square  feet,  and  r  =  hy- 

draulic mean  depth  in  feet  and  also  »J~r  and  a\fr  ..............     57 

Table  9  —  Channels  having  a  trapezoidal  section  with  side  slopes  of  •£ 

to  1.     Values  of  the  factors  a,  r,  ^  and  a*/r'  ................      73 

Table  10—  Sectional  areas  in  square  feet,  of  trapezoidal  channels,  with 

side  slopes  of  J  to  1  ..........................................     82 

Table  11  —  Channels  having  a  trapezoidal  section  of  side  slopes  of  1^ 

to  1.     Values  of  the  factors  a,  r,  \/f"and  a\/r~  ................     85 

Table  1:2  —  Sectional  areas  in  square  feet,  of  trapezoidal  channels, 

with  side  slopes  of  1  \  to  1    ....................................      94 

Table  13  —  Channels  having  a  rectangular  cross-section.  Values  of  the 

factors  a,  r,  \/r  and  a\/r  ....................................     97 

Table  14  —  V-shaped  flurne,  right-angled  cross-section,  based  on  Kut- 

ter's  formula  with  n  =  .013,    giving  values  of  the  factors  a,  r, 

c-s/r  and  ac^/r"  ..............................................    103 

Table  15—  Based  011  Kutter's  formula  with  n  —  .009.      Values  of  the 

factors  c  and  c\/r^  ...........................................    104 

Table  16  —  Based  on   Kutter's  formula  with  n  =  .010.     Values  of  the 

factors  c  and  c-^/r   ...........................................    109 

Table  17  —  Based  on  Kutter's  formula  with  «  =  .011.     Values  of  the 

factors  c  and  c\/lr  ............................................    112 

Table  18  —  Based  on  Kutter's  formula  with  n  =  .012.     Values  of  the 

factors  c  and  c  \/r  ..........................................    .    116 

Table  19  —  Based  on  Kutter's  formula  with  n  =  .013.     Values  of  the 

factors  c  and  c\/l-  ...........................................    120 

Table  20  —  Based  on  Kutter's  formula  with  n  ==  .015.     Values  of  the 

factors  c  and  c\/r    ...........................................    124 

Table  21  —  Based  on  Kutter's  formula  with  n  =  .017.     Values  of  the 

factors  c  and  c\/7  .  .  .........................................    128 

Table  22  —  Based  on  Kutter's  formula  with  n  =  .020.     Values  of  the 


factors  c  and  c^r    .....................  .  .....................    133 

Table  23  —  Based  on  Kutter's  formula  with  n  —  .0225.     Values  of  the 

factors  c  and  c^/r    ...........................................    138 


VI  TABLE    OF    CONTENTS, 

Page 
Table  24 — Based  on  Kutter's  formula  with  n  =  .025.     Values  of  the 

factors  c  and  c\/r  143 

Table  2'5 — Based  on  Kutter's  formula  with  n  =  .0275.  Values  of  the 

factors  c  and  c^/r  148 

Table  26 — Based  on  Kutter's  formula  with  n  =  .030.  Values  of  the 

factors  c  and  c\/r-  15,'} 

Table  27 — Based  on  Kutter's  formula  with  n  =  .035.  Values  of  the 

factors  c  and  c\/r-   158 

Table  28 — Value  of  c\/r  to  be  used  only  in  the  application  of  the  sec- 
ond type  of  Baziii's  formula  for  open  channels,  with  an  even  lining 
of  cut  stone,  brickwork,  or  other  material  with  surfaces  of  equal 
roughness,  exposed  to  the  flow  of  water 163 

Table  29 — Giving  the  length  of  two  side  slopes  of  a  trapezoidal  chan- 
nel. The  side  slopes,  plus  the  bed  width,  are  equal  to  the  perimeter  164 

Table  30— Giving  the  velocities  and  discharges  of  trapezoidal  chan- 
nels in  earth,  according  to  Bazin's  formula  (37)  for  channels  in 
earth 165 

Table  31 — Velocities  and  Discharges  in  Trapezoidal  Channels  based 
on  Kutter's  formula  with  n  =  .025.  Side  slopes  1  horizontal  to  1 
vertical 169 

Table  32 — Velocities  and  Discharges  in  Trapezoidal  Channels  based  on 
Kutter's  formula  with  n  =  .03.  Side  slopes  |  horizontal  to  1  ver- 
tical   171 

Table  33 — Giving  fall  in  feet  per  mile;  the  distance  or  slope  corres- 
ponding to  a  fall  of  one  foot,  and  the  values  of  ,s-  and  v/-s 182 

ARTICLE  14. — Formula*  for  mean  velocity  in  Pipes,  Sewers,  Conduits,  etc.  195 

D'Arcy's  formula  for  clean  cast-iron  pipes (51)   196 

Flynn's  modification  of  D'Arcy's  formula  (51) (52)   196 

D'Arcy's  formula  for  old  cast-iron  pipe (53)   196 

Flynn's  modification  of  D'Arcy's  formula  (5;>) (54)  196 

Molesworth's  modification  of  Kutter's  formula  (40) (55)   196 

Flynn's  modification  of  Kutter's  formula  (40) (56)  196 

Lampe's  formula   (57)  196 

Weisbach's  formula (58)  197 

Prony's  formula (59)   197 

Eytelwein's  formula  is (60)  197 

Another  formula  of  Eytelweiii (61)  197 

D'Aubisson's  formula (62)  197 

Hawksley's  formula (63)  197 

Poncelet's  formula (64)  197 

Blackwell's  formula (65)  197 

Neville's  formula (66)  197 


TABLE    OF    CONTENTS.  Vll 


Hughes'  modification  of  Eytelwein's  formula  (61) (67)  197 

Blackwell's  modification  of  Eytelwein's  formula  (61) (68)  198 

Kirkwood's  formula  for  tuberculated  pipes (69)   198 

ARTICLE  15.     Remarks  on  the  formulae 198 

Major  Alleu  Cunningham's  experiments -rr— . 200 

48-inch  Glasgow  water  pipes 201 

Table  34 — Giving  the  value  of  c  in  the  formula  v  =  c^/rs  in  ten  dif- 
ferent formulse 203 

ARTICLE  16 — Values  of  c  and  cv^for  Circular  Channels  flowing  full. 

Slopes  greater  than  1  in  2640 204 

Table  35 — Giving  the  value  of  c  for  different   values   of  \/r  and  s  in 

Kutter's  formula  with  n  =  .013 204 

ARTICLE  17 — Construction  of  Tables  for  Circular  Channels 205 

ARTICLE  18 — The  Tables  as  a  Labor-Saving  Machine .....    206 

Table  36 — Giving  the  discharge  in  cubic  feet  per  second,  of  Circular 

and  Egg-shaped  Sewers,  based  on  Kutter's  formula,  with  n  =  .013  207 
Table  37 — Giving  the  velocity  in  feet  per  second  in  Pipes,  Sewers,  Con- 
duits, by  Kutter's  formula,  with  n  =  .011 207 

ARTICLE  19 — Discussion  on  Kutter's  formula 208 

Table  38 — Giving  the  co-efficients  of  discharge,  c,  in  Circular  Pipes,  of 

different  diameters  and  different  grades,  with  n  —  .013 211 

Table  39 — Giving  values  of  c,  the  co-efficient  of  discharge,  according 

to  different  modifications  of  Kutter's  formula,  with  n  =  .013 213 

Table  40 — Giving  the  mean  velocity  in  feet  per  second,  of  pipes  of  dif- 
ferent diameters  and  grades,  with  n  -~=  .013 214 

Mr.  Guilford  Molesworth's  note 215 

ARTICLE  20 — Flynn's  modification  of  Kutter's  formula 215 

Table  41 — Giving  the  value  of  K,  for  use  in  Flynn's  modification  of 

Kutter's  formula 216 

Table  4% — Giving  values  of  \/r  for  Circular  Pipes,  Sewers  and  Con- 
duits of  different  diameters 217 

ARTICLE  21 — D^Arcy's  formula 217 

Four  feet  Glasgow  Water  Pipes 218 

D'Arcy's  formula  for  finding  the  mean  velocity  in  clean  cast-iron 

pipes 220 

D'Arcy's  formula  for  finding  the  velocity  in  old  cast-iron  pipes .  .   222 

ARTICLE  22 — Comparison  of  the  co-efficients  for  small  diameters,  of  the 

Formula*  of  D'Arcy,  Kutter,  Jackson  and  Fanning 223 

Table  43 — Of  co-efficients  (c),-  from   the  formulae  of  D'Arcy,   Kutter, 

Jackson  and  Fanning 224 

ARTICLE  23 — Pipes,  Sewers,  Conduits,  etc.,  having  the  same  velocity .  .  .   226 

Table  44 — Pipes,  Sewers  and  Conduits  having  the  same  valocity  and 
the  same  grade,  but  with  different  velocities  and  different  values 
of  n,  based  on  Kutter's  formula 227 


Vlll  TABLE    OF    CONTENTS. 

Page 

Table  45 — Egg-shaped  Sewers  having  the  same  velocity  and  the  same 
grade,  but  with  different  dimensions  and  different  values  of  n, 
based  on  Kutter's  formula 228 

ARTICLE  24 — Pipes,  Sewers  and  Conduits  having  the  same  discharge. .    228 

Table  46 — Pipes,  Sewers  and  Conduits  having  the  same  grade  and  the 
same  or  nearly  the  same  discharge,  but  with  different  diameters 
and  different  values  of  n 229 

ARTICLE  25 — Egg-shaped  Seiuers 230 

ARTICLE  26 — Explanation  and  Use  of  the  Tables 231 

Pipes,  Sewers  and  Conduits 231 

Example  21 — Given  the  diameter,  length,  fall  and  value  of  n  of  an 

inverted  Pipe  Syphon,  to  find  its  mean  velocity  and  discharge. . . .  231 

Example  22 — Given  the  discharge  and  cross-sectional  dimensions  of 
a  rectangular,  masonry  Inverted  Syphon,  to  find  its  grade  or  fall 
from  the  surface  of  water  at  inlet  to  its  outlet 232 

Example  23 — Given  the  diameter  and  grade  of  a  Pipe,  to  find  its 
mean  velocity  and  discharge  by  D'Arcy's  formula  (51)  for  clean 
cast-iron  pipes 234 

Example  24 — Given  the  grade,  mean  velocity  and  value  of  n  of  a  Cir- 
cular Sewer  to  find  its  diameter 235 

Example  25 — Given  the  discharge,  grade  and  value  of  n  of  a  Circular 

Sewer  to  find  its  diameter 236 

Example  26 — Given  the  diameter,  the  value  of  n  and  the  mean  velocity 

in  a  Pipe  to  find  its  inclination  or  grade 236 

Example  21 — Given  the  diameter,  discharge  and  value  of  n  of  a  Cir- 
cular Conduit  flowing  full  to  find  the  slope  or  grade 237 

Example  28 — To  find  the  diameter  in  three  sections  of  an  intercepting 
sewer,  with  increasing  discharge,  the  grade  or  inclination  being 
the  same  throughout,  and  the  value  of  n  being  given 237 

Example  29 — To  find  the  value  of  c  and  n  of  a  pipe 239 

Example  30 — Given  the  diameter  of  an  old  pipe,  to  find  the  diameter 

of  a  new  pipe  to  discharge  double  that  of  the  old  pipe 240 

Example  31 — Given  the  discharges  and  grades  of  a  system  of  pipes  to 

find  the  diameters 240 

Example  32— To  find  the  dimensions  of  an  Egg-shaped  Sewer  to  re- 
place a  Circular  Sewer 242 

Example  33 — To  find  the  diameter  of  a  Circular  Sewer  whose  dis- 
charge, flowing  full  depth,  shall  equal  that  of  an  Egg-shaped 
Sewer  flowing  one-third  full  depth 243 

Example  34— In  the  same  way  as  in  Example  33,  we  can  find  the 
diameter  of  a  Circular  Sewer,  whose  velocity  flowing  full  shall 
equal  the  velocity  of  an  Egg-shaped  Sewer  flowing  one-third  full 
depth 243 

Example  35 — To    find    the   dimensions  and  grade  of  an  Egg-shaped 

Sewer  flowing  full,  the  mean  velocity  and  discharge  being  given. .   243 


TABLE    OF    CONTENTS.  IX 

Page 

Example  36 — The  diameter  and  grade  of  a  Circular  Sewer  being  given, 
to  find  the  dimensions  and  grade  of  an  Egg-shaped  Sewer,  whose 
discharge,  flowing  two-thirds  full  depth,  shall  equal  that  of  the 
Circular  Sewer  flowing  full  depth,  and  whose  mean  velocity  at  the 
same  depth  shall  not  exceed  a  certain  rate .  „  _^, ._..  244 

Example  37 — To  find  the  dimensions  and  grade  of  an  Egg-shaped 
Sewer,  to  have  a  certain  discharge  when  flowing  full,  and  whose 
mean  velocity  shall  not  exceed  a  certain  rate  when  flowing  two- 
thirds  full  depth 245 

Table  4? — Giving  the  hydraulic  mean  depth,  r,  for  Circular  Pipes, 

Conduits  and  Sewers , 248 

Table  48 — For  Circular  Pipes,  Conduits,  etc.,  flowing  under  pressure. 
Based  on  D'Arcy's  formula  for  clean  cast-iron  pipes.  Value  of 
the  factors  a,  c\/r  and  ac\/r 249 

Table  49 — For  Circular  Pipes,  Conduits,  etc.,  flowing  under  pressure. 
Based  on  D'Arcy's  formula  for  old  cast-iron  pipes  lined  with  de- 
posit. Value  of  the  factors  a,  c-v/Fand  ac\/r. 251 

Table.  50 — For  Circular  Pipes,  Conduits,  Sewers,  etc.  Based  on  Kut- 
ter's  Formula  with  n  =  .009.  Value  of  the  factors  a,  c\/r  and 
ac\/r 253 

Table  51 — For  Circular  Pipes,  Conduits,  Sewers,  etc.  Based  011  Kut- 
ter's  formula  with  ?i  =  .01.  Values  of  the  factors  a,  c\/r~  and 
ae-v/F 255 

Table  52 — For  Circular  Pipes,  Conduits,  Sewers,  etc.  Based  on  Kut- 
ters  formula  with  ?i  =  .011.  Values  of  the  factors  a,  cv"Y"aiid 
ac^/r 257 

Table  53 — For  Circular  Pipes,  Conduits,  Sewers,  etc.  Based  011  Kut- 
ter's  formula  with  n  —  -012.  Values  of  the  factors  a,  c\/r  and 
ac^/r 259 

Table  54 — For  Circular  Pipes,  Conduits,  Sewers,  etc.  Based  011  Kut- 
ter's  formula  with  n  =  .013.  Values  of  the  factors  a,  c\/r  and 
ac^/r 261 

Table  55 — For  Circular  Pipes,  Conduits,  Sewers,  etc.  Based  on  Kut- 
ter's  formula  with  n  =  .015.  Values  of  the  factors  a,  c\/r  and 
acx/r  ; 263 

Table  56 — For  Circular  Pipes,  Conduits,  Sewer's,  etc.  Based  on  Kut- 
ter's  formula  with  w  =  .017.  Values  of  the  factors  a,  c\/r  and 
ac^/r. .  .  265 


X  TABLE    OF    CONTENTS. 

Page 
Table  57 — For  Circular  Pipes,  Conduits,  Sewers,  etc.     Based  on  Kut- 

ter's  formula  with  n  =  .020.     Values   of  the  factors   a,  c-^/r  and 

ac^/7 266 

Table  58 — Giving  the  value  of  the  hydraulic  mean  depth,  r,  for  Egg- 
shaped  Sewers  flowing  full  depth,  two-thirds  full  depth,  and  one- 
third  full  depth 267 

Table  59— Egg-shaped  Sewers  flowing  full  depth.     Based  on  Kutter's 

formula  with  n  =  .011.     Values  of  the  factors  a,  c\/r~a,ud  ac-^/r..   268 
Table  60 — Egg-shaped  Sewers  flowing  two-thirds  full  depth.     Based 

on  Kutter's  formula  with  n  =  .011.     Values  of  the  factors  a,  c^/7 

and  ac-^/r   269 

Table  61 — Egg-shaped  Sewers  flowing  one-third  full  depth.     Based  on 

Kutter's   formula  with  n  —  .011.      Values    of  the  factors   a,  c^/r 

and  ac^r 270 

Table  62 — Egg-shaped  Sewers  flowing  full  depth.     Based  on  Kutter's 

formula  with  n  =  .013.     Values  of  the  factors  a,  cv'Fand  ac-^/^r. .   271 
Table  63 — Egg-shaped  Sewers  flowing  two-thirds  full  depth.    Based  on 

Kutter's  formula,  with  n  =  .013.   Values  of  the  factors  a,  c\/r~and 

acx/?7 7 272 

Table  64 — Egg-shaped  Sewers  flowing  one-third  full  depth.    Based  on 

Kutter's   formula   with  n  =•.  .013.     Values  of  factors  a,  c^/c  and 
acVr 273 

Table  65 — Egg-shaped  Sewers  flowing  full  depth.     Based  on  Kutter's 

formula,  with  n  =  .015.     Values  of  the  factors  a,  c\/r^aud  ac\/r.  274 
Table  66--Egg-shaped  Sewers  flowing  two-thirds  full  depth.    Based  on 

Kutter's  formula,  with  n  =  .015.    Values  of  the  «,  cv'r'and  ac\/~275 
Table  67 — Egg-shaped  Sewers  flowing  one-third  full  depth.    Based  on 

Kutter's  formula,  with  n  =  .015.      Values  of   the  factors  a,  c\/r 

and  ac-s/r~ , 276 

Table  68 — Giving  Velocities  and  Discharges  of  Circular  Pipes,  Sewers 

and  Conduits.  Based  on  Kutter's  formula,  with  n  =  .013 277 

Table  69 — Giving  Velocities  and  Discharges  of  Egg-shaped  Sewers. 
Based  on  Kutter's  formula,  with  n  =  .013.  Flowing  full  depth. 
Flowing  f  full  depth.  Flowing  $  full  depth 279 

j£>r0^  LIST    OF    ILLUSTRATIONS  Page 

1  Trapezoidal  Channels 30 

2  Rectangular  Channel 30 

3  V-Flume 30 

4  Cross-section  of  Egg-shaped  Sewer 230 

5  Profile  of  Inverted  Syphon 231 


FLOW   OF   WATRR 


IRRIGATION  CANALS 


AND 


Open  and  Closed  Channels  Generally. 


Article  i.     Introduction. 

Almost  all  the  old  hydraulic  formulsG,  given  below, 
for  finding  the  mean  velocity  in  open  and  closed  chan- 
nels have  constant  co-efficients,  and  are  therefore  correct, 
for  only  a  small  range  of  channels.  They  have  often 
been  found  to  give  incorrect  results  with  disastrous 
effects,  as  011  the  Rhone,  in  France,  and  the  Upper 
Ganges  Canal,  India.  The  results  of  the  gauging  of 
large  rivers,  such  as  the  Mississippi,  by  Humphrey  and 
Abbott;  the  Irrawaddy,  by  Gordon;  the  Upper  Ganges 
Canal,  by  Cunningham;  small  open  channels,  by  Bazin 
and  D'Arcy,  and  cast-iron  pipes  by  D'Arcy,  prove  con- 
clusively the  inaccuracy  of  the  old  formulae  and  the 
accuracy,  within  certain  limits,  of  the  formulae  of 
Kutter,  Bazin  and  D'Arcy.  Ganguillet  and  Kutter 
thoroughly  investigated  the  American,  French  and 
other  experiments,  and  they  gave,  ,as  a  result  of  their 
labors,  the  formula  now  generally  known  as  Kutter's 
formula. 


2  FLOW    OF    WATER    IN 

There  are  so  many  varying  conditions  affecting  the 
flow  of  water,  that  all  hydraulic  formula)  are  only  ap- 
proximations to  the  correct  result,  and  the  hest  that  an 
engineer  can  do  is  to  use  the  most  correct  of  all  the 
known  formulae. 

Major  Allan  Cunningham,  R.  E.,  carried  out  experi- 
ments, on  a  most  extensive  scale,  lasting  over  four  years, 
(1874-79),  on  the  Upper  Ganges  Canal,  near  Roorkee, 
India.  Major  Cunningham  states: — '* 

"  The  main  object  of  the  undertaking  was  to  interpo- 
late something  between  Mr.  Bazin's  experiments  on 
small  canals  and  the  experiments  on  American  rivers, 
chiefly  with  a  view  to  discharge  measurement  on  large 
canals,  the  proper  measurement  of  such  discharge  being 
of  great  practical  importance,  but  hitherto  attended  with 
much  uncertainty.  For  any  such  work  there  are  good 
opportunities  in  India  from  its  system  of  canals,  both 
large  and  small,  pre-eminent  among  which  is  the  Ganges 
Canal. 

'  The  extensive  scale  of  the  operations  can  be  judged 
from  the  following  abstract: —     *     "*     * 

"The  total  number  of  velocity  measurements  was 
about  50,000,  Besides  these,  there  were  many  occasional 
special  experiments,  which  together  form  an  important 
addition.  *  *  * 

"  An  important  feature  in  this  work  is  the  great  range 
of  conditions  and  data,  and  therefore  of  results  obtained, 
this  being  essential  to  the  discovery  of  the  laws  of  com- 
plex motion.  Thus  the  velocity  work  was  done  at 
thirteen  sites,  differing  much  in  nature,  some  being  of 
brick,  some  of  earth;  in  figure,  some  being  rectangular, 
some  trapezoidal;  and  in  size,  the  surface-breadth  vary- 
ing from  193  feet  to  13  feet,  and  the  central  depth  from 

*  Recent  Hydraulic  Experiments  in  the  Minutes  of  Proceedings  of  the 
Institution  of  Civil  Engineer's,  Volume  71. 


OPEN    AND    CLOSED    CHANNELS.  3 

11  feet  to  8  inches.  At  one  of  the  sites  the  ranges  of 
some  of  the  conditions  and  results  were:  central  depth, 
from  10  feet  to  8  inches;  surface  slope,  from  480  to  24  per 
million;  velocity,  from  7.7  feet  to  0.6  feet  per-seeond; 
cubic  discharge,  from  7,364  to  114  cubic  feet  per 
second.  *  *  * 

"  After  discussing  various  known  formulae  for  mean 
velocity,  the  only  ones  that  appeared  worth  extended 
trial  were  Bazin's  *  formulas  for  the  co-efficients  ft  and  0, 
and  Kutter's  for  the  co-efficient  C.  Accordingly,  the 
values  of  these  co-efficients,  from  the  published  Tables, 
have  been  printed  alongside  the  experimental  mean 
serial  values,  seventy-six  of  /?  and  eighty-three  of  C.  As 
to  Bazin's  two  co-efficients  (ft,  C),  the  discussion  shows 
that  neither  is  reliable,  and  that  the  use  of  the  former 
with  surface-velocity  leads  to  under-estimation  of  mean 
velocity,  and  that  the  latter  is  defective  in  not  contain- 
ing s.  As  to  Kutter's  co-efficient  (7,  the  discrepancies 
between  the  eighty-three  experimental  and  computed 
values  were: — 

11  Thirteen,  over  10  per  cent. 

"  Five,  over  7J  per  cent. 

"  Fifteen,  over  5  per  cent. 

"  Seventeen,  over  3  per  cent. 

"  Thirty-three,  under  3  per  cent. 

"  Now  in  all  the  discrepancies  over  10  per  cent.,  it 
was  found  that  the  state  of  water  was  unfavorable  for 
the  slope-measurement.  Taking  this  into  account,  along 
with  the  varied  evidence  in  Kutter's  work,  it  seems  fair 
to  accept  Kutter's  co-efficient  as  of  pretty  general  appli- 
cability; also  that  when  the  surface  slope  measurement 
is  good,  it  will  give  results  seldom  exceeding  7J  per  cent, 
error,  provided  that  the  rugosity-co-efficient  of  the 

*  "Eecherches  experimentales  sur  Fecoulement  de  Feau  dans  les  cauaux 
decouverts." 


4  FLOW    OF    WATER    IN 

formula  be  known  for  the  site.  For  practical  applica- 
tion extreme  care  would  be  necessary  about  the  slope- 
measurement,  and  the  rugosity-co-efficient  could  only 
be  determined,  according  to  present  knowledge,  by 
special  preliminary  experiments  at  each  site.  * 

"  The  accuracy  of  the  D'Arcy-Bazin  experiments,  on 
which  so  much  stress  had  been  laid,  had  never  been 
questioned.  The  suggestion  that  the  failure  of  their  co- 
efficients, when  applied  to  the  Roorkee  results,  was  due  to 
the  disparity  of  proportions  of  the  D'Arcy-Bazin  canals, 
and  the  Ganges  Canal,  was  very  likely  correct,  and 
amounted  to  an  admission  of  the  want  of  generality  of 
those  co-efficients,  as  urged  in  'the  paper.  *  * 

"  Much  special  experiment  was  done  (with  surface 
slope  measurement),  and  with  the  definite  result  that 
Kutter's  formula  was  the  only  one  not  requiring  velocity 
measurement  of  pr?tty  general  applicability,  and  would 
under  favorable  conditions,  give  results  differing  by  not 
more  than  7J  per  cent.,  from  actual  velocity  measure- 
ments. This  was  surely  a  definite  and  important  re- 
sult," 

The  above  is  conclusive  as  to  the  correctness  of 
Kutter's  formula.  For  small  open  channels  D'Arcy  and 
Bazin's  formulae,  and  for  cast-iron  pipes  D'Arcy's 
formulae,  are  generally  accepted  as  being  approximately 
correct.  Engineers,  who  desire  to  keep  up  with  the 
progress  of  Hydraulic  Science,  now  generally  use  one  or 
all  of  the  formulae  of  Kutter,  D'Arcy  and  Bazin,  in  prefer- 
ence to  the  old  and  inaccurate  formulae  formerly  in 
universal  use.  The  objection  to  the  former  formulas, 
however,  is  that  they  are  in  a  form  not  adapted  for 
rapid  work,  and  that  they  are  tedious  and  troublesome 
in  application. 

The  object  of  this  work  by  the  writer  is  to  simplify 
and  facilitate  the  application  of  these  formulae,  so  as  to 


OPEN    AND    CLOSED    CHANNELS.  5 

effect  a  great  saving  of  both  time  and  labor,  which  is  a 
matter  of  great  importance  to  an  engineer  in  active 
practice. 

Article  2.     The  application  of  Kutter's  Formula  simpli- 
fied and  facilitated  by  the  use  of  the  Tables. 

The  plan  on  which  the  tables  are  constructed  will  be 
briefly  stated  here,  and  their  use  will  be  fully  explained 
in  Article  13. 

The  solution  of  problems,  relating  to  open  channels 
given  in  this  work,  is  similar  to  the  methods  given  by 
the  writer  in  No.  67  of  Van  Nostrand's  Science  Series 
(1883),  entitled  Hydraulic  Tables  based  on  Kutter's  Form- 
ula, and  also  given  in  No.  84  (1886),  entitled  The  Flow 
of  Water  in  Open  Channels,  Pipes,  Sewers  and  Conduits. 
The  present  work  is  based  on  the  same  principles,  and 
is  intended  to  facilitate  and  simplify  the  computations 
relating  to  Open  Channels  in  a  somewhat  similar  way 
to  that  already  adopted  for  closed  channels. 

Kutter's  formula  for  measures  in  feet  is: — 


n 


and  putting  the  first  factor  on  the  right  hand  side  of  the 
equation  =c,  we  have:  — 


v.s  =  c  X  }r  X 
Q  =  av  =  cXa  \/r  X  j/s 

The  factors  on  the  right  hand  side  of  the  equation  are 
tabulated,  for  different  grades  and  dimensions  of  chan- 
nel, and  also  for  different  surfaces  of  channel  over  which 

the  water  flows.     The  tables  give  the  value  of  c,  c-[/r,  a, 
r}  ]/r,  a\/r  and  \/s.     All  that  is  then  necessary,  for  the 


6  FLOW    OF    WATER    IN 

solution  of  any  problem  relating  to  open  channels,  is  to 
find  out  in  the  tables  the  value  of  the  factors  for  the 
channel  under  consideration,  and  to  substitute  these 
values  in  such  of  the  formulae,  41  to  49,  as  may  be  suit- 
able for  the  work  in  hand,  and  then,  by  simple  multi- 
plication and  division,  the  solution  of  the  problem  can 
be  quickly  obtained. 

For  example  : —  Find  the  velocity  in  a  channel  having 
a  bottom  width  of  18  feet,  a  depth  of  2  feet,  side  slopes 
of  1  to  1,  a  grade  of  1  in  1000  and  -n=.0275. 

In  Table  8  we  find  under  a  bed  width  of  18  feet,  and 

opposite  a  depth  of  2  feet,  that  \/r—I.3.  In  Table  25, 
with  n= . 0275,  under  a  slope  of  1  in  1000,  and  opposite 

V/'/'=1.3,  we  find  the  value  of  q/V=73.9.  In  Table  33, 
opposite  1  in  1000,  we  find  \/~s=. 031623. 

Substituting  the  values  of  c\/r  and  v/s,  in  formula 
(41),  we  have: — 

v  ---=  73.9  X  .031623  =  2.33  feet  per  second. 

This  is  a  much  quicker  method  than  computing  the 
velocity  by  working  out  Kutter's  formula  (40). 

Article  3.    Formulae  for  Mean  Velocity  in  Open  Channels. 

In  the  following  formulae  and  in  what  follows: — 

v  =  mean  velocity  in.  feet  per  second. 

t>max  =  maximum  surface  velocity  in  feet  per  second. 

vb  =  bottom  velocity  in  feet  per  second. 

Q  —  discharge  in  cubic  feet  per  second. 

a  =  area  of  cross  section  of  water  in  square  feet. 

p  =  wetted  perimeter  or  length  of   wetted  border  in 

lineal  feet. 
w  =  width  of  surface  of  water  in  channel  in  feet. 


OPEN    AND    CLOSED     CHANNELS.  7 

r  hydraulic  mean  depth  in  feet;   =  area  of 
r  =  --  =  <  cross  section   in   square   feet,  divided  by 
?         ^  wetted  perimeter  in  lineal  feet. 


h  =  fall  of  water  surface  in  any  distance  Z. 

I  =  length  of  water  surface  for  any  fall  A. 

s  =  fall  of  water  surface  (h)  in  any  distance  (I)  divided 

by  that  distance  '==  ~r=  sine  of  slope. 

L 

/  —  fall  in  feet  per  mile. 

c  =  co-efficient  of  mean  velocity. 

(       the  natural  co-efficient  depending  on  the  nature 
,  j    =  of  the  bed;  that  is,  the  lining  or  surface  of  the 

channel  over  which  the  water  flows. 
g  =  acceleration  of  gravity  =  32.16. 
The  following  extract  on  the  value  of  g  is  from  Mer- 
rimaii's  Hydraulics: — 

"The  symbol  g  is  used  in  hydraulics  to  denote  the 
acceleration  of  gravity;  that  is,  the  increase  in  velocity 
per  second  for  a  body  falling  freely  in  a  vacuum  at  the 
surface  of  the  earth.  *  *  *  * 

"  The  following  formula  of  Pierce,  which  is  partly 
theoretical  and  partly  empirical,  gives  the  value  of  g  in 
feet  for  any  latitude  Z,  and  any  elevation  e  above  the 
sea  level,  e  being  taken  in  feet: — 

g  =  32. 0894(1  -{-0.0052375  sin2  Z)  (1— 0.0000000957e), 
and  from  this  its  value  may  be  computed  for  any  locality. 
"  For  the  United  States  the  practical  limiting  values 
are 

L  ==  49°,  e  =  0;  whence  g  =  32 . 186; 
L  =  25°,  e  =  10000  feet;   whence  g  =  32.089. 
The  value  of  the  acceleration  is  taken  to  be,  unless 
otherwise  stated, — 

g  =  32.16  feet  per  second; 


8  FLOW    OF    WATER    IN 

from  which  the  frequently  recurring  quantity  j/%  is 
found  to  be 

j/20  =8.02. 

"If  greater  precision  be  required,  which  will  rarely 
be  the  case,  g  can  be  computed  from  the  formula  for  the 
particular  latitude  and  elevation  above  the  sea." 

The  following  collection  of  formulae,  for  finding  the 
mean  velocity  in  open  channels,  is  compiled  from  various 
authorities.  It  is  believed  that  such  a  collection  will  be 
useful,  not  only  for  reference,  but  also  for  comparison  of 
the  old  with  the  most  modern  and  accurate  formulae. 
It  is  also  believed  to  contain  almost  all  the  formula}  in 
general  use  at  various  times  and  places  up  to  date.  All 
the  formulae  are  given  in  feet  measures. 

D'Aubisson's 
Taylor's 


Downing's 
Beardmore's 
Leslie's 
Pole's 


formula  for  large  ) 

-,         .,     .  [i>= 

and  rapid  rivers    } 


/1X 
(1) 


Leslie,  for  small  streams:  v  =  68  j/rs (2) 

Stevenson,  for  streams  over      )          n/3     / —  /0\ 

v  =  96  yrs (3) 

2,000  cubic  feet  per  minute  \ 

Stevenson,  for  streams  under  )          ac. 

\v  =  69  i/T8 (4) 

2,000  cubic  feet  per  minute  ) 

D'Aubisson,  for  velocities )          nr  „     , —  /rx 

U  =  95.6vAs (5) 

over  2  feet  per  second     ) 

D'Aubisson :  v  =  (8976 .  5rs  +  .  012)  -- .  109 (6) 

Beardmore  v  =  94 . 2  \/rs (7) 

Eytelwein:v  =  93.4  \/rs (8) 


OPEN    AND    CLOSED    CHANNELS.  9 

Eytelwein :  v  =  (8975 . 43  r  s  +  .  011589)*  —  .  1089  ...     (9) 

Neville,  straight  rivers  with  velocity  \  ^  __  ^  3 

up  to  1 . 5  feet  per  second  ( 

—  — _ 
Neville,  straight  rivers  with  velocity  )  v  __  93  g     /-; 

above  1.5  feet  per  second  \ 

Neville. v  =  140  ^/rs  —  11  f^rs (12) 

Dwyer:v  =  0.92  \/2fr (13) 

This  formula  corresponds  with  v  =  94 . 2  i/rs. 

Dupuit:<y=     sra    +(.0067  +  9114^  —.082 (14) 


(  r»      (  B  V)* 
Youngs  formula:,^  jS2+(j52)  ( 

where  A  = 


.0296 
and  5  = 


i 

1,-hyp.  log(±-}-1.6) 
«  / 


.5 
Young's  formula:  v==84.3v/r«  ...................  (16) 

Dubuat's  formula 

88.49(^-0.03) 


where  hyp.  log  =  2.302585. 

Girard's  formula:  v=(10567.8r8  +  2.67)s  —1.64.  ____  (18) 


Girard's  formula  v  =  103  T/^—  1.64  ..............  (19) 

De  Prony's  formula  for  canals:  — 

v=(0.  0556  +  10593rs)*  —0.2357  ..........  (20) 

For  canals  and  pipes  :v=(Q.  0237  +  9966?\s)J—  0.1542  (21) 


10  FLOW    OF    WATER    IN 

Weisbach's  coefficient:v=(0.  00024  +  8675rs)*—  0.0154(22) 

St.  Venant's  formula:  v=  106.  068(rs)"  ............  (23) 

Ellet's  formula  :v=0.  64  (  A  /  )*  +  0.04  A/  ......  (24) 

where  A=rnaxium  depth  of  stream  in  feet. 

Provis's  formula  :v=60  i/rs  +  120  ^rsf.  .........  (25) 

Hagen's  formula  :v=4.  39  (r)*  X(s)J  ..............  (26) 

Schlichting's  derivation  of  Hagen's  formula:  — 
For  large  rivers  and  canals  :i>=6  (r)*X(s)fc  ........  (27) 

Ganguillet  and  K  utter   condemn  Hagen's  formulae  as 

tl  absolutely  useless." 


Tanning's  formula:  v=  .  .  (28) 

\  m 

j  2qrs 

and  in  =-£-— 


Humphrey's  and  Abbot's  formula:-  — 


vc=  .!     1  .  00816  +  (225rj8*)>—  .  09&*  I  —  2  '  4  ^^-  .....  (29) 
(  \  )          1+1' 

1    AQ 

Where  6=  function  of  depth  for  small  streams  — 


and  vl=  value  of  first  term  in  expression  for  v. 

For  rivers  whose  hydraulic  mean  depth  exceeds  12  or 
15  feet,  b  may  be  assumed  to  be  0.1856,  which  will  make 
the  numerical  value  of  the  term  involving  b  so  small 
that  it  may  be  generally  neglected,  reducing  the  above 
equation  to 

^={(22^18*)*—  .0388}2  ......................  (30) 

Gauchler's  formulae: 

When  s  is  greater  than  .0007,  that  is  greater  than  1  in 
1429, 

(«;)*=  1.219XfciXr*XS*  .......................  (31) 

When  s  is  less  than  .0007,  that  is  less  than  1  in  1429 

.............  .............  (32) 


OPEN    AND    CLOSED     CHANNELS. 


11 


TABLE  1.     Giving   the  values    of    the    co-efficients,   klf   k.,,   to  be   em- 
ployed in  Gauchler's  formulae  for  canals  and  rivers  and  other  open  channels: 


NATURE   OF   CHANNEL. 


s  greater  than  .0007     s  less  than  .( 


Masonry,  cut  stone  and  mortar.  .  . 

From  8.5  to  10 
"     7.6  "  8.5 

From  8.5 

8.0 

to  9.0 

"   8.5 

Masonry  sides;  earth  bottom 

"     6.6  "  7.6 

"       77 

"80 

Small  water-courses  in  earth  free 
of  weeds  

"     5.7  "6.7 

"      70 

"  7.7 

Small  water-courses  in  earth,  grass 
on  slopes  .           

"     5.0  "5.7 

6.6 

"  7.0 

Rivers  

Nil 

6.3 

"  7.0 

Molesworth's  formula: 
v  =  \/kr8 


TABLE  2.     Giving  the  value  of  the  co-efficients  k  in  Molesworth's  formula 
for  canals  and  rivers. 


NATURE   OF   CHANNEL. 


VALUES   OF    k   FOR   VELOCITIES. 


Less  than  4  feet  per  second. 

More  than  4  feet  per  second. 

Brickwork 

8800 

8500 

Earth 

7200 

6800 

Shingle  .        ... 

6400 

5900 

Rough,  with  bowlders..  .  . 

5300 

4700 

In  very  large  channels,  rivers,  etc.,  the  description  of 
the  channel  affects  the  result  so  slightly  that  it  may  be 
practically  neglected,  and  assumed=from  8,500  to  9,000. 

Bazin's  formulae: 

For  very  even  surfaces,  fine  plastered  sides  and  bed, 
planed  planks,  etc  • 


v=  J  1-^.0000045 


(34) 


12  FLOW    OF    WATER    IN 

For  even  surfaces,  such  as  cut  stone,  brickwork,  un- 
planed  planking,  mortar,  etc.: 


v  =  -Jl-i-. 000013  (4. 354+-^  XiA*..  .  (35) 

\  \  r/ 

For  slightly  uneven  surfaces,  such  as  rubble  masonry: 

<  i/rx (36) 

For  uneven  surfaces,  such  as  earth: 


v  =  Jl--.  00035  ^0.2438  +-  -  -  W  vA*  ............  (37) 

A   modification   of   Bazin's    formula   (37),   known   as 
D'Arcy  Bazin's: 


(38) 


. 
.08534r  +0.35 

Brandreth's  modification  of  Bazin's  formula  (37)  is: 

2r 

XV//  ..........................  (39) 


V/7  +  1.7066r 

where  /=  fall  in  5,000  feet,  which  is  the  length  of  the 
old  English  mile,  now  used  on  Indian  irrigation  canals. 


Kutter's  formula  is: 

•('       1^1+41. 

n 

v  =  /  — 


X\/T8 (40) 


and  calling  the  first  term  of  the  right-hand  side  of  the 
equation  equal  c,  we  have  Chezy's  formula: 

v=cX\/rs  =  c  X  v/^X  V~* (41) 

^•==---- ••••• (42> 


OPEN    AND    CLOSED    CHANNELS. 
x—             V 

-\/  s  — 

13 
(43) 

V  d           /  —  .... 
cyr 

„_  (  -  ...  Y 

.  (44) 

Vr/ 

Now  <2=av=aXcv/rX\/8"  ) 

.  (45) 

==a  t/FXcXv/*         ) 

:'...«=« 

.  (46) 

r 
acv/r—  -  ^ 

.  (47) 

i/s 
v/<-      « 

.  (48) 

ac\/f 

/    «    V 

.  (49) 

\ac\/T     / 
,_          F        „           Q 

.   (50) 

X  \/s       a  \/r  X 

Article  4.     Remarks  on  the  Formulae. 

Most  of  the  old  formulae  have  constant  co-efficients, 
and  therefore  give  accurate  results  for  only  one  channel, 
having  a  hydraulic  mean  radius  of  a  certain  value. 
Only  four  of  the  authorities,  whose  formula  are  given 
in  Article  3,  have  taken  into  account  the  nature  of  the 
material  forming  the  surface  of  the  channel.  These  are 
Gauchler,  Bazin,  Molesworth  and  Kutter.  The  value 
of  the  co-efficients  in  Bazin's  formulae  depends  on  the 
nature  of  the  surface  of  the  material  over  which  the 
water  flows,  and  also  the  hydraulic  mean  depth.  These 
co-efficients  are  not  affected  by  the  slope. 

For  small  channels  of  less  than  20  feet  bed  Bazin's 
formula,  for  earthen  channels  in  good  order,  gives  very 
fair  results,  and  tables  based  on  it  have  been  used  by 
the  Irrigation  Departments  in  Northern  India,  for  com- 


14 


FLOW    OP    WATER    IN 


puting  the  velocities  in  the  distributing  channels  (raj- 
buhas),  but  Kutter's  formula  is  superseding  it  there,  as 
in  almost  all  other  countries  where  its  accuracy  has 
been  thoroughly  investigated. 

The  formulae  of  Gauchler,  Molesworth  and  Kutter 
have  varying  co-efficients,  which  depend  for  their  value 
on  three  things  : — 

The  hydraulic  mean  depth, 

The  slope  or  grade  of  bed,  and 

The  nature  of  the  surface  of  the  material,  or  the 
wetted  peimeter,  over  which  the  water  flows. 

The  following  table  shows  the  value  of  c,  in  Kutter's 
formula,  for  a  wide  range  of  channels  in  earth,  that  will 
cover  anything  likely  to  occur  in  the  ordinary  practice 
of  an  engineer. 

TABLE  3.     Values  of  c  for  earthen  channels  by  Kutter's  formula. 


Slope 

B=.035 

^/r  in  feet. 

v'V  in  feet. 

I  in 

0.4 

1.0 

1.8 

2.5 

4.0  ! 

0.4 

1.0 

1.8 

2.5 

4.0 

c 

c 

c 

c 

c 

c 

c 

c 

c 

c 

1000 

35.7 

62.5 

80.3 

89.2 

99.9 

19.7 

37.6 

51.6 

59.3 

69.2 

1250 

35.5 

62.3 

80.3 

89.3 

100.2 

19.6 

37.6 

51.6 

59.4 

69.4 

1667 

35.2 

62.1 

80.3 

89.5 

100.6 

19.4 

37.4 

51.6 

59.5 

69.8 

2300 

34.6 

61.7 

80.3 

89.8 

101.4 

19.1 

37.1 

51.6 

59.7 

70.4 

3333 

34. 

61.2 

80.2 

90.1 

102.2 

18.8 

36.9 

51.6 

59.9 

71.0 

5000 

33. 

60.5 

80.3 

90.7 

103.7 

18.3 

36.4 

51.6 

60.4 

72.2 

7500 

31.6 

59.4 

80.3 

91.5 

106.0 

17.6 

35.8 

51.6 

60.9 

73.9 

10000 

30.5 

58.5 

80.3 

92.3 

107.9 

17.1 

35.3 

51.6 

60.5 

75.4 

15840 

28.5 

56.7 

80.2 

93.9 

112.2 

16.2 

34.3 

51.6 

62.5 

78.6 

20000 

27.4 

55.7 

80.2 

94.8 

115.0 

15.6 

33.8 

51.5 

63.1 

80.6 

All  inspection  of  the  tables  will  show  the  difference  in 
the  value  of  c,  caused  by  the  difference  in  slope,  and  also 
of  hydraulic  mean  depth.  It  shows,  for  instance,  that 


OPEN    AND    CLOSED     CHANNELS.  15 

with  n  =  .0225  and  a  slope  of  1  in  1000  the  value  of  c 
corresponding  to  \/r  =  0.4  is  35.7,  while  the  value  of  c 

corresponding  to  ]/r  ===  4.0  is  99.9,  or  an  increase  of 
about  180  per  cent.  By  the  old  formulae  the  channel, 
with  the  small  hydraulic  mean  depth,  would  have  the 
same  co-efficient  as  the  larger  channel,  and  would  there- 
fore give  very  inaccurate  results. 

We  also  see  that  with  the  same  \/r  =  4.0,  the  value  of  c 
for  a  slope  of  1  in  1000  is  99.9,  and  the  value  of  c  for  a  slope 
of  1  in  20000  is  115.0,  or  an  increase  of  about  15  per  cent., 

while  with  \/r  =  0.4  there  is  a  decrease  from  35.7  to 
27.4,  or  a  decrease  of  about  23  per  cent. 

We  again  find  that  when  \/r  =  1.8  (which  is  the  near- 
est value  of  i/rto  1.811)  the  co-efficients  for  the  same  value 

of  n  are  the  same  for  all  slopes ;  that  when  \/r  has  a  less 
value  than  1.8  the  co-efficients  increase  with  an  increase 

of  slope,  and  when  \/r  has  a  greater  value  than  1.8  the 
co-efficients  increase  with  the  decrease  of  slope. 

D'Arcy's  formuke  will  be  referred  to  in  the  Article  on 
the  Flow  of  Water  in  Pipes,  etc . 

Article  5.     Bazin's  Formula  for  Channels  in  Earth. 

For  small  channels  in  earth  in  moderately  good  order 
Bazin's  formula  (37)  gives  a  tolerable  close  approxima- 
tion to  the  mean  velocity. 

Table  30,  giving  mean  velocities  and  discharges  up  to 
20  feet  bed  width,  was  computed  for  the  Punjab  Irriga- 
tion Department  by  Captain  Allen  Cunningham,  E.  E. 
The  table  was  computed  by  a  modification  of  Bazin's 
formula  (37)  given  by  Captain  A.  B.  Brandreth,  R.  E., 
for  channels  whose  beds  and  sides  are  of  earth.* 

*  Volumes  4  and  5  of  'Second  Series  of  Professional  Papers  on  Indian 
Engineering. 


16  FLOW    OF    WATER    IN 

This  modified  form  formula  (39)  was  adopted,  as  it  was 
better  suited  for  computation  of  tables  than  Bazin's 
formula  (37).  This  formula  is: — 

2r 

x  i/y 


,    7+  1.7066  r 

where /is  the  fall  in  5,000  feet,  in  feet.  The  length  of 
the  old  English  mile  now  used  on  Indian  canals  is  5,000 
feet. 

In  order  to  show  how  the  modified  form  of  Bazin  is 
derived,  it  is  given  below. 

Bazin's  formula  for  earthen  channels  is: — 


1 

1\ 

X  l/rs 


.00035  +  (.2438  +    -\  ) 

but  y'rs  =  i/r  X  J    *     =  2  v/7-  X  J-^— 
\  5000  \  20000 

substitute  this  value  of  -\/r8  and  reduce  and 


*«J I xVrX  J     •'' 

\  .00008533  ?•  +  .00035  \  20000 

2r 

X  i// 


V/7  -{- 1.7066  r 

Article  6.     Comparing  Kutter's  and  Bazin's  Formulae. 

The  following  table  gives  a  comparison  between  the 
results  obtained  by  Bazin's  formula  (37)  for  earthen 
channels,  and  Kutter's  formula  with  ?i— .025  and 
n  —  .0275,  and  it  shows  that,  for  the  given  channels, 
Bazin's  formula  agrees  very  nearly  with  Kutter  n  =  .0275 
up  to  3  feet  in  depth,  and  with  Kutter  n  =  .025  from  3 
to  5  feet  in  depth.  It  is  also  shown  that  Bazin's 
formula  is  almost  a  mean  between  Kutter  with  n  =  .025, 


OPEN    AND    CLOSED    CHANNELS. 


17 


and  n  =  .0275;  that  is,  that  it  almost  suits  canals  and 
rivers  in  earth  of  tolerably  uniform  cross-section,  slope  and 
direction,  in  moderately  good  average  order  and  regimen 
and  free  from  stones  and  tceeds,  and  also  canals  ancljriverft 
in  earth  beloiv  the  average  in  order  and  regimen. 

The  results  again  show  that  it  gives  too  low  a  velocity 
for  canals  in  earth  above  the  average  in  order  and  regimen 
with  n  =  .0225  or  a  less  value  of  n,  and  it  further  shows 
that  it  gives  too  high  a  velocity  for  canals  and  rivers  in 
earth,  in  rather  bad  order  and  regimen,  having  stones  and 
weeds  occasionally,  and  obstructed  by  detritus,  n  =  .030. 

Bazin's  formula  (37)  gives  correct  results  for  earthen 
channels  with  only  one  value  of  n,  while  Kutter's 
formula  is  suited  to  any  channel  having  either  a  very 
rough,  medium  or  very  smooth  surface. 

TABLE  4.     Giving  the  velocity  and  discharge  of  earthen  channels  ac- 
cording to  the  formulae  of  Bazin  and  also  Kutter. 

v  —  mean  velocity  in  feet  per  second. 
Q  =  discharge  in  cubic  feet  per  second. 

Bed  width  10  feet.     Side  slopes  1  to  1.     Slope  1  in  2500.     <^/7=  .02. 


B 

i 

?i 

ffi* 

[                          i 
Bazin,  for 
Earthen 

Kutter, 

Kutter, 

& 

^  P" 

CD    P    ^ 

Channels.     ! 

n  =  .025 

n  =  .0275 

P" 

a  02 

\/r 

? 

•    ^ 

fll 

r*" 

•      CD 

:       ^°" 

;      v 

Q     ;        v 

Q 

v           Q 

1.0 

11.00 

0.858 

0.93 

0.83 

9.17 

0.97 

10.67 

0.87 

9.57 

1.5 

17.25 

1.211 

.10 

1.14 

19.63| 

1.26 

21.73 

1.14 

19.66 

2.0 

24.00 

1.533 

.24 

1.40 

33.56 

1.51 

36.24 

1.36 

32.64 

2.5 

31.25 

1.831 

.35 

1.63 

50.85 

1.72 

53.75 

1.56 

48.75 

3.0 

39.00 

2.110 

.45 

1.83 

71.48 

1.91 

74.49 

1.73 

67.47 

3.5 

47.25 

2.375 

.54 

2.02 

95.46 

2.08 

98.28 

1.89 

89.30 

4.0 

56.00 

2.628 

.62 

2.19    122.81J 

2.24 

125.44 

2.03    113.68 

4.5 

65.25 

2.871 

.70 

2.35  1153.  611    2.39 

155.95 

2.17    141.59 

5.0     75.00 

3.107 

.76 

2.51  !l87.91!|  2.53 

189.75 

2.29  1171.75 

1 

!              i 

i 
i             i 

18 


FLOW    OF    WATER    IN 


Bed  width  20  feet.     Side  slope  1  to  1.     Slope  1  in  2500.     x/«  =  -02. 


B" 

& 

CD 

|i 

5'  3^ 

* 

Baziii,  for 

Earthen 
:    Channels. 

Kutter, 
n  =  .025 

Kutter, 
n  —  .0275 

V 

Q 

V 

Q 

V 

g 

1.0 
1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
4.5 
5.0 

21.00 
32.25 
44.00 
56.25 
69.00 
82.25 
96.00 
110.25 
125.00 

0.920 
1.330 
1.715 
2.078 
2.422 
2.751 
3.066 
3.369 
3.661 

0.96 
1.15 

1.31 
1.44 
1.55 
1.66 
1.75 
1.83 
1.91 

0.89 
1.24 
1.54 
1.81 
2.05 
2.28 
2.48 
2.67 
!  2.85 

18.66 
39.85 
67.74 
101.80 
141.68 
187.15 
238.03 
294.21 
555.64 

\   1.02 
1.36 
1.64 
1.89 
2.12 
2.32 
2.50 
2.67 
2.83 

21.42 
43.86 
72.16 
106.31 
146.28 
190.82 
240.00 
294.37 
353.75 

0.91 
1.22 
1.48 
1.71 
1.91 
2.10 
2.27 
2.43 
2.58 

19.11 
39.34 
65.12 
96.19 
131.79 
172.72 
217.92 
267.91 
322.50 

Article  7      Value  of  n. 

The  accuracy  of  Kutter's  formula  depends,  in  a  great 
measure,  on  the  proper  selection  of  the  co-efficient  of 
roughness  n.  Experience  is  required  in  order  to  give 
the  right  value  to  this  co-efficient,  and,  to  this  end,  great 
assistance  can  be  obtained  in  making  this  selection,  by 
consulting  and  comparing  the  results  obtained  from 
experiments  on  the  flow  of  water  already  made  in  dif- 
ferent channels. 

In  some  cases  it  would  be  well  to  provide  for  the  con- 
tingency of  future  deterioration  of  channel,  by  selecting 
a  high  value  of  n,  as,  for  instance,  where  a  dense  growth 
®f  weeds  is  likely  to  occur  in  small  channels,  and  also 
where  channels  are  likely  not  to  be  kept  in  a  state  of 
good  repair. 

Table  5,  giving  the  value  of  n  for  different  materials, 
is  compiled  from  Kutter,  Jackson  and  Hering,  and  this 
value  of  n  applies  also,  in  each  instance,  to  the  surfaces 
of  other  material  equally  rough. 


OPEN    AND    CLOSED     CHANNELS.  19 

Table  5.     Giving  the  value  of  n  for  different  channels. 

7i  =  .009,  well-planed  timber,  in  perfect  order  and  align- 
ment; otherwise,  perhaps  .01  would  be  suitable. 

n  —  .010,  plaster  in  pure  cement  :  planed  timber ; 
glazed,  coated,  or  enamelled  stoneware  and  iron 
pipes  ;  glazed  surfaces  of  every  sort  in  perfect 
order. 

n  =  .011,  plaster  in  cement  with  one-third  sand  in  good 
condition;  also  for  iron,  cement,  and  terra-cotta 
pipes,  well  joined  and  in  best  order. 

n  =  .012,  unplaned  timber,  when  perfectly  continuous 
on  the  inside;  flumes. 

7i  =  .013,  ashlar  and  well-laid  brickwork  ;  ordinary 
metal;  earthenware  and  stoneware  pipe  in  good 
condition,  but  not  new  ;  cement  and  terra-cotta 
pipe  not  well  jointed  nor  in  perfect  order;  plaster 
and  planed  wood  in  imperfect  or  inferior  condi- 
tion ;  and,  generally,  the  materials  mentioned 
with  n  —  .010,  when  in  imperfect  or  inferior  con- 
dition. 

<tt  =  .015,  second-class  or  rough-faced  brickwork;  well- 
dressed  stonework ;  foul  and  slightly  tubercu- 
lated  iron;  cement  and  terra-cotta  pipes,  with  im- 
perfect joints  and  in  bad  order;  and  canvas  lining 
on  wooden  frames. 

n  =.017,  brickwork,  ashlar,  and  stoneware  in  an  in- 
ferior condition;  tuberculated  iron  pipes;  rubble 
in  cement  or  plaster  in  good  order;  fine  gravel, 
well  rammed,  J  to  f  inches  diameter;  and,  gener- 
ally, the  materials  mentioned  with  n  -=  .013 
when  in  bad  order  and  condition. 


20  FLOW    OF    WATER    IN 

n  —  .020,  rubble  in  cement  in  an  inferior  condition; 
coarse  rubble,  rough-set  in  a  normal  condition; 
coarse  rubble  set  dry;  ruined  brickwork  and 
masonry;  coarse  gravel,  wrell  rammed,  from  1  to 
1J  inch  diameter;  canals  with  beds  and  banks  of 
very  firm,  regular  gravel,  carefully  trimmed  and 
rammed  in  defective  places;  rough  rubble,  with 
bed  partially  covered  with  silt  and  mud;  rectan- 
gular wooden  troughs,  with  battens  on  the  inside 
two  inches  apart;  trimmed  earth  in  perfect  order. 

n  —  .0225,  canals  in  earth  above  the  average  in  order 
and  regimen. 

n  ==  .025,  canals  and  rivers  in  earth  of  tolerably  uniform 
cross-section,  slope,  and  direction,  in  moderately 
good  order  and  regimen,  and  free  from  stones 
and  weeds. 

n  =  .0275,  canals  and  rivers  in  earth  below  the  average 
in  order  and  regimen. 

n  =.  .030,  canals  and  rivers  in  earth  in  rather  bad  order 
and  regimen,  having  stones  and  weeds  occasion- 
ally, and  obstructed  by  detritus. 

n  =  .035,  suitable  for  rivers  and  canals  with  earthen 
beds  in  bad  order  and  regimen,  and  having 
stones  and  weeds  in  great  quantities. 

n  =  .05,  torrents  encumbered  with  detritus. 


OPEN    AND    CLOSED     CHANNELS. 


21 


TABLE  5  (continued).  The  following  table,  giving  values  of  n  for  dif- 
ferent surfaces  exposed  to  the  flow  of  water,  is  taken  from  Jackson's  trans- 
lation of  Kutter.  The  dimensions  are,  however,  changed  from  metrical  to 
feet  measures. 

r=  hydraulic  mean  depth  in  feet. 

s  =  sine  of  slope. 


SERIES  OF  BAZIN. 

T 
in  feet. 

. 

s 

Breadth  at 
water  sur- 
face in  feet 

Depth 
in 
feet. 

n 

Xo. 

28 
29 
24 
2 
25 

26 
9] 

Carefully  planed  plank.  .  . 

In  cement  —  semi-circular. 
"           rectangular.. 
In  cement,  with  one-third 
sand  —  semi-circular  .  .  . 

Plank  —  semi-circular  .... 
trapezoidal  

0.07 
0.05 
0.82 
0.49 

0.85 

0.91 

0  82 

0.0048922 
0.0152370 
0.0014243 
0.005060 

0.0013802 

0.0015227 
0  0015213 

0.328 
0.328 
3.28 
5.9 

3.28 

3.6 
4  6 

0.14 
0.079 
1.47 
0.59 

1.61 

1.61 
1  24 

0.0096 
0.0087 
0.01005 
0.01040 

0.01113 

0.01195 
0  01255 

<>9 

<« 

0  65 

0  0048751 

4  36 

0  98 

0  01190 

23 
6 

triangular  45°..  .  . 
rectangular  

0.65 
0.65 

0.004655 
0  0022136 

4.36 
6  5 

1.87 
0  85 

0.0119 
0  13 

7 

0  52 

0  004889 

6  5 

0  6° 

0  0119 

8 

0  46 

0  0081629 

6  5 

0  52 

0  0115 

9 

0  72 

0  0014678 

6  5 

0  91 

0  0129 

10 

0  46 

0  0058744 

6  5 

0  55 

0  0117 

11 

0  42 

0  0083805 

6  5 

0  49 

0  0114 

18 
19 

0.65 
0  49 

0.0045988 
0  0042731 

3.9 
2  6 

0.91 
0  82 

0.0114. 
0  0114 

*>0 

0  32 

0  0059829 

1  6 

0  62 

0  0114 

27 

RAMMED  GRAVEL 
f-  to  i  inches  thick  —  semi- 
circular   

0  75 

0  0013639 

3  28 

1  34 

0  0163 

4 

|  to  £  inches  thick  —  rect- 
angular   

0.65 

0  0049736 

6  0 

0  85 

0  0170 

12 
13 
14 
15 
16 
17 

1  ? 

BATTENS  PLACED 

1  inch  apart  —  rectangular 
((           < 

<  i           f 

2  inches  ' 

(  i           < 

«           < 
Ashlar  —  rectangular  .  . 

0.75 
0.55 
0.49 
0.95 
0.69 
0.63 

1  77 

0.0014678 
0.0059664 
0.0088618 
0.0014678 
0.0059976 
0.0088618 

0  0008400 

6.4 
6.4 
6.4 
6.4 
6.4 
6.4 

8  5 

1.01 
0.65 
0.59 
1.31 
0.88 
0.78 

3  0 

0.0149 
0.0147 
0.0149 
0.0208 
0.0211 
0.0215 

0  0133 

3 
39 

Brickwork  —  rectangular  .  . 
Ashlar  

0.55 
0  59 

0.0050250 
0  0081 

3.0 
3  9 

0.65 
0  85 

0.0129 
0  0129 

32 

RUBBLE, 
Rather  damaged  —  rectan- 
gular.. 

0  52 

0  10076 

5  9 

0  63 

0  0167 

FLOW    OF    WATER    IN 


TABLE  5. — (Continued.) 


SERIES  OF  BAZIX. 

r 

in  feet. 

s 

Breadth  at 
water  sur- 
face in  feet 

Depth 
in 
feet. 

n 

No. 

33 

EUBBLE, 
Rather  damaged  —  rectan- 
gtila,r  . 

0  65 

0  036856 

5  9 

0   88 

0  0170 

1.4 
1.3 
1.6 
1.5 
44 

Rather  damaged  —  new...  . 

With  deposits  on  the  bed, 
rectangular 

0.63 
0.72 

0.82 
0.88 

1  47 

0.060 
0.029 
0.014 
0.0122 

0  00032 

3.28 
3.28 
3.28 
3.28 

6  56 

0.95 
1.18 
1.54 
1.60 

2  62 

0.0180 
0.0184 
0.0182 
0.0192 

0  0204 

46 
35 

With  deposits  on  the  bed, 
rectangular  
Damaged   rubble  —  trape- 
zoidal   

1.31 
1  21 

0.00032 
0.014221 

6.56 
4.9 

2.29 
2.29 

0.0210 
0.0220 

OTHER  OBSERVATIONS  : 
Gontenbachschale,      new 
rubble  —  semi  -circular  .  . 
G'rumbachschale  —  semi- 
circular, damaged  
Gerbebachschale  —  semi- 
circular, damaged  

0.32 
0.46 
0.19 

0.044 
0.09927 
0.168 

5.5 

8.5 
3.7 

0  59 
0.82 
0.29 

0.0145 
0.0175 
0.0185 

Alpbachschale  —  semi-cir- 
cular, much  damaged  .  . 

Marseilles  Canal  

0.72 
2  87 

0.0274 
0  00043 

8.2 
19.6 

1.18 
4.4 

0.0230 
0  .  0244 

Jard  Canal  

I  97 

0  .  0004 

19.6 

4.4 

0.0255 

Chesapeake  Ohio  Canal  .  . 
Canal  in  England  .. 

3.7 
2  43 

0.000698 
0  000063 

22.6 

17  7 

7.9 
3  9 

0.033 
0  0184 

Lanter  Canal,  at  Newbury 
Pannerden  Canal,  in  Hol- 
land   

1.81 
10  2 

0.000664 
0  000224 

29.5 

558. 

1.8 

9.8 

0.0262 
0  .  0254 

Canal  of  Marmels 

2  31 

0  0005 

26  2 

2  6 

0  0301 

Linth  Canal  

7  8 

0.00034 

123. 

10.8 

0.0222 

Hiibengraben 

0  6 

0  0013 

4  8 

0  8 

0  0237 

Hockenbach 

0  87 

0  000787 

11   1 

1  1 

0.0243 

Speyerbach  . 

1  46 

0  000667 

16.4 

1.9 

0.0260 

Mississippi.  . 

65  6 

0  000667 

2493. 

16.4 

0.0270 

Bayou  Plaquemine 

16  8 

0.00017 

275. 

25.6 

0.0294 

Bayou  La  Fourche 

13  1 

0  00004 

220 

23  o 

0  0200 

Ohio,  Point  Pleasant  
Tiber,  at  Rome  

6.7 
9.4 

0.000093 
0.00013 

1066. 
239. 

7.9 

14.8 

0.0210 

0.0228 

Newka  . 

17  4 

0  000015 

886. 

21 

0.0252 

Newa 

35  4 

0.000014 

1214. 

19.7 

0.0262 

Weser 

9.5 

0.0002 

394. 

9.8 

0.0232 

Elbe  .                    

10.9 

0.00031 

315. 

43.6 

0.0285 

Rhine,  in  Holland  

12.4 

0.00015 

1312. 

14.7 

0.0243 

Seine  at  Paris 

12  1 

0.000137 

0.025 

Seine   at  Poissy 

13.4 

0.00007 

0.026 

Saone  at  Raconnay 

11  8 

0  00004 

0.028 

Haine  .  . 

5.2 

0.0001 

0.026 

OPEN    AND    CLOSED     CHANNELS. 


23 


TABLE  5. — (Continued.) 


SERIES  OF  BAZIN. 

r 

in  feet. 

s 

Breadth  at 
water  sur- 
face in  feet 

Depth 
in 
feet. 

n 

CHANNELS  OB  TRUCTED  BY  DETKITU3. 

Rhine,  at  Speyer         

9  7 

0  000112 

1440 

9.7 

0  026 

Rhine    at  Germersheim  

10.8 

0  000247 

748 

0.0227 

Rhine,  at  Basle  

6.9 

0.001218 

660 

9.1 

0.03 

Lech  

3.1 

0.00115 

157 

3.8 

0  .  022 

Saalach  . 

1  4 

0  0011 

68 

2  1 

0  027 

Salzach.. 

4  1 

0  0012 

38 

11  8 

0  028 

Issar  

3.9 

0  0025 

164 

4  4 

0  0305 

Escher  Canal     

4.0 

0  003 

72 

4  9 

0  03 

Plessur  

3.5 

0  00965 

42 

4  6 

0  027 

Rhine,  at  Rhiuewald  

.79 

0  0142 

14 

.99 

0  031 

Mosa,  at  Misox  
Rhine,  at  Domleschgerthal  .  .  . 
Simme,  at  Leuk  .... 

1.2 
1.9 

1.6 

0.01187 
0.0075 
0.0105 

13 
16 

1.3 
2.4 

0.031 
0.035 
0.0345 

In  order  to  show  to  what  extent  the  value  of  n  affects 
the  velocity  and  discharge  of  channels,  two  examples 
are  given  in  table  6. 


TABLE  6.     Showing  the  effect  of  the  co-efficient  of  roughness  n  on  the 
velocity  in  channels. 


Value  of 

Bed  width 
in  feet. 

Depth  in 
feet 

Side  Slopes. 

Grade  in  feet 
per  mile. 

Mean  velocity 
in  feet 

Discharge  in 
cubic  feeb  per 

: 

per  second. 

second. 

.0225 

10 

2 

1    to    1 

'.  " 
8 

3.32 

79.7 

.025 

10 

2 

8 

2.96 

71.0 

0275 

10 

2 

8 

2.67 

64.1 

.03 

10 

2 

8 

2.43 

58.3 

.035 

10 

2 

8 

2.05 

49.2 

.0225 

80 

5 

Hto  l 

2 

3.49 

1527. 

.025 

80 

5 

2 

3.15 

1378. 

.0275 

80 

5 

2 

2.87 

1256. 

.03 

80 

5 

2 

2.64 

1155. 

.035 

80 

5 

2 

2.28 

998. 

In  the  first  channel  with  a  bed-width  of  10  feet,  the 
difference  in  results  shows  that  with  a  value  of  n  =  .0225 
the  channel  has  a  discharge  of  over  60  per  cent,  more 
than  when  its  value  of  ?i  =  .035.  This  shows  the  great 
necessity  of  keeping  small  irrigation  channels  clear  of 


24  FLOW    OF    WATER    IN 

sand  bars,  brush,  weeds,  grass  and  other  obstructions  to 
the  flow. 

Again,  in  the  larger  channel  with  a  bed-width  of  80 
feet,  the  difference  in  results,  obtained  from  the  highest 
and  lowest  values  of  n,  given  in  table  6,  shows  a  varia- 
tion of  over  53  per  cent,  in  the  velocity  and  discharge. 
It  is  shown  that  the  smaller  the  channel  the  greater  is 
the  percentage  of  loss  by  keeping  it  in  a  bad  state  of 
repair. 

Article  8.     Side  Slopes. 

Tables  8,  9,  11  and  13  are  computed  for  channels  hav- 
ing side  slopes  of  1  to  1,  1  to  1,  1|  to  1,  and  vertical  or 
rectangular. 

When  the  bed  width  is  greater  .than  60  feet,  the  side 
slopes  have  very  little  effect  on  the  velocity.  Table  7, 
given  below,  well  exemplifies  this.  Six  channels  are 
given,  with  varying  bed  widths,  depths  and  grades,  and 
each  channel  has  five  different  side  slopes.  On  inspec- 
tion, it  will  be  seen  that  the  change  in  the  side  slope 
makes  no  appreciable  change  in  the  velocity  so  long  as 
the  bed  width,  depth  and  grade  or  longitudinal  slope 
remains  the  same.  For  instance,  with  a  bed  width  of 
70  feet,  a  depth  of  1  foot,  and  a  slope  of  1  in  5000,  the 
mean  velocity  is  0.74  feet  per  second  for  the  five  side 
slopes.  Again,  with  a  bed  width  of  300  feet,  a  depth 
of  14  feet,  and  a  grade  of  1  in  20,000,  the  mean  velocity 
varies  so  little  that  it  is  substantially  the  same  for  the 
five  channels,  the  greatest  velocity  being  2.35  feet  per 
second,  and  the  least  velocity  2.32  feet  per  second.  The 
table  shows,  however,  that  the  discharge  is  increased 
with  the  increased  flatness  of  the  slopes. 

In  Table  8,  with  side  slopes  of  1  to  1,  the  values  of 

the  factors  a,  \/r  and  a\/r  are  given  for  channels  up  to 


OPEN    AND    CLOSED     CHANNELS.  25 

a  bed  width  of  300  feet.  In  Tables  9,  11  and  13,  the 
values  of  these  factors  are  given  only  for  channels  up  to 
a  bed  width  of  60  feet.  For  all  channels  having  a  greater 
bed  width  than  60  feet,  and  side  slopes  differeitt-fr-orn 
1  to  1,  the  velocity  can  be  found  for  a  channel  with  the 
same  bed  width,  but  with  side  slopes  of  1  to  1,  and  this 
will  be  the  velocity  required.  To  find  the  discharge, 
this  velocity  can  be  multipled  by  the  area  of  channel. 
For  example,  let  the  velocity  and  discharge  be  required 
for  a  channel  Jiaving  a  bed  width  of  160  feet,  depth  of 
10  feet,  a  grade  of  1  in  15,840,  or  4  inches  per  mile, 
and  with  n  =  .025,  and  side  slopes  of  li  to  1.  As  the 
tables  do  not  give  the  value  of  the  factors  for  a  channel 
of  these  dimensions  with  side  slopes  H  to  1,  let  us  look 

out,  in  Table  8,  the  value  of  ]/r  for  a  similar  channel, 
but  with  side  slopes  of  1  to  1,  and  we  find  that  it  is  equal 

to  3.005.  Now  the  actual  value  of  \/r  for  a  side  slope 
of  1J  to  1  is  equal  to  2.988,  so  that,  practically,  the  value 
given  in  Table  8  is  correct. 

Now,  working  out  the  velocities,  we  find  that  side 
slopes  of  1  to  1  give  a  mean  velocity  of  2.09  feet  per  sec- 
ond, and  side  slopes  of  1J  to  1  give  a  velocity  of  2.08 
feet  per  second,  as  shown  in  Table  7. 

The  discharge,  however,  is  increased  in  proportion  to 
the  increase  of  area  of  the  channel  by  the  increased 
flatness  of  the  slopes.  This  is  shown  by  the  last  column 
of  Table  7,  showing  the  discharge  of  the  channels.  In 
the  instance  just  given,  Table  7  shows  that  with  side 
slopes  of  1  to  1  the  discharge  is  3553.7  cubic  feet  per 
second,  but  with  side  slopes  of  1J  to  1  the  discharge  is 
3631.3  cubic  feet  per  second. 


26 


FLOW    OF    WATEK    IN 


TABLE  7.     Showing    the  velocity  and  discharge  of   channels   having 
different  side  slopes.     ?i=.025. 

Bed  70  feet.     Depth  1  foot.     Slope  1  in  5,000.     n=.0'25. 


CROSS  SECTION       n                r 

Vr 

c-v/r 

Vs 

Velocity  in 
feet  per 
second. 

Discharge 
in  cubic 
feet  per 
second. 

Eectangular 

70.0 

0.972 

0.986 

52.438 

.014142 

0.7415 

51.91 

I  to  1  

70.5 

.976 

.988 

52.604 

.014142 

0.744 

52.45 

I     to  1  

71.0 

.975 

.987 

52.521 

.014142 

0.743 

52.75 

Hto  l  

71.5 

.971 

.986 

52.438 

.014142 

0.742 

53.05 

2    to  1  

72.0 

.969 

.983 

52.189 

.014142 

0.738 

53.14 

Bed  70  feet.     Depth  6  feet.     Slope  1  in  5,000.     n  =  .025. 


CROSS  SECTION 

a 

r 

V'r 

c\/r 

•vA 

Velocity  in 
feet  per 
second. 

Discharge 
in  cubic 
feet  per 
second. 

Rectangular 
i  to  1 

420 
438 

5.122 
5  258 

2.263 
2  293 

179.504 
182  744 

.014142 
014142 

2.5385 
2  5844 

1066.2 
1132  0 

1    to  1  . 

456 

5  243 

2  289 

182  312 

014142 

2  5782 

1175  7 

H  to  1  . 

474 

5  172 

2  270 

180  260 

014142 

2  5492 

1°08  3 

2    to  1  

492 

5.081 

2.254 

178.532 

.014142 

2.5248 

1242.2 

Bed 

160  feet.     Depth  2  feet.     Slope  1  in  15,840.     ?*  =  .025. 

!  Velocity  in  Discharge 

CROSS  SECTION 

I 

a 

r 

Vr 

cVr 

^/s        \    feet  per 
|     second. 

feet  per 
second. 

Rectangular 

320 

1.951 

1  .  397 

89.715 

.007946 

0.7129 

228.1 

i  to  1  

322 

1.958 

1.413 

91.074 

.007946 

0.7237 

233.0 

1    to  1  

324 

1.956 

1  .  398 

89.810 

.007946 

0.7136 

231.2 

1|  to  1  

326 

1.950 

1  .  396 

89.620 

.007946 

0.7121 

232.1 

2    to  1  

328 

1.942 

1.393 

89.335 

.007946 

0.7099  i     232.8 

Bed  160  feet.     Depth  10  feet.     Slope  1  in  15,840.     n  =  .025. 

j 

- 

" 

Velocity  in 

Discharge 

CROSS  SECTION 

CL 

T 

Vr 

cVr 

Vs 

feet  per 
second. 

in  cubic 
feet  per 
second 

Rectangular 

1600 
1650 

8  889 
9.048 

2.981 
3.008 

260.334 
263.420 

.007946 
.007946 

2.0686 
2.0931 

3309.8 
3453.6 

1    to  1  

1700 

9.029 

3.005 

263.075 

.007946 

2.0904 

3553.7 

H  to  1  ..... 

1750 

8,926 

2.988 

261.132 

.007946 

2.0750 

3631.3 

2    to  1  

1800 

8.793 

2.965 

258.510 

.  007946 

2.0541 

3697.4 

OPEN    AND    CLOSED     CHANNELS.  27 


Bed  300  feet.     Depth  2  feet.     Slope  1  in  20,000.     n=  .025. 


"     !   ' 

Velocity  in;  Dtachajge 

CROSS  SECTION 

a      \        r             \/r 

c^/r 

Vs 

feet  per 
second. 

ill  CUBIC 

feet  per 
second. 

Rectangular 

600 

1.974        1.405      90.490 

.007071 

0.6399 

"38T.9 

|  to  1  

602 

1.977 

1.406 

90.588 

.007071 

0.6405 

385.6 

1    to  1  

604 

1.976 

1.405 

90.490 

.007071 

0  6399 

386.5 

Uto  1    .... 

606 

1  .  973 

1.404 

90.384 

.007071 

0.6391 

387.3 

2    to  1  

608 

1.968 

1.403 

90.294 

.007071 

0.6385 

388.2 

Bed  300  feet.     Depth  14  feet.     Slope  1  in  20,000      n  ==  .025. 


CROSS  SECTION        &               ^                ^/r 

c\/r           \/s 

Velocity  in 
feet  per 
second. 

.Discharge 
in  cubic 
feet  per 
second. 

Rectangular 

4200 

12.835        3.583      330.594.007071 

2.3376 

9818 

|  to  1  .•  

4298 

12.973 

3.600      332.600.007071 

2.3518 

10108 

1    to  1  i  4396 

12.940 

3.597      332.  246;.  007071 

2.3493 

10328 

H  to  1  

4494 

12.823 

3.581  i  330.  358  '.007071 

2  .  3360 

10498 

2    to  1  

4592 

12.664 

3.560     327.8801.007071 

2.3184 

10646 

Article  9.     Open  Channels  Having  the  Same  Velocity. 

Channels  having  the  same  slope,  the  same  value  of  n, 

and  also  the  same  value  of  ]/r}  have  the  same  velocity. 
For  example,  a  channel  70  feet  wide  on  hot  torn,  depth 
of  water  4  feet,  side  slopes  1  to  1,  grade  1  in  1,544,  and 
n  =  .03,  has  a  mean  velocity  of  2.98  feet  per  second. 

The   \/T  of    this    channel   will    be    found    in    Table    8, 
=  1.9,  and  if  we  examine  this  table  we  find  channels  of 
the  following  dimensions   that   have  the  same  value  of 

V/r,  and  therefore  the  same  velocity. 

Bed  70  feet,  depth  4  feet,  \/r  =  1.9 
Bed  45  "  4.25  "  i/r  =  1.9 

Bed  25  "  "  4.75  "  .\/r  =  1.9 
Bed  20  "  "  5  "  ^  =  1.9 
Bed  14  "  "  5.50  "  /r  =  1.9 


28  FLOW    OF    WATER    IN 

These  five  channels  have  the  same  velocity.  They 
have,  however,  different  discharges,  varying  with  the 
area  of  each  channel.  Channels  having  the  same 
velocity  can  also  be  found  having  side  slopes  of  J  to  1 
and  1J  to  1,  and  also  rectangular  in  section. 

Article  10.     Open  Equivalent  Discharging  Channels. 

Channels  having  the  same,  or  nearly  the  same,  value 

of  i/r  and  a  have  the  same  discharging  capacity.  For 
example,  a  channel  having  a  bed  width  of  12  feet, 
depth  3  feet,  side  slopes  of  1  to  1,  a  grade  of  5  feet  per 
mile,  and  n  =  .0275,  has  a  discharge  of  123.75  cubic 
feet  per  second.  Now  all  channels  with  the  same  area, 

45  square  feet,  and  the  same  value  of  \/r  =  1.482,  will 
have  the  same  discharge  when  s  and  n  are  the  same. 
An  inspection  of  Table  8,  with  side  slopes  of  1  to  1,  will 
show  channels  of  a  nearly  equivalent  discharge,  thus: — 

Bed  10  feet,  depth  3.25  feet,  \/r  =  1.498,  a  =  43 
Bed  15    "          "       2.75    "     ^/r  =  1.464,  a  =  48.8 

Again,  a  depth  or  width  being  first  given,  the  corres- 
ponding width  or  depth  to  give  the  required  discharge 
can  be  found  after  a  few  trials. 

Article  n.     Interpolating. 

In  tables  15  to  27  inclusive,  there  is  given  a  column 
headed  "  diff.",  which  gives  the  differences  of  c  and 

c  \/r,  equivalent  to  a  difference  of  value  =  .01  in  j/V,  and 
this  column  will  be  found  useful  in  interpolating  values 

of  c  and  c  \/r  between  those  given  in  the  tables.  For 
instance,  we  have  a  channel  which  has  a  grade  of  1  in 

1000,  its  value  of  n  =  .02  and  \/r=  1.44,  and  we  want 
the  value  of  c  corresponding  to  this  value  of  y/r. 


OPEN    AND    CLOSED    CHANNELS.  29 

In  Table  22,  n  =  .02  and  under  a  slope  of  1  in  1000,  the 

nearest  value  to  \/r  =  1.44  that  we  find  is  1.4,  and  the 
value  of  c  opposite  this  82.6.  The  column  of  differ- 
ences shows  that  for  a  value  of  \/r  =  .01  the  correspond- 
ing value  of  c  =.22,  therefore  .22x4  =  .88  has  to  be 
added  to  87.6  thus: — 

\/r  =1.4  and   corresponding  value  of  c  =  82.6 
I/V  =  0.04  and  corresponding  valve  of  c  =    0.88 

.  \  |//'  ==  1. 44  and  corresponding  value  of  c  =  83.48 
Frequently  in  the   examples,  in   order  to  avoid  long 
explanations,  it  is  proposed  to  find  the  value  of  c  or  c  y/r, 

equivalent  to  a  value  of  \/r  not  given  in  the  tables,  but 
it  is  understood  that  the  method  of  interpolation,  just 
explained,  is  intended  to  be  used  to  find  the  values  of  c 

and  c  \/r. 

Article  12.     Preliminary  Work. 

In  the  examples  given  below,  the  values  of  the  fac- 
tors are  in  some  cases  taken  to  several  places  of  decimals. 
Where  strict  accuracy  is  not  required,  as  in  preliminary 
designs,  interpolation  may  be  omitted  and  the  compu- 
tations can  be  still  further  reduced  by  working  to  fewer 
places  of  decimals.  For  instance,  at  the  end  of  Example 
3,  we  have: — 

Q  =  a  \/r  X  c  X  vA 
=  729.5  X  81.4  X  .016854 
=  1000  cubic  feet  per  second. 

Instead  of  taking  a  \/r  =  729.5  le.t  us  omit  decimals 
and  take  it  =  729,  and  in  table  23  with  n  =  .0225  under 
a  slope  of  1  in  3333  and  opposite  \/r  =  1.9  we  find, 


30 


FLOW    OF    WATER    IX 


omitting  decimals  that  c  =  82,  and  for  1  in  3520  let  us 
take  v/«  =  .0168  instead  of  .016854.  Substituting  these 
values  in  formula  (45)  we  have: — 

Q  =  729X  82  X  .0168 

=  1004  cubic  feet  per  second, 

being  in  excess  less  than  one-half  of  one  per  cent,  which 
is  near  enough  for  preliminary  work  for  all  practical 
purposes. 


V-FLUME. 


Article  13.     Explanation  and  Use  of  the  Tables. 

After  the  dimensions,  slope,  etc.,  of  the  channel  have 
been  determined  by  the  use  of  the  Tables,  it  is  advisa- 
ble, in  order  to  take  every  precaution  to  obtain  accuracy, 
that,  as  a  final  check,  the  work  should  be  computed  by 
Kutter's  formula  (40). 


OPEN    AND    CLOSED    CHANNELS.  31 

EXAMPLE  1. — To  find  mean  velocity  and  discharge  of  a 

canal. 

Required  the  mean  velocity  and  discharge  of  a  canal 
having  a  bed  width  of  70  feet,  a  depth  of  water  of '4~feBt, 
with  side  slopes  of  1J  to  1,  a  longitudinal  slope  or  grade 
of  1  in  1544,  and  with  the  co-efficient  of  the  surface  of 
the  material  of  the  bed =.03. 

State  also  the  quantity  of  land  this  canal  will  irrigate, 
the  duty  of  water  being  190  acres  per  cubic  foot  per 
second. 

The  velocity  and  discharge  may  be  found  by  three 
methods: 

First,  by  arithmetic. 
Second,  by  logarithms. 
Third,  by  the  tables  in  this  work. 

We  will  compute  the  above  example  by  each  of  these 
methods. 

1.     Computing  by  arithmetic: — 

s  = 1544  ==  .000647668,  and  v/*  =  .025449. 

In  Table  33  of  slopes,  the  value  of  s  and  \/s  can  be 
found  quickly  by  inspection. 

Area  of  water  section  =  (70H-6)X4=304 

Perimeter  of  water  section— 70+2  X  v/62+4~2--=84. 42 

fy  r\  A 

Hydraulic  mean  depth  r=—   =^.  ^==3. 


and  yr  —  y^.601  =  1.9 

K  utter 's  formula  is: — 

1.811  .00281 


32  FLOW    OF    WATER    IN 

Substituting  the  values  of  n,  s  and  r  above  given,  in 
this  formula,  we  have: — 


,  ^    ^  ,         -00281 

.03 


X  i/3.6 X. 000647668 


Computing  this  equation  we  find 

v=2.98  feet  per  second;  and 

Q=2.98X  304=906  cubic  feet  per  second. 

2.      Computing  by  logarithms: — 

First,  we  compute  the  value  of  each  term  in  the  nu- 
merator of  the  large  parenthesis,  and  take  their  sum. 

Second,  we  compute  the  value  of  each  term  in  the  de- 
nominator, and  take  their  sum. 

Third,  find  the  value  of  numerator  divided  by  denom- 
inator, and  this  is  equal  to  c. 

Fourth,  find  the  value  of  \/rs  and  multiply  it  by  e, 
and  this  last  result  is  equal  to  v. 

From  log  1.811=     0.2579 
Deduct  log  .03  =    -2.4771 

1.7808  log  of 60.370 

The  second  term  is 41.600 

From  log  .00281          =—3.4487 
Deduct  log  .0006477  =  — 4.8114 


0.6373  log  of..     4.338 

.*.  Numerator  in  large  parenthesis 106.308 

For  the  denominator  we  add  the  values  already  found 
of  the  second  and  third  terms  of  the  numerator: — • 


OPEN    AND    CLOSED    CHANNELS.  33 

41.600+4.338=45.938=45.94  nearly, 

and  log  of  45.94  =   1.6622. 
From  log  .03  -2.4771 

deduct  log  3.601--2  =     0.2782 

=—2.1989 


-1.8611-  log  of   0.7262 
Add  first  term  in  denominator..  .1.000 


1.7262 

106.308 
Andc  = 


As  v=q/V«,  we  have  now  to  find  value  of  \/rs 
log  3.601  0.5564 

log  .0006477=  -4.8114 

-3.3678 
and  this-f-2=  —  2.6839,  the    number    corresponding    to 

which  is  ,0483=i/rs 

.-.  v=cvAvs=61.  59  X.  0483  =  2.975  feet  per  second. 
Q=aX?;=304x2.975=904.4  cubic  feet  per  second 

3      Computing  by  tables  in  this  work. 
Look  out,  in  Table  11,  under  bed  width  70  feet,  and 
opposite   depth   4  feet,   and   we  find  a=304,   r=3.601, 

j/V  =  1.9,    a-\/r  =  578.      Look  out,  in  Table  26,  where 

7i  =  .03  and  ]  >=1.9,  and  under  the  slope  1  in  1666 
(which  is  the  nearest  slope  to  1  in  1544),  and  we  find 

c=61.6,  and  q/r=  117.0.  In  Table  33  the  nearest  slope 
to  1  in  1544  is  1545,  and  the  \/*  of  1545  -=.025441.  Sub- 
stitute the  values  of  c\/r  and  \/  s  in  formula  (41), 

v=c\/rX\/s 
and  we  have 

v=117x.  025441=2.98  feet  per  second. 
Q=va=2.  98X304=906  cubic  feet  per  second. 


34  FLOW    OF    WATER    IN 

Now,  as  a  check  on  this,  we  substitute  the  values  of 
the  other  factors  given,  and  we  have 


=61.  6X1.9X.  025441  =  2.  99  feet  per  second. 
Q=cXav/rX\/s 

=61.  6X578X.  025441=906  cubic  feet  per  second. 
As  each  cubic  foot  per  second  will  irrigate   190  acres 
of  land,   we  have    906X190  =  172,140  acres,  the  area 
which  the  canal  can  irrigate. 

This  example  shows  the  great  saving  of  time  and  labor 
effected  by  the  use  of  the  tables,  and  with  the  additional 
advantage  of  having  a  check  on  the  accuracy  of  the 
work. 

EXAMPLE  2.  —  Given  the  discharge,  bottom  width  and  depth 

to  find  the  grade  of  channel. 

A  canal  is  designed  to  discharge  410  cubic  feet  per 
second.  It  is  to  be  30  feet  on  bed,  4  feet  deep,  with  side 
slopes  of  1  to  1.  What  is  the  grade  necessary  to  pro- 
duce the  given  discharge,  the  value  of  n  being  .025  ? 

First  method  : 

The  area  of  section=136  square  feet,  and 

Q     410 
"===3  feet' 


Look  out,  in  Table  8,  under  a  bed  width  of  30  feet  and 

a  depth  of  4  feet,  and  we  find  \/r  =  1.81. 

In  Table  32,  with  a  value  of  ?i=.03,  the  slope  of  1  in 
13,23  is  found  in  a  channel  of  the  given  dimensions  to 
produce  a  velocity  of  3  feet  per  second. 

Now,  in  Table  24,  with  7i=.025,  and  under  a  slope  of 
1  in  1250,  wrhich  is  the  nearest  slope  to  1323,  and  op- 

posite y/r=1.8,  we  have  c=72.3;  and  similarly,  in  Table 
26,  with  n  =  .03  we  have  ci  =  60.2. 


OPEN    AND    CLOSED    CHANNELS.  35 

But  I  :  li  :  :  c-f  :  <?  substitute  values  and 
1323X72.32 


60. 2s 

Therefore  the  approximate  slope  is  1  in  1908. 

Second  method  : 

Finding  by  Table  32,  as  a  first  approximation,  that 
when  -ft=.03'the  slope  to  produce  the  given  velocity  is 
1  in  1323,  and  we  therefore  know  that  when  7i=.025  the 
slope  must  be  flatter  to  give  the  same  velocity.  We 
therefore  look  out  in  the  next  flatter  slope,  in  Table  24, 
with  TI=. 025,  which  we  find  is  1  in  1666,  and  we  find  op- 
posite \/r=l.Sl  that  cv/r  =  131.11. 

Substituting  the  value  of  c\/r  and  v  in  formula  (43), 


c  yr 
and  we  have 

=  '  °22888 


«=.  022883 
8=.0228832 


and     "^ 


But  -    =ratio  of  slope. 

Now  by  logarithms: 

From  log  1  .............................  0  .  0000000 

deduct  log  .022883  =  2.3595130X2=  .......  4.7190260 

3  .  2809740 

which  corresponds  to  1910.  As  the  computed  slope  1  in 
1910  has  almost  the  same  value  of  c  as  the  assumed  slope 
1  in  1666,  therefore  the  required  slope  is  1  in  1910. 


36  FLOW    OF    WATER    IN 

Third  method  : 

Find  in  the  same  way.  as  shown  in  Second  Method,  that 
V/s=.  022883 

Now,  in  Table  33  of  slopes,  look  out  the  slope  corre- 
sponding to  this  \/8,  and  it  will  be  found  equal  to  1  in 
1910.  This  is  the  quickest  method  of  finding  the  slope. 

As  a  check  on  this  work:    by  formula  (45), 


Substitute  the  values  of  a,  c\/r  and  \/s,  and  we  have: 

Q=136X131.1X.02288S 
=408  cubic  feet  per  second. 

EXAMPLE  3.  —  Given  the  discharge,  bottom  width  and  grade 
of  canal,  to  Jind  the  depth. 

A  main  irrigation  canal  has  a  bed  width  of  100  feet, 
side  slopes  of  1  to  1,  and  an  inclination  of  18  inches  per 
mile.  At  what  depth,  above  the  bed  of  the  main  canal, 
must  the  sill  of  the  head  gate  of  a  branch  canal  be  placed, 
so  that  the  main  canal  will  be  flowing  1,000  cubic  feet 
per  second,  before  any  water  flows  into  the  branch  canal; 
Ti^.0225?  By  Table  33,  18  inches  per  mile=l  in  3520, 

and  v/*=.  016854. 
By  formula  (47), 

Q          1000 


Therefore,  the  product  of  the  factors  a\/r  and  c=59333. 

All  that  is  now  required  is  to  find  in  Table  8,  and  un- 

der a  bed  width  100  feet,  such  a  depth  that  the  product 

of  the  factors  c  (7i=.0225)  and  a\/r  shall  be=59333. 
In  Table  8,  and  under  bed  width  100  feet,  look  down 

column  a\/r,  and  also  in  Table  23,  under  slope  1  in  3333 
(which  is  the  nearest  slope  to  1  in  3520),  look  down  col- 


OPEN    AND    CLOSED    CHANNELS.  37 

umii  c,  and  opposite  the  same  or  nearly  the  same  value 

of  \/T  in  each  column,  until  the  product  of  the  two  fac- 
tors is  equal  or  nearly  equal  to  59333. 

Thus,  in  Table  8,  under  a  bed  width  of  100  feetTanct 

depth  3.75,  we    find  y'r= 1.875  and  av/r— 729.5.     In 
Table  23,  under  a  slope  of  1  in  3333,  we  find  opposite 

V/r=1.8       that  c=80.2 
.-•'.  v/^=0.075  that  c=  1.2 


.-.  v/~  -1.875  that  c=81.4 

Now,  729.5  X  81.4=59381,  being  near  enough,  for  all 
practical  purposes,  to  59333. 

The  required  depth  is,  therefore,  3.75  feet. 

As  a  check  on  the  above,  let  us  compute  the  discharge 
of  the  channel  with  the  depth  found.  In  Table  8,  under 
a  bed  width  of  100  feet,  and  depth  of  3.75  feet,  the  value 

of  av/r=729.5.     In  Table  23,  under  a  slope  of  1  in  3333, 

we    find    by   interpolation    that    when    \/r= 1.875    that 
c=81.4. 

As  before  found,  for  18  inches  per  mile  y/.si=.016854. 

Now  substitute  these  values  of  av/r,  c  and  \/s,  in 
formula  (45): — 

Q=a\/r  XcX  \/s  and  we  have 
Q=729.5  X  81.4  X  .016854 
=  1000  cubic  feet  per  second. 

EXAMPLE  4. — Given  the  hydraulic  mean  depth  and  mean 
velocity  of  a  channel,  to  find  the  slope  or  grade. 

A  canal  has  a  hydraulic  mean  depth  of  9.18  feet,  and 
a  mean  velocity  of  5.5  feet  per  second.  The  canal  is 
trapezoidal  in  cross-section,  but  slightly  rounded,  and  it 
is  free  from  detritus.  Under  these  favorable  conditions 


38  FLOW    OF    WATER    IN 

the  value  of  n  is  assumed  =.0225.     What  is  the  slope  of 
the  water  surface  of  this  canal  ? 

r  being  =  9.18  .  •.  \/r  =  3.03. 

We  assume  as  an  approximation  that  the  slope  is  1  in 
1800. 

We  look  out,  in  Table  23  (/i—  .0225),  and  under  slope 
1  in  1666.6,  which  is  nearest  to  1  in  1800,  and  opposite 

v/r  =  3.03,  we  find  the  value  of  r  =  94.3,  and 
.-.ci/r  =  94.3  X  3.03  =  285.7. 

v          5.5 
Now,  formula  (43),  v/a=--      ==-==.  019251. 


Now  look  out,  in  Table  33,  and  the  nearest  value  of 

V/*  to  .019251  is  .019245  opposite  a  slope  of  1  in  2700. 

We  thus  find  a  slope  of  1  in  2700,  but  as  the  assumed 
slope  was  1  in  1800,  we  will  compute  again  for  a  closer 
approximation  with  the  slope  1  in  2700. 

In  Table  23,  and  opposite  y/r=3.03>  and  between 
slopes  1  in  2500  and  1  in  3333,  we  interpolate,  and  find 
the  value  of  c  to  be  =  95,  and  c  X  \/r=95X3.03  =  287.85. 


Now,  formula  (43),  l/^^^ 


Look  out,  in  Table  33  of  slopes,  and  opposite  y/.s= 
.019104,  the  nearest  one  in  the  table  to  .019107,  we  find 
the  slope  to  be  1  in  2740,  which  is  the  slope  required. 

EXAMPLE  5.  —  Given  the  discharge,  velocity  and  grade  of  a 
channel,  to  find  the  bed  icidth  and  depth. 

What  must  be  the  bed  width  and  depth  of  a  canal  to 
discharge  300  cubic  feet  per  second,  at  a  mean  velocity 
of  2  feet  per  second  ?  The  side  slopes  are  1J  to  1;  in- 
clination, 16  inches  to  the  mile;  and  ?i=.025. 


OPEN    AND    CLOSED     CHANNELS.  39 

In  Table  33,  we  find  16  inches  in  a  mile  =  a  slope  of 
1  in  3960,  and  also  v/s=.  015891. 

Q     300 
By  formula  (46),  a=  —  —  -^-^ISO  square  feet. 

By  formula  (42),  ^=--=-  = 


Look  out  now,  in  Table  24,  with  n  =  .025,  and  under 
slope  1  in  3333  (which  is  nearest  to  1  in  3960),  and  we  get 

cv/r=119.9,  value  of  y^l.7 
cv/r=130.1,  value  of  |A'  =  l-8 

Therefore  for  cv/r=125.9,  value  of  \/r  may  be  taken 
at  1.75. 

.-.  a  X  i/r=150  X  1.75  =  262.5 

Look  now  in  Table  11,  and  under  the  same  bed  width 
for  a  value  of  v/Y=1.75,  and  a;/V—  262.5,  and  we  find 
the  nearest  values  of  these  factors  to  be,  under  a  bed 
width  of  35  feet  and  depth  3.5  feet,  v/?=1.72,  and  a\/r 
=,242.4;  and,  depth  3.75  feet,  v/r=1.77,  and  a\/r= 

269.6. 

Now  ?.62.5—  242.4=20.1, 

and  269.6—242.4=27.2. 

.\  27.2   :  depth  .025   ::  20.1   :   .19, 

the  required  increased  depth,  approximately,  over  3.5 
feet  is  0.19  feet.  The  approximate  depth  is  therefore 
3.5  +  0.19  =  3.69  feet 

As  a  check,  we  will  now  find  the  discharge  with  this 
depth,  3.69  feet,  and  a  bed  width  of  35  feet.  The  area 
of  section  =  149.57  square  feet.  The  perimeter  =  48.01. 

a      149.57 
The  value    of  r=  —  =  48  Q1  =3.1154. 

And  v/?=1.77. 


40  FLOW    OF    WATER    IN 

In  Table  24,  with  n  =  .025,  and  under  a  slope  of  1  in 
3333,  we  find,  when 

V/r=1.7  ,  that  c=70.5 
and  by  interpolation,   y7?'— 0.07,  that  c=   1.3 


and  .-.  \/r=1.77,  that  c  =  71.8 

Now  substitute  values  of  c,  y^'}  and  \/s,  in  formula  (41) 

t'==c  X  \/r  X  v/«, 
and  we  have: 

v=71.8  X  1.77  X  .015891  =  2.0195  feet  per  second; 
and  Q=av=149.57  X  2.0195=302  cubic  feet  per  second. 

This  is  near  enough  for  most  purposes,  but  if  the  ex- 
act dimensions  be  required,  one  square  foot  can  be  taken 
off  the  area  by  diminishing  either  the  depth  or  bed  width 
of  channel,  and  as  the  velocity  is  2  feet  per  second,  the 
discharge  will  then  be  300  cubic  feet  per  second. 

EXAMPLE  6. — Gauging  a  stream  to  find  its  velocity  and 
discharge,  and  the  number  of  acres  it  is  capable  of  irri- 
gating. 

It  is  required  to  ascertain  how  many  acres  of  orchard 
land  a  stream  will  irrigate,  the  duty  of  the  water  being 
assumed  at  400  acres  per  cubic  foot  per  second. 

In  a  straight  reach  of  the  stream/and  where  it  was 
tolerably  uniform,  three  cross-sections  were  taken  300 
feet  apart. 

The  first  had  an  area  =22. 3  square  feet,  and  wetted 
perimeter  =  14.76  lineal  feet. 

The  second  had  an  area  =  23.1  square  feet,  and  wetted 
perimeter  =  14.07  lineal  feet. 

The  third  had  an  area  =  23.9  square  feet,  and  wetted 
perimeter  =  13.68  lineal  feet. 

The  surface  slope  of  the  stream  was  found,  by  level- 


OPEN    AND    CLOSED    CHANNELS.  41 

ing,  to  fall  0.287  feet  in  600  feet.  As  the  stream  was 
irregular,  and  was  choked  occasionally  with  vegetation, 
the  value  of  n  was  assumed  at  .03.  We  have  now  the 
information  required  to  find  the  discharge  of  the^steeam. 
Add  the  three  areas,  and  divide  by  3,  and  we  get  the 
mean  area  =  23.1  square  feet.  Again  add  the  three 
wetted  perimeters  and  divide  by  3,  and  we  find  the  mean 
perimeter  =  14.17  lineal  feet. 

Now  r  ==- =—^==1.83, 

p      14. 1/ 

and  v/n53  =  1.28  feet. 

A  slope  of  0.287  feet  in  600  feet  =  1  in  2090,  and  Table 
33  for  this  slope,  \/s=. 021874. 

In  Table  26,  with  71  =  .03,  we  do  not  find  a  slope  of  1 
in  2090. 

We  do,  however,  for  1  in  1666,  and  \/r=1.2,  that  c=49.4; 

and  for  1  in  2500,  and  v/r=1.2,  that  c=49.2; 

and  as  1  in  2090  is  about  a  mean  of  these  slopes,  we  take 

for  vA-=1.2,     that  c=  49.3 
and  for  y^—0.08,  that  c=     1.76 


therefore  for  v/r=1.28,  that  c=  51.06 

Substituting  the  values  of  c,  \/r,  and  \/s,  in  formula 
(41), 

v=c\/rX  }/&,  we  have 

v=51.06xl.28x.021874=1.43  feet  per  second. 
Q=va=  1.43x23. 1=33.033  cubic  feet  per  second. 

But  as  each  cubic  foot  per  second  is  capable  of  irri- 
gating 400  acres,  we  have  33.033  X  400  ===  13,213  acres, 
the  quantity  of  land  the  stream  is  capable  of  irrigating. 


42  FLOW    OF    WATER    IN 

EXAMPLE  7. — Given  the  dimensions  of  a  canal  in  earth,  to 
find  the  width  of  a  masonry  channel  having  the  same 
discharge,  the  two  channels  having  the  same  depth  and 
grade . 

A  canal  in  earth,  with  n  =.0275,  a  bed  of  50  feet, 
depth  4  feet,  side  slopes  of  J  to  1,  and  a  grade  of  2 
feet  per  mile,  is  passed  over  a  river  by  a  masonry  aque- 
duct. The  aqueduct  is  to  be  rectangular  in  cross-sec- 
tion, with  the  same  depth  as  the  canal,  and  the  same 
grade.  What  must  be  the  width  of  the  masonry  channel 
to  discharge  the  same  quantity  of  water  as  the  canal,  its 
value  of  n  being  taken  =.017  ?  This  value  of  n  is  taken 
high,  .017,  as  the  bed  and  sides  of  the  aqueduct  are  to 
be  roughly  plastered. 

For  earthen  channel,  Q=ciX«v//rX  ]/s- 

Substitute  the  values  of  the  factors  at  the  right-hand 
side  of  the  equation,  and  we  have 

Q=66.9X  391 X.  019463 
=509  cubic  feet  per  second. 

We  have  now  to  fix  the  width  of  a  masonry  channel 
to  discharge  509  cubic  feet  per  second,  with  a  depth  of 
4  feet,  a  slope  of  2  feet  per  mile,  and  n  =  .017. 

By  formula  (47), 


Now  look  out  the  value  of  ayr,  in  Table  13,  for  rec- 
tangular channels, .and  also  the  value  of  c  in  Table  21, 
with  n  =  .017,  until  we  find  that  the  product  of  the  fac- 
tors av/rXc=26152. 

In  Table  13  we  find,  under  bed  width  35  feet  and  depth 

4  feet,    that  av/r=248.9,   and  its  corresponding  \/r= 
1.778=1.8  nearly.     At  the  same  time  we  find,  in  Table 


OPEN    AND    CLOSED     CHANNELS.  43 

21,  7i=.017,  that  under  a  slope  of  1  in  2500,  and  opposite 

V/r=1.8,  the  value  of  c  =  106.2,  and  we  have  248.9  >< 
106.2  =  26433,  which  is  near  enough  to  26152;  therefore 
the  required  width  is  35  feet. 

As  a  check  on  this  work,  look  out,  in   Table  13,   the 

value  a\/  r  for  a  rectangular  channel  35  feet  wide  and  4 
feet  deep,  and  substitute  this,  and  also  the  value  of  cand 

s,  in  formula  (45), 


=  106.2X  248.9  X  .019463 
=  514  cubic  feet  per  second, 
which  is  near  enough  for  all  practical  purposes, 

EXAMPLE  8.  —  Increased  discharge  of  an  earthen  channel  by 
clearing  it  of  grass  and  u-eeds. 

A.  drainage  channel  originally  excavated  to  a  bed 
width  of  12  feet,  a  depth  of  water  of  4  feet,  with  side 
slopes  of  1  to  1,  and  a  grade  of  1  in  1760,  or  3  feet  per 
mile,  has  been  for  some  years  neglected,  and  its  bed  and 
banks  are  covered  with  long  grass  and  weeds.  Assuming 
its  value  of  n  in  this  state  —  .035,  what  will  be  its  in- 
crease in  discharge  when  it  is  cleared  of  all  grass,  weeds 
and  sharp  bends  ?  In  the  latter  case  we  will  assume 


Let  us  first  find  the  discharge  in  the  obstructed  chan- 
nel. 


In  Table  8  we  find  a=64,  and  \/r  =  1.657. 
In  Table  33  we  find,  opposite  a  slope  of  1  in  1760,  that 
V/*  =  023837. 

In  Table  27,  with  n=.Q35  under      slope  of  1  in  1666.7 

(which  is  the  nearest  to  1  in  1760),  and  opposite  \/r  = 
1.657,  the  value  of  c=49.55. 


44  FLOW    OF    WATER    IN 

Now  substitute  the  values  of  a,  c,  \/r  and  y^s ,  in 
formula  (45), 

Q=ac\/rX\/s 

=  64  X  49.55  X  1-657  X  .023837 
=  125.3  cubic  feet  per  second, 
being  the  discharge  of  the  obstructed  channel. 

Let  us  now  find  the  discharge  of  the  same  channel 
after  it  has  been  cleared,  at  slight  expense,  of  brush, 
weeds,  silt  deposit,  sharp  bends,  etc.,  so  as  to  bring  its 
value  of  ??,:=. 025. 

In  Table  24,  with  7i=.025,  under  a  slope  of  1  in  1666.7 
and  opposite  \/r  =1.657  (found  by  interpolation),  the 
value  of  c=69.87.  Now  substitute  this  value  of  c  with 
the  given  values  of  a,  \/.r  and  \/s  in  formula  (45),  and 

we  have: — 

Q  =  64  X  69.87  X  1.657  X  .023837 

==:  176.6  cubic  feet  per  second, 
being  the  discharge  of  the  improved  channel. 

We  thus  see  that  by  clearing  out  the  channel  its  dis- 
charge has  been  increased  by  more  than  40  per  cent. 

EXAMPLE  9. — Increase  of  discharge  by  improving  in  smooth- 
ness the  masonry  surface  of  a  channel. 

A  semi-circular  open  channel  of  coarse  rubble  set  dry, 
of  2  feet  radius  and  a  grade  of  1  in  500,  and  with  n=.02, 
is  to  be  improved  by  filling  up  all  interstices,  and  giving 
its  surface  a  coat  of  medium  smooth  plaster,  so  as  to 
make  its  value  of  ?i=.013.  What  is  the  percentage  of 
increase  in  discharge  of  the  improved  channel  ? 

The  hydraulic  mean  depth,  r,  of  a  circular  channel 
flowing  full  or  half  full  is  equal  to  half  the  radius,  there- 
fore r  of  this  channel  =  1,  and  \/r  =  1. 


OPEN    AND    CLOSED    CHANNELS.  45 

The  value  of  c  for  all  slopes  greater  than  1  in  1000  is 
the  same  as  for  1  in  1000. 

In  Table  22,  with  n=.02,  under  a  slope  of  1  in  1000 
and  opposite  ^/V—  1,  the  value  of  c=71.5. 

In  Table  33,  opposite  a  slope  of  1  in  500,  the  value  of 
V/s  —.044721. 

Substitute  the  values  of  c,  \/r  and  \/~s  in  formula  (41), 


and  v=71.5xlX-  044721 

v=3.2  feet  per  second, 

the  velocity  of  the  channel  with  a  surface  of  coarse 
rubble. 

Now,  to  find  the  velocity  in  plastered  channel.     Look 
out,   in  Table    19,  ?i—  .013,  and  under   a  slope   of   1  in 
1000,  and  opposite  y'V  =  1,  we  find  c\/r  =  116.5. 
Substitute  the  values  of  c\/r  and  \/s  ,  and  we  have 
v=116.5x.  044721 

=5.2  feet  per  second, 

the  mean  velocity  in  the  plastered  channel;  which  shows 
an  increase  in  velocity  and  discharge  of  63  per  cent. 
over  the  coarse  rubble  channel. 

EXAMPLE  10.  —  To  find  the  velocity  and  discharge  of  a 
channel  having  bed  width,  depth  and  side  slopes  not 
given  in  the  tables. 

What  is  the  velocity  and  discharge  of  a  channel  hav- 
ing bed  width  110  feet,  depth  of  water  7.2  feet,  side 
slopes  2  to  1,  and  grade  1  in  5000,  the  value  of  n  being 
equal  to  .0275? 

a  =  110  +  (7.2  X  2)  X  7.2  =  895.68  square  feet. 


46  FLOW    OF    WATER    IN 

In  Table  29  of  length  of  side  slope,  we  find,  under  a 
slope  of  2  to  1  and  opposite  1  foot,  4.472  feet.  Multiply 
this  by  the  depth,  7.2,  and  we  have  the  length  of  two 
side  slopes,  and,  therefore: — 

p  =  110  +  (4.472  X  7.2)  =  142.2 

895.68 
'= I42-2—6-3 

and  v/?~  =v/*^3=2.51. 

In  Table  25,  with  ?i=.0275,  under  a  slope  of  1  in  5000, 
and  opposite  i/?=2.61,  the  value  of  t:=75.5. 

In  Table  33,  opposite  a  slope  of  1  in  5000,  the  value 
of  v/«=.  014142. 

Substitute  the  values  of  c,  \/r  and  \/s  in  formula  (41), 

v  =--  c  X  i/r  X  i/s 
and  v  =  75.5  X  2.51  X  .014142 

=  2.68  feet  per  second, 
and  Q  —  av 

-895.68x2.68 
=  2400  cubic  feet  per  second. 

EXAMPLE  11. — Given  the  discharge,  grade  and  ratio  of  bed 
^u^dth  to  depth,  to  find  bed  width  and  depth. 

A  mining  ditch  is  to  discharge  130  feet  per  second, 
and  its  grade  is  1  in  1000.  What  must  be  its  bed  width 
and  depth  the  ratio  of  bed  width  to  depth  being  as  2  to 
1  ?  Its  side  slopes  are  to  be  |-  to  1,  and  its  value  of  n  = 
.025. 

By  Table  33,  a  slope  of  1  in  1000  has  v/e=. 031623. 
Substitute  the  value  of  ,s  and  also  the  value  of  Q  given 
in  formula  (47), 

Q  130 


OPEN    AND    CLOSED    CHANNELS.  47 

Now  look  out  the  value  of  the  factors  c  and  a\/rt  in 
Tables  10  and  24,  until  their  product  is  equal  or  nearly 
equal  to  4111.  The  value  of  c  is  found  in  Table  24  with 
-n  =  .025,  under  the  given  slope  1  in  1000,  and  opposite- 

the  y/V  corresponding  to  the  value  of  a\/r. 

After  inspection,  we  find  in  Table   10,  under  a  bed 

width  8  feet  and  depth  4  feet,  that  a\/r  =61.47,  and  \/r 
=  1.54. 

Also  in  Table  24,  with  ?i=.025,  under  a  slope  of  1  in 
1000  and  opposite  v/V=1.54,  we  find  c=67.9;  therefore, 

acv/r-=61.  47x67.  9=4131,  which  is  sufficiently  near  to 
4111  for  practical  work. 

Let  us  check  this  discharge. 


=67.  9X61.  47  X-  031623 
=  132  cubic  feet  per  second. 

The  dimensions  of  the  channel  are  therefore  8  feet 
wide  on  bed,  4  feet  deep,  and  with  side  slopes  of  J  to  1. 

EXAMPLE   12.  —  Diminution    of    discharge    of  channel  by 
grass  and  weeds. 

The  above  channel,  Example  11,  after  construction, 
has  not  been  repaired  or  cleaned  out  for  several  years. 
It  is  obstructed  by  grass  and  weeds,  and  its  value  of  n 
increased  to  .035.  Find  the  percentage  of  diminution 
of  discharge. 

In  Table  27,  with  ?i=.035,  under  a  slope  of  1  in  1000 
and  opposite  \/r  =  1.54,  we  find  c=47.8. 

Substituting  this  value,  and  also  the  values  a\/r  and 
]/,s,  in  formula  (45),  we  have:  — 


=47.  8X61.47X-  031623 
=92.9  cubic  feet  per  second. 


48  FLOW    OP    WATER    IN 

This  shows  that,  in  this  case,  the  grass  and  weeds  di- 
minished the  discharge  by  about  30  per  cent,  of  the 
original  discharge. 

EXAMPLE  13.  —  Given  discharge,  velocity  and  the  ratio  of  bed 
width  to  depth,  to  find  the  slope  or  grade. 

A  canal  is  to  discharge  3000  cubic  feet  per  second. 
Its  mean  velocity  is  to  be  2.5  feet  per  second.  Its  bed 
width  is  to  be  15  times  the  depth,  its  side  slopes  1  to  1, 
and  its  value  of  7i=.0'25.  Find  the  slope  required. 

Q     3000 
tt=—  =          =1200  square  feet. 

Letic^depth;   then 


p=(8.66xl5)-j-(8.66x2.828)  =  154.39 

a        1200 
=p=154.39==7'7' 

y^r  :  =\/T.JT2=<2.8  nearly. 

In  order  to  aid  in  the  selection  of  the  slope,  look  out 
in  Table  32,  with  rc  =  .03,  under  bed  width  140  feet, 
depth  9  feet,  and  we  find,  as  a  rough  approximation, 
that  the  slope  for  a  velocity  of  2|  feet  per  second 

11453  -1-4822 
is=-     —  g  --  =8138,  that  is,  1  in  8138.     But  as  the 

slope  for  7i=.025  is  flatter  than  when  7i=.03,  we  may 
assume  a  flatter  slope  than  1  in  8138.  The  nearest  slope 
to  this  in  the  tables  is  1  in  10000. 

We  now  find  in  Table  24,  with  rt=.025,  under  a  slope 
of  1  in  10000,  and  opposite  v/?=2.8,  that  c\/r  =  245.3. 


OPEN    AND    CLOSED    CHANNELS.  49 

Now  substitute  the  values  of  c\/r  and  v  in  formula  (43), 

v/s=  —  T= 
C\/T 

2.5 
and  we  have  v/s—  oTc~q  =.010191. 

Now  look  out  in  Table  33,  and  the  nearest  value  of  \/* 
to  this  will  be  found  opposite  a  slope  of  1  in.  9600. 

As  a  check  on  this,  find  value  of  c  in  Table  24,  under 
a  slope  of  1  in  10000,  and  opposite  \/r  =  2.8,  we  find  it 
equal  to  87.0. 


=87.  6X2.8X.  010191 
=2.5  feet  per  second 
Q=at;=1200-x2.5 
=3000  cubic  feet  per  second. 

EXAMPLE  14.  —  Given  the  bed  width,  depth  and  grade  of  a 
channel  not  given  in  the  tables,  to  find  the  velocity  and 
discharge. 

A  canal  has  a  bed  width  of  80  feet,  a  depth  of  six  feet, 
and  side  slopes  of  1J  to  1.  Its  grade  is  1  in  5000,  and 
its  value  of  ?i=.025.  Find  its  velocity  and  discharge. 

The  table  for  channels  with  side  slopes  of  1^  to  1  does 
not  extend  beyond  a  bed  width  of  60  feet;  but,  as  before 
explained,  the  velocity  in  channels  having  a  greater  bed 
width  than  60  feet  is  not  practically  changed  by  a  change 
in  the  side  slopes  usually  adopted;  that  is,  as  an 
instance,  the  velocity  in  a  channel  80  feet  wide  and  6 
feet  deep,  with  side  slopes  of  1  to  1,  is  practically  the 
same  as  a  channel  having  the  same  width  and  depth 
but  with  side  slopes  of  1|  to  1. 

Let  us,  therefore,  find  first  the  velocity  in  the  former 
channel. 
4 


50  FLOW    OF    WATER    IN 

In  Table  8,  with  side   slopes  of  1  to   1,  under  a  bed 
width  of  80  feet,  and  opposite  a  depth  of  6  feet,  the  value 

of  v/r=2.307. 

In  Table  24,  with  ?i=.025,  and  under  a  slope  of  1  in 

5000,  we  find,  corresponding  to  a  value  of  i/V=2.3Q7, 
that  the  value  of  c=80.7. 

In  Table  33  of  slopes,  and  opposite  a  slope  of   1  in 
5000,  the  v"«  =.014142. 

Substitute  the  values  of  c,  \/r  and  \/s  in  formula  (41), 


and  we  have  v=80.7  X  2.307  X  .014142 
—2.63  feet  per  second. 


=  1404  cubic  feet  per  second. 

Let  us  now  check  this. 

The  area  of  a  channel  80  feet  on  bed,  6  feet  deep,  and 
with  side  slopes  of  1J  to  1,  is  equal  to 

(80  +  6  X  15)  X  6  =  534  square  feet. 

In  Table  29  of  length  of  side  slopes,  we  find  opposite 
a  depth  of  6  feet,  and  under  a  slope  of  1J  to  1,  that  the 
length  of  the  two  side  slopes  =  21.634  feet.  To  this  has 
to  be  added  bed  width  80  feet,  making  the  perimeter  = 
101,  634  feet. 

a          534 

Now  r  =  —  —  im    aoA  —  5.2541 
p      101.634 

and  v/r  =  2.292. 

We  have  already  found  that  the  value  of  \/r  with  side 
slopes  of  1  to  1  is  2.307,  showing  a  difference  of  less  than 
1  per  cent,  with  side  slopes  of  1J  to  1. 

We  therefore  see  that,  for  all  practical  purposes,  the 
velocity  found  from  the  tables  with  side  slopes  of  1  to  1 
is  sufficiently  correct. 


OPEN    AND    CLOSED    CHANNELS.  51 

EXAMPLE  15. — To  find  the  value  of  c  and  n  in  an  open 

channel. 

A  channel  is  gauged,  and  its  perimeter  is  found  equal 
to  26.48  lineal  feet,  and  its  area  equal  to  63  squaTC~feet. 
Its  discharge  is  101.5  cubic  feet  per  second,  and  the  slope 
of  its  water  surface  is  equal  to  22  inches  per  mile.  Find 
the  value  of  c  and  n. 

a         63 
=  ^"=2QA8  = 

and  v/r=v/2".4"=1.55 

Q       101.5 

v  =  — = — ™ —  =  1.61  feet  per  second. 
a  bo 

In  Table  33,  .Mid  opposite  22  inches  per  mile,  \/s~ 
.018634. 

Substituting  the  value  of  \/st  v  and  s  in  formula, 

v  , 

c—     ,-     — -,—  we  have 
Vr  X  Vs 

1.61  _ 

"1.65X  .018634  = 

A  slope  of  1  in  2500  is  the  nearest  in  the  tables  of  n 
to  22  inches  per  mile.  Now  look  under  the  .different 
values  of  n,  and  under  a  slope  of  1  in  2500,  and  opposite 

J/T— 1.55,  and  the  value  of  c  that  is  nearest  to  55.8  will 
be  found  under  the  required  value  of  n.  In  this  case, 
in  Table  26,  under  a  value  of  7i=.03,  and  under  a 

slope  of  1  in  2500  and  opposite  y/r=1.5,  we  find  the 
value  of  c=55.2,  which  is  the  nearest  value  in  the 
tables  to  55.8.  Therefore,  the  required  value  of  c— 
55.8,  and  n=.Q3. 

As  a  check  on  this,  look  out  in  Table  26,  with  ti=.03, 

under  a  slope  of  1  in  2500,  and  opposite  \/r=1..55t  and 


02  FLOW    OF    WATER    IN 

c  is  found,  by  interpolation,  =56.  1  .  Substitute  this  value 
of  c,  and  also  the  values  of  \/r  and  \/s,  in  formula  (41), 

v=cXl/rX\/# 

and  we  have  v=56.lx  1.55  X  .018634 
=  1.62  feet  per  second. 

EXAMPLE  16.  —  To  find  the  velocity  and  discharge  of  a  brick 
aqueduct  by  Seizin's  formula,  the  dimensions  and  grade 
being  given. 

An  aqueduct  constructed  of  brick  work,  rectangular 
in  cross-section,  4  feet  wide  on  bottom,  and  with  ver- 
tical sides,  carries  2  feet  in  depth  of  water  and  has  a 
slope  of  1  in  160,  What  is  its  velocity  and  discharge 
by  Bazin's  formula  for  open  channels  ? 

In  Table  13  for  rectangular  channels,  we  find  under  a 

bed  width  4  and  opposite  depth  2  that  \/r=l.  As  the 
channel  is  of  brick-work,  it  comes  under  the  head  of  the 
second  type  of  Bazin's  channels,  formula  (35),  by  which 
Table  28  is  computed.  Now,  in  Table  28,  and  opposite 

l/r=l,  we  find  that  C]/T  =  118.5. 

We  also  find,  in  Table  33,  and  opposite  a  slope  of  1  in 
160,  that  \/s=.  079057.  Substituting  this  value  and 
also  the  value  of  cy/r  in  formula  (41), 


we  have  v=118.5X-  079057=9.  37  feet  per  second 
and  Q=av=8x9.  37=74.  96  cubic  feet  per  second. 

EXAMPLE  17.  —  Increase  of  discharge  of  a  channel  in  rock- 
cutting  by  plastering  its  surface. 

Near  the  head  of  a  small  irrigation  canal  the  supply 
of  water  is  carried  in  a  rock-cutting  10  feet  wide  at  bot- 
tom, 12  feet  wide  at  surface  of  water  5  feet  in  depth, 
and  having  a  slope  of  1  in  880. 


OPEN    AND    CLOSED    CHANNELS.  53 

The  water  supply  carried  in  this  cutting  being  insuf- 
ficient, it  is  determined  to  increase  the  supply  without, 
however,  increasing  the  cross-sectional  area  of  channel 
or  its  slope.  The  bottom  and  sides  of  the  rock-cutting 
are  very  rough,  and  in  order  to  give  them  a  smoother 
surface  and  increase  the  discharge,  it  is  determined  to 
fill  up  all  the  hollows  in  them  with  masonry,  and  after 
this  to  lay  on  carefully  a  coat  of  cement  plaster  with 
one-third  sancl,andto  make  the  surfaces  in  contact  with 
the  water  smooth  and  even. 

After  the  plastering  is  finished  the  dimensions  of  the 
channel  will  be:  width  at  bottom  9.8  feet,  width  at  water 
surface  11.8  feet,  depth  of  water  4.9  feet,  and  the  slope 
as  before,  1  in  880. 

It  is  assumed  that  a  near  approximation  to  the  value 
of  n  for  the  rock-cutting  =.0225,  and  for  the  plastered 
channel  n=. Oil. 

Find  the  increase  in  discharge  in  the  plastered  chan- 
nel over  that  in  the  original  channel. 

In  the  original  channel 

area  55 

r=        7-3 = r—  =  s-A— 5=2.7228 

wetted   perimeter     20  .  2 


j/V==  v/2.7228  =  1.65 

Table  33  shows,  for  a  slope  of  1  in  880,  that  \/s= 
.03371. 

Table  23  shows,  by  interpolation,  under  a  slope  of  1 
in  1000  (which  has  the  same  co-efficient  as  a  slope  of  1 
in  880),  and  opposite  \/r=1.65,  that  cv/r=128.4. 

Substitute  the  values  of  \/s  and  c[/rt  in  formula  (41), 
and  we  have: — 

v=128.4X- 03371=4.328  feet  per  second. 

Now,  Q=va=4. 328x55=238  cubic  feet  per  second. 


54  FLOW    OF    WATER    IN 

a      52.92 
In  the  plastered  channel  r=  -     =pr7Q~===2^67 

and  iA=v/2.673:=1.64  nearly. 

In  Table  17,  with  ?i=.011,  we  find,  by  interpolation, 
under  a  slope  of  1  in  1000  and  opposite  \/r=1.64,  that 
the  value  of  c\/r=2Q4.2. 

Substituting  this  value  of  c\/r  and  \/s  ,  in  formula  (41), 
and  we  have: — 

v=264.2X- 03371  =  8.9  feet  per  second, 
and  Q=va=S. 9x52.92=471  cubic  feet  per  second. 

We  here  see  the  effect  of  a  smooth  surface  in  increas- 
ing the  velocity  and  discharge  of  a  channel.  Although 
the  cross-sectional  area  has  been  diminished,  still  the 
effect  of  giving  a  smooth  surface  to  the  channel  has  been 
to  more  than  double  its  velocity  and  to  almost  double  the 
discharge.  The  old  formula  would  give  almost  the  same 
velocity  and  discharge  to  the  two  channels,  as  these 
formulae  do  not  take  into  account  the  surfaces  exposed 
to  the  flow  of  water. 

FLUMES. 

EXAMPLE  18. — To  find  the  velocity  and  discharge  of  a  rect- 
angular fiume. 

A  rectangular  flume  8  feet  wide,  and  flowing  4  feet  in 
depth  of  water,  has  a  slope  of  1  in  500.  The  flume  is 
old,  and  its  surface  exposed  to  the  flow  of  water  is  rough. 
Its  value  of  n  is,  therefore,  taken  as  =.015.  Find  its 
velocity  and  discharge. 

In  Table  13,  for  rectangular  channels,  under  a  bed  of 
8  feet,  and  opposite  a  depth  of  4  feet,  we  find  i/?=l-414. 

As  the  value  of  c  for  all  slopes  steeper  than  1  in  1000 
is  the  same  as  for  1  in  1000,  we  now  find  in  Table  20, 


OPEN    AND    CLOSED    CHANNELS.  55 

with  ?i  =  .015,  under  a  slope  of  1  in   1000,  and  with  \/r 
=  1.414,  that  the  value  of  c  by  interpolation  =112.25. 

In  Table  33  of  slopes,  we  find  that  1  in  500  has_a_  value 
V/*=  .044721. 

Substitute  these  three  values  in  formula  (41), 

v  =  cX  VT  X  V* 
and  we  have  v  =  112.25  X  1.414  X  .044721 

'  =7.1  feet  per  second. 
Q  =  av  =  32  X  7.1  =  227.  2  cubic  feet  per  second. 

EXAMPLE  19.  —  To  find  the  velocity  and  discharge  of  a 

V-  flume. 

A  right-angled  V-flume  is  flowing  with  a  depth  of  water 
in  the  center  of  9  inches  and  grade  of  1  in  180.  Find 
its  velocity  and  discharge. 

The  flume  is  new  and  made  of  uiiplaned  timber,  and 
its  surface  exposed  to  the  water  continuous  on  the  iii- 
side,  and  in  fairly  good  condition.  Its  value  of  n  may 
therefore  be  taken  =.012,  but,  to  be  on  the  side  of 
safety,  it  is  taken  =.013. 

In  Table  14,  for  V-flumes  with  7i=.013,  and  opposite  a 
depth  of  .75  feet,  we  find  a=.  56  square  feet,  c'v/V=44.55, 
and  ac\/r=24;.95. 

In  Table  33  of  slopes,  we  find  for  a  slope  of  1  in  180 
that  i/ii=  .  074536. 

Substitute  the  values  of  c\/r  and  \/~s  in  formula  (41), 


and  we  have  v=44.  55  X-  074536 

=3.32  feet  per  second; 
and  Q=a  ^=.56x3.32 

=  1.86  cubic  feet  per  second. 


56  FLOW    OF    WATER    IN 

As  a  check  on  this  we  have  formula  (45), 

Q=ac]/rX  y' * 
Substitute  values,  and 

Q=24.95x.  074536 
=  1.86  cubic  feet  per  second. 

EXAMPLE  20. — Given  bed  ividth,  depth  and  discharge  of  a 
rectangular  flume,  to  find  its  grade  or  slope. 

Find,  by  Kutter's  formula,  the  slope  of  a  flume  con- 
structed of  unplaned  planks,  5  feet  wide  at  bottom,  with 
vertical  sides  2J  feet  high,  in  order  that  it  may  discharge 
102  cubic  feet  per  second. 

In  Table  13  under  a  bed  width  of  5  feet  and  opposite  a 

depth  of  2.5  feet,  we  find  \/r  ==  1.118  =  1.12,  nearly. 

Let  us  assume  that  Table  18,  with  n  =  .012,  is  appli- 
cable to  this  channel  and  in  it,  under  a  slope  of  1  in 
1000,  we  find 

l/r=l.l     that  c  =  131.6 

V/r=0.02  that  c=      0.7 

.-.  v/?=1.12  that  c=132.3 

v= — =TH- £=8.16  feet  per  second. 
a       J.  z .  o 

Substitute  the  value  of  c,  \/r,  and  ?;,  in  formula  (43), 

1/8=--  —/=  and  we  have 
cXVr 

8.16 

"= 13273^02=  -0550'- 

Now  look  out,  in  Table  33,  the  nearest  value  of  \/s 
to  this,  and  we  find  it  to  be  opposite  a  slope  of  1  in  330, 
which  is  the  slope  required. 


OPEN    AND    CLOSED    CHANNELS. 


57 


TABLE   8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1.  Values 
of  the  factors  «r=area  in  square  feet,  and  r  ~.~  hydraulic  mean  depth  in 
feet,  and  also  \/r  and  a^r  for  use  in  the  formula- 

v  =  c  X  \/r~ X  \/*~  and  Q  —  c  X  a*/r~  X  \A~ 


BED  1  FOOT. 

BED  2  FEET. 

Depth 
in 
Feet. 

a             r       ;   \/r     i    a-*/r 

a 

r 

VT 

a\/r 

Depth 
in 

Feet. 

0.5 

0.75      0.311 

0.577 

.433 

1.25 

0.366 

.605 

.756 

0.5 

0.75 

1.31      0.425 

0.652      .856 

1     2.06 

0.500 

.707 

1.46 

0.75 

1. 

2.          0.522 

0.723;   1.45 

3. 

0.621 

.788 

2.36 

1. 

1.25 

2.81 

0.620 

0.787'  2.21 

i     4.06 

0.734 

.856 

0.48 

1.25 

1.5 

3.75 

0.715 

0.846    3.17 

5.25 

0.841 

.917 

4.8 

1.5 

1.75 

4.81 

0.809 

0.899    4.32 

6.56 

0.942 

.971      6.4 

1.75 

2. 

6. 

0.901 

0.950 

5.70 

8. 

1.045 

1.022!     8.2 

2. 

2*26 

9.56 

1.143 

1.069    10.2 

2.25 

2.5 

11.25 

1.240 

1.113    12.5 

2.5 

2.75 

13.06 

1.336 

.156    15.1 

2.75 

3. 

15. 

1.431 

.196    17.9 

3. 

3.25 

17.06 

1.525      .235    21.1 

3.25 

3.5 

19.25 

1.618 

.272    24.5 

3.5 

3.75 

21.56 

1.703 

.305    28.1 

3.75 

4. 

24. 

1.803 

.342 

32.2 

4. 

BED  3  FEET. 

BED  4  FEET. 

Depth 

Depth 

in 
Feet. 

a             r 

Vr 

a\/r 

a 

r 

\/r     \    a\/r 

in 

Feet. 

0.5 

1.75 

0.396 

0.629 

1.1 

2.25 

0.416 

0.645        1.5 

0.5 

0.75 

2.81 

0.549 

0.741 

2.1 

3.56 

0.582 

0.763        2.7 

0.75 

1. 

4. 

0.686 

0.828 

3.3 

5. 

0.732 

0.856        4.3 

1. 

1.25 

5.31 

0.812 

0.901 

4.8 

6.56 

0.871 

0.933        6.1 

1.25 

1.5 

6.75 

0.932 

0.965 

6.5 

8.25 

1.000 

.000       8.3 

1.5 

1.75 

8.31 

1.045 

1  .  022 

8.5 

10.06 

.124 

.060      10.7 

1.75 

.> 

10. 

1.155 

1.075 

10.8 

12. 

.243 

.115 

13.4 

2. 

5!  25 

11.81 

1.261 

1.123 

13.3 

14.06 

.357 

.165 

16.4 

2.25 

2.5 

13.75 

1.365 

1.168 

16.1 

16.25 

.468 

.211 

19.7 

2.5 

2.75 

15.81 

1.466 

1.211 

19.1 

18.56 

.576 

.255 

23.3 

2.75 

3. 

18. 

1.567 

1.252 

22.5 

21. 

.682 

.297 

27.2 

3. 

3.25 

20.31 

1.666 

1.290 

26.2 

23.56 

.786 

.339 

31.5 

3.25 

3.5 

22.75 

1.764 

1.328 

30.2 

26.25 

1.889 

.375 

36.1 

3.5 

3.75 

25.31 

1.831 

1.364 

34.5 

29.06 

1.990 

.411 

41.0 

3.75 

4. 

28. 

1  .  956 

1.398 

39.1 

32. 

2.090 

.446      46.3 

4. 

4.25 

30.81 

2.051 

1.432 

44.1 

35.06 

2.189 

.480     51.9 

4.25 

4.5 

33.75 

2.146 

1.465 

49.4 

38.25 

2.287 

.512      57.8 

4.5 

4.75 

36.81 

2.240 

1.497 

55.1 

41.56 

2.384 

.544      64.2 

4.75 

5. 

40. 

2.333 

1.527 

61.1 

45. 

2.480 

1.575      70.9 

5. 

58 


FLOW    OF    WATER    IN 


TABLE    8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1 .  Values 
of  the  factors  a  =  area  in  square  feet,  and  r  =  hydraulic  mean,  depth  in 
feet,  and  also  ^/7~i\i\d  a^/'r~for  use  in  the  formula; 

•v  =  c  X  V~  X  V~  aiid  Q       c,  X  t<*/7~  X  V#~ 


BED  5  FEET. 

BED  6  FEET. 

Depth 
in 
Feet. 

a             r          \/r         a-^/r 

a 

r          V'' 

a\/r 

Depth 
in 
Feet. 

0.5 

•2.75      0.429   O.G55 

1.8 

3.25 

0.438 

0.662 

2.15    0.5 

0.75 

4.31      0.607    0.779 

3.4 

5.06 

0.623 

0.781 

3.95 

0.75 

1. 

6.          0.766 

0.875        5.2 

7. 

0.793    0.891 

6.2 

1. 

1.25 

7.81      0.915 

0.956 

7.5 

9.06 

0.950    0.975 

8.8 

1.25 

1.5 

9.75        .054 

1.027 

10. 

11.25 

1.098    1.048 

11.8 

1.5 

1.75 

11.81        .186 

1.089 

12.9 

13.56 

1.238    1.113 

15.1 

1.75 

•7 

14.             .314 

1.147 

16.1 

16.           1.373    1.172 

18.8 

2 

2.25 

16.31        .436 

1.198 

19.5 

18.56      1.502    1.226 

22.8      2.25 

2.5 

18.75        .553 

1.246 

23.4 

21.25      1.626    1.275 

27.1      2.5 

2.75 

21.31         .668 

1.292 

27.5 

24.06      1.747    1.321 

31.8      2.75 

3. 

24.             .780 

1  .  334 

32. 

27.        1   1.864    1.365 

36.9  ;  3. 

3.25 

26.81         .889 

1.374 

36.8 

30.06 

1.9791   1.407 

42.3  !  3.25 

3.5 

29.75  i     .997 

1.413 

42. 

33.25 

2.091 

1.446 

48.1 

3.5 

3.75 

32.81      2.103 

1.450 

47.6 

36.56 

2.201 

1.483 

54.2      3.75 

4. 

36.          2.207 

1.486 

53.5 

40. 

2.311 

1.520;     60.8      4. 

4.5 

42.75      2.412 

1.533 

65.5 

47.25 

2.523 

1.589      75.1      4.5 

5. 

50.          2.612 

1.616 

80.8 

55. 

2.731 

1.653      90.9 

5. 

6. 

66.          3.004 

1.733J   114.4 

72. 

3.134    1.770|  127.4 

6. 

BED  7  FEET. 

BED  8  FEET. 

Depth 

Depth 

in 

Feet. 

a             r      ;    \/r         a\/r            a             r 

^/r        a^/r 

in 
Feet. 

0.5 

3.75      0.446 

0.667 

2.50 

4.25 

0.451 

0.672 

2.85 

0.5 

0.75 

5.81 

0.637 

0.798 

4.64 

6.56 

0.648 

0.805 

5.28 

0.75 

1. 

8. 

0.814 

0.902 

7  22 

9. 

0.831 

0.911 

8.2 

1. 

1.25 

10.31 

0.979 

0.989 

10.2 

11.56 

1.002 

.000 

11.6 

1.25 

1.5 

12.75 

1.134 

1.065    13.6 

14.25 

1.164 

.079 

15.4 

1.5 

1.75 

15.31 

1.281 

1.132    17.3 

17.06 

1.318 

.152 

19.7 

1.75 

2. 

18. 

1.422 

1.192!  21.5 

20. 

1.464 

.210 

24.2 

2. 

2.25 

20.81 

1.560 

1.249    26. 

23.06 

1.606 

.267 

29.2 

2.25 

2.5 

23.75 

1.688 

1.300J  30.9 

26.25 

1.742 

.320 

34.7 

2.5 

2.75 

26.81 

1.815 

1.347    36.1 

29.56 

1.873 

.368 

40.4 

2.75 

3. 

30. 

1.938 

1.392 

41.8 

33. 

2.002 

.415 

46.7 

3. 

3.25 

33.31 

2.057 

.434 

47.8 

35.56 

2.069 

.439 

51.2 

3.25 

3.5 

36.75 

2.169 

.473 

54.1 

40.25 

2.269 

.506 

60.6 

3  5 

3.75 

40.31 

2.290 

.513 

61. 

44.06 

2.368 

.539 

67.8 

3.75 

4. 

44. 

2.403 

.550 

68.2 

48. 

2.486 

.577 

75.7 

4. 

4.5 

51.75 

2.623 

.619 

83.8 

56.25 

2.714 

.647 

92.6 

4.5 

5. 

60. 

2.838 

.684 

101. 

65. 

2.936 

713i  111.3 

5. 

6. 

78. 

3.254 

.804 

140.7 

84. 

3.364 

1.834    154.1 

6. 

OPEN    AND    CLOSED    CHANNELS. 


59 


TABLE   8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1 .    Values 
of  the  factors  a  =  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 

feet,  and  also  \/r  and  a^/r  for  use  in  the  formulas 

v  =  c  X  Vr  X  V»  and  Q  =  c  X  a^r   X  % 


BED  9  FEET. 


BED  10  FEET. 


Depth 

1 

Depth 

in 

Feet. 

a 

r 

Vr 

a\/r 

a 

r 

vT 

a^/r 

in 

Feet. 

0.5 

4.625 

0.444 

0.667 

3.08 

5.25 

0.460 

0.678 

3.56 

0.5 

0.75 

7.031 

0.632 

0.795 

5.59 

8.06 

0.665 

0.815 

7.01 

0.75 

1  . 

10. 

0.845 

0.919 

9.19 

11. 

0.858 

0.926 

10.2 

1. 

\.25 

12.81 

1.022 

1.011 

12.95 

14.06 

1.039 

.019 

14.3 

1.25 

1  .5 

15.75 

1.189 

1.090 

17.2 

17.25 

1.211 

.100 

19. 

1.5 

1.75 

18.81 

1.349 

1.161 

21.8 

20.56 

1  .  375 

.173 

24.1 

1. 

o 

22 

1.501 

1  .  225 

27. 

24. 

1.533 

.238 

29.7 

2.75 

2^25 

25!  31 

1.650 

1.284 

32.5 

27.56 

1.684 

.290 

35.6 

2.25 

2.5 

28.75 

1.789 

1.330 

38.2 

31.25 

1.831 

1.353 

42.3 

2.5 

2.75 

32.31 

1  .  927 

1.388 

44.8 

35.06 

1.972 

1.404 

49.2 

2.75 

3. 

36. 

2.059 

1.435 

51.7 

39. 

2.110 

1.452 

56.6 

3. 

3.25 

39.81 

2.189 

1.479 

58.9 

43.06 

2  .  244 

1.498 

64.5 

3.25 

3.5 

43.75 

2.315 

1.521 

66.5 

47.25 

2.375 

1.541 

72.8 

3.5 

3.75 

47.81 

2.439 

1.562 

74.7 

51.56 

2.502 

1  .  582 

81.6 

3.75 

4. 

52. 

2.560 

1.600 

83.2 

56. 

2.628 

1.621 

90.8 

4. 

4.5 

60.75 

2.796 

1.672 

101.6 

65.25 

2.871 

1.694 

110.5 

4.5 

5. 

70.          3.025 

1.739 

121.7 

75. 

3.107 

1.763 

132.2 

5.       . 

5.5 

79.75 

3.248 

1.802 

143.7 

85.25 

3.336 

1.826 

155.7 

5.5 

6. 

90. 

3.466 

1.862 

167.6 

96. 

3.560 

1.887 

181.2 

6. 

BED  11  FEET. 

BED  12  FEET. 

Depth 

Depth 

in 

Feet. 

a             r           \/r 

a\/r~ 

a 

r 

\/r        u\/r 

in 
Feet. 

0.5 

5.625 

0.453    0.674 

3.79J     6.25 

0.466 

0.682        4.26 

0.5 

0.75 

8.531 

0.643 

0.802 

6.84 

9.56 

0.677 

0.823       7.87 

0.75 

1. 

12. 

0.868 

0.932 

11.2 

13. 

0.877 

0.936J     12.2 

1. 

1.25 

15.31 

1.053 

1.026 

15.7 

16.56 

1.066 

1.032      17.1 

1.25 

1.5 

18.75 

1  .  230 

1.109 

20.8 

20.25 

1.246 

1.116      22.6 

1.5 

1.75 

22.31 

1.399 

1  .  183 

26.4 

24.06 

1.420 

1.192!     28.7 

1.75 

2 

26. 

1.561 

1.249 

32.5 

28. 

1.586 

1.259      35.3 

2 

2'  25 

29.81 

1.719 

1.311 

39.1 

32.06 

1.746 

1.321;     42.4 

2^25 

2.5 

33.75 

1.868 

1.367 

46.1 

36.25 

1  .  901 

1.3791     50. 

2.5 

2.75 

37.81 

2.015 

1.419 

53.7 

40.56 

2.051 

1.432      58.1 

2.75 

3. 

42. 

2.156 

1.466 

61.6 

45. 

2.197 

1.482i     66.7 

3. 

3.25 

46.31 

2.291 

1.5J3 

70.1 

49.56 

2.339 

1.529;     75.8 

3.25 

3.5 

50.75 

2.428 

1.558 

79.1 

54.25 

2.477 

1.5741     85.4 

3.5 

3.75 

55.31 

2.561 

1.600 

88.5 

59.06 

2.612 

1.616!     95.4 

3.75 

4. 

60. 

2.689 

1.640 

98.4 

64. 

2.745 

1.657      106. 

4. 

4.5 

69.75 

2.940 

1.715 

119.6 

74.25 

3.003 

1.733    128.7 

4.5 

5. 

80. 

3.182 

1.784 

142.7 

85. 

3.252 

1.803    153.3 

5. 

5.5 

90.75 

3.417 

1.848 

167.7 

96.25 

3.493 

1.869;    179.9 

5.5 

6. 

102. 

3.647     1.910 

194.8 

108. 

3.728 

1.931:  20S.6 

6. 

60 


FLOW    OF    WATER    IN 


TABLE   8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1.    Values 
of  the  factors  a  —  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in. 

feet,  and  also  \/r  and  a\/r  for  use  in  the  formulas 

v  =  c  X  \/r   X  -s/s"  and  Q  =  c  X  a^r   X  \/*~ 


BED  13  FEET. 

BED  14  FEET. 

Depth 
in 
Feet. 

a 

r 

Vr 

a\/f 

a 

r 

x/r 

a<x/V 

Depth 
in 

Feet. 

0.5 

6.62 

0.460 

0.677 

4.49 

7.37 

0.467 

0.683 

5.03 

0.5 

0.75 

10.03 

0.663 

0.814 

8.17 

11.34 

0.679 

0.824 

9.34 

0.75 

1  . 

14. 

0.884 

0.940 

13.10 

15. 

0.891 

0.944 

14.2 

1. 

1.25 

17.81 

1.077 

1.038 

18.5 

19.06 

.087 

1.043 

19.9 

1.25 

1.5 

21.75 

1.262 

1  .  123 

24.4 

23.25 

.275 

1  .  129 

26.2 

1.5 

1.75 

25.81 

1.439 

1.200 

31. 

27.56 

.454 

1.206 

33.2 

1.75 

2. 

30. 

1.608 

1.268 

38. 

32. 

.628 

1.276 

40.8 

2 

2^25 

34.31 

1.774 

1  .  333 

45.7 

36.56 

.795 

1.340 

49. 

2*25 

2.5 

38.75 

1.931 

1  .  382 

53.6 

41.25 

.958 

1  .  398 

57.7 

2.5 

2.75 

43.31 

2.085 

1.444 

62.5 

46.06 

2.115 

1.454 

67. 

2.75 

3. 

48. 

2.234 

1  .  493 

71.7 

51. 

2.268 

1.506 

76.8 

3. 

3.25 

52.81 

2.380 

1.543 

81.5 

56.06 

2.417 

1.555 

87.2 

3.25 

3.5 

57.75 

2.522 

1.554 

89.7 

61.25 

2.563 

1.601 

98.1 

3.5 

3  .  75 

62.81 

2.661 

1.631 

102.4 

66.56 

2.709 

1.646 

109.6 

3.75 

4. 

68. 

2.797 

1.672 

113.7 

72. 

2.845 

1.687 

121.5 

4. 

4.5 

78.50 

3.051 

1.746 

137.1 

83.25 

3.115 

1.765 

146.9 

4.5 

5. 

90. 

3.316 

1.821 

163.9 

95. 

3.376 

1.810 

171.9 

5. 

5.5 

101.75 

3.563 

1.887 

192. 

107.25 

3.630 

1  .  905 

204.3 

5.5 

6. 

114. 

3.804 

1.950 

222.3 

120. 

3.875 

1.968 

236  .  2 

6. 

BED  15  FEET. 

BED  16  FEET. 

Depth 

Depth 

in 
Feet. 

a 

r 

Vr 

a\/r 

a             r          \/r       a\/r 

in 

Feet. 

0.5 

7.62 

0.465 

0.682 

5.20 

8.37    0.471 

0.686        5.74 

0.5 

0.75 

11.53 

0.674 

0.821 

9.47 

12.84    0.687 

0.828'     10.63 

0.75 

1. 

16. 

0.897 

0.947 

15.2 

17.      1  0.903 

0.950      16.1 

1. 

1.25 

20.31 

1.096 

1.047 

21.3 

21.56    1.104 

1.051      22.6 

1  .  25 

1.5 

24.75 

1.286 

1.134 

28.1 

26.25    1.297 

1.139      29.9 

1.5 

1.75 

29.31 

1.469 

1.212 

35.5 

31.06    1.482 

1.217      37.8 

1.75 

2 

34. 

1.646 

1.283 

43.6 

36. 

1.662 

1.289      46.4 

2. 

2.25 

38.81 

1.818 

1.348 

52.3 

41.06 

1.835 

1.354:     55.6 

2.25 

2.5 

43.75 

1.982 

1.408 

61.6 

46.25i  2  005 

1.416      65.5 

2.5 

2.75 

48.81 

2.144 

1.464 

71.5 

51.56    2.168 

1.472      75.9 

2.75 

3. 

54. 

2.300 

1.516 

81.9 

57. 

2.328 

1.526      87. 

3. 

3.25 

59.31 

2.452 

1.566 

92.9 

62.56 

2.484 

1.576      98.6 

3.25 

3.5 

64.75 

2.601 

1.612 

104.4 

68.25    2.635 

1.623    110.8 

3.5 

3.75 

70.31 

2.746 

1.657 

116.5 

74.06    2.783 

1.668 

123.5 

3.75 

4. 

76. 

2.888 

1.700 

129.2 

80.        2.929 

1.711 

136.9 

4. 

4.5 

87.75 

3.165 

1.779 

156.1 

92.25    3.211 

1.792 

165.3 

4.5 

5. 

100. 

3.431 

1.852 

185.2 

105.        3.484 

1.866 

195.9 

5. 

5.5 

112.75 

3.690 

1.921 

216.6 

118.25    3.748 

1  .  936 

228.9 

5.5 

6. 

126. 

3.941 

1  .  985 

250.1 

132.        4.004 

2.0011  264.1 

6. 

OPEN    AND    CLOSED    CHANNELS. 


61 


TABLE  8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1.    Values 
of  the  factors  a  —  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 

feet,  and  also  ^r  and  a\/r  for  use  in  the  formulae 

v  =  c  X  VF'X  V*  and  Q  =  c  X  a^/r   X 


BED  17  FEET. 

BED  18  FEET. 

Depth 

i 

Depth 

IB 

Feet. 

a 

r 

N/F 

a\/r            a             r 

Vr 

a\/r 

in 

Feet. 

0.5 

8.62 

0.468 

0  684 

5.90 

9.25 

0.477 

0.690 

6.38 

0.5 

0.75 

13.03 

0.682 

0.825 

10.75 

14.06 

0.694 

0.833 

11.7 

0.75 

1. 

18. 

0.908 

0.953 

17.2 

19. 

0.912 

0.955 

18.1 

1. 

1.25 

22.81 

.111 

1.052 

24. 

24.06 

1.117 

1.057 

25.4 

1.25 

1.5 

27.75 

.306 

1.143 

31.7 

29.25 

1.315 

1.147 

33.5 

1.5 

1.75 

32.81 

.495 

1.222 

40.1 

34.56 

1.506 

1.227 

42.4 

1.75 

2. 

38. 

.677 

1.295 

49.2 

40. 

1.691 

1.300 

52. 

2. 

2.25 

43.31 

.853 

1.361 

58.9 

45.56 

1.870 

1.367 

62.3 

2.25 

2.5 

48.75 

2.025 

1.423 

69.4 

51.25 

2.044 

1.430 

73.3 

2.5 

2.75 

54.31 

2.193 

1.481 

80.4 

57.06 

2.213 

1.487 

84.8 

2.75 

3. 

60. 

2.354 

1.534 

92. 

63. 

2.379 

1.542 

97.1 

3. 

3.25 

65.81 

2.513 

1.585 

104.3 

69.06 

2.541 

1.594 

110.1 

3.25 

3.5 

71  .75 

2.667 

1.633 

117.2 

75.25 

2.697 

1.642 

123.6 

3.5 

3.75 

77.81 

2.819 

1.679 

130.6 

81.56 

2.851 

1.688 

137.7 

3.75 

4. 

84. 

2.967 

1.722 

144.6 

88. 

3.002 

1.733 

152.5 

4. 

4.5 

96.75 

3.255 

1.804 

174.5 

101.25 

3.296 

1.810 

183.8 

4.5 

5. 

110. 

3.532 

1.880 

206.8 

115. 

3.578 

1.891 

217.5 

5. 

5.5 

123.75 

3.801 

1.950 

241.3 

129.25 

3.852 

1.962 

253.6 

5.5 

6. 

138. 

4.062 

2.015 

278.1 

144. 

4.117 

2.029 

292.2 

6. 

7. 

168. 

4.565 

2.137 

359. 

175. 

4.630 

2.152 

376.6 

7. 

BED  19  FEET. 

BED  20  FEET. 

Depth  ' 

j                  !   Depth 

,&.    •     '    ^ 

a\/r 

a 

^     !    ^     |    F& 

1 

0.5          9.62      0.471 

0.686 

6.60 

10.25 

0.479 

0.692 

7.09!  0.5 

0.75      14.53      0.688 

0.830 

12.1 

15.56 

0.704 

0.839 

13.1 

0.75 

1.          20.          0.876 

0.936 

18.7 

21. 

0.920 

0.959 

20.1 

1. 

1.25 

25.31 

1.123 

.060 

26.8 

26.56    1.129 

1  .  063 

28.2      1.25 

1.5 

30.75 

1.323 

.150 

35.4 

32.25    1.330 

1.153 

37.2 

1.5 

1.75      36.31 

1.516 

.231 

44.7 

38.06    1.525 

1.235 

47. 

1.75 

2.          42. 

1.703 

.305 

54.8 

44.         1.715 

1.309 

57.6 

2. 

2.25      47.81 

1.886 

.373 

65.6 

50.061   1.898 

1.377 

68.9 

2.25 

2.5 

53.75 

2.062 

.436 

77.2 

56.25 

2.078 

1.442 

81.1 

2.5 

2.75 

59.81 

2.234 

.494 

S9.4 

62.56 

2.252 

1.501 

93.9 

2.75 

3. 

66. 

2.401 

.550 

102.3 

69. 

2.422 

1.556 

107.4 

3. 

3.25     72.31 

2.565 

.601 

115.8 

75.56 

2.589 

1.609 

121.6 

3.25 

3.5     !  78.75 

2.725 

.651 

130. 

82.25 

2.751 

1.659 

136.5 

3.5 

3.75  !  88.31 

2.882 

.700 

150.1 

89.06 

2.998 

1.731 

154.2 

3.75 

4.       i  92. 

3.035 

.742 

160.3 

96. 

3.066    1.751 

168.1 

4. 

4.5      105.75 

3.333 

.825 

193. 

110.25!  3.369 

1.835 

202.3 

4.5 

5. 

120. 

3.621 

.903 

228.4 

125.      i  3.661 

1.913 

239.1 

5. 

5.5 

134.75 

3.899 

.975|  266.1 

140.25 

3.944 

1.986 

278.5 

5.5 

6. 

150. 

4.170 

2.042    306.3       156. 

4.220 

2.054 

320.4 

6. 

7. 

182. 

4.691 

2.166J  394.2  i    189.      i  4.748 

2.179 

411.8 

7. 

8. 

216. 

5.189 

2.2761  491.6  i    224.        5.255 

2.292 

513.4 

8. 

FLOW    O¥    WATER    IN 


TABLE  8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1.  Values 
of  the  factors  a  =  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 
feet,  and  also  \/r~  and  a^/r~fov  use  in  the  formulae 

v  —  c  X  \/^~  X  \A'    and  C*       c  X  «\/V   X  \A 


BED  25  FEET. 

BED  30  FEET. 

Depth 

i 

Depth 

in 

Feet. 

a 

r          Vr 

a\/r 

a             r         vV 

a\/r 

in 

Feet. 

0.5 

12.25 

0.464 

.681        8.34 

15.25    0.486      .697 

10.63 

0.5 

0.75 

19.31 

0.712 

.844      16.3 

23.06!  0.718      .847 

19.5 

0.75 

1. 

26. 

0.934 

.966j     25.1 

31.        0.944      .976 

30.3 

1. 

1.25 

32.81 

1.150 

1.0721     35.2 

39.06!  1.165      .079 

42.1 

1.25 

1.5         39.75 

1.359 

1.166 

46.3 

47.25i   1.380      .175 

55.5 

1.5 

1.75       46.81 

1.563 

1.250 

58.5 

55.56    1.592      .261 

70.1 

1.75 

2.            54. 

1.761 

1.327      71.7 

64.        1.795      .340 

85.8 

2. 

2.25       61.31 

1.954 

1.397     85.6 

72.56    1.995!      .412 

102.5 

2.25 

2.5          68.75    2.144    1.464    100.7 

81.25    2.172    1.474 

119.8 

2.5 

2.75        76.31    2:328i   1.526    116.4 

90.06    2.384    1.544 

139.1 

'2.  75 

3.            84. 

2.509    1.584;   133.1 

99. 

2.573S   1.604 

158.8 

3. 

3.25        91.81 

2.684    1.639    150.5 

108.06 

2.758    1.661 

179.5 

3.25 

3.5 

99.75 

2.858    1.691    168.7 

117.25 

2.939    1.711 

200.  G 

3.5 

3.75 

107.81 

3.028 

1.7401   187.6 

126.56 

3.141    1.772 

224.3 

3.75 

4. 

116. 

3.193 

1.787 

207.3 

136. 

3.291 

1.814 

246.7 

4. 

4^25      124.31 

3.358 

1.832 

227.7 

145.56 

3.464 

1.861 

270.9 

4.2f> 

4.5        132.75 

3.519 

1.876 

249. 

155.25 

3.633    1.906 

295.9 

4.5 

4.75 

141.31 

3.677 

1.917 

270.9 

165.06 

3.800    1.949 

321.7 

4.75 

5. 

150. 

3.831 

1.957    293.6 

175. 

3.965 

1.991 

348.4 

5. 

5.25      158.81 

3.985 

1.971!  313. 

185.06 

4.126 

2.031 

375.9 

5.25 

5.5        167.75 

4.136 

2.034    341.2 

195.25 

4.286 

2.070 

404.2 

5.5 

5.75      176.81 

4.285 

2.070    366. 

205.56 

4.443 

2.108 

433.3 

5.75 

6. 

186. 

4.432 

2.105    391.5       216. 

4.599 

2.145 

463.3 

6. 

6.25 

195.31 

4.576 

2.1391  417.8  N  226.56 

4.752 

2,179 

493.7 

6.25 

6.5 

204.75 

4.720 

2.172    444.7       237.25 

4.903 

2.214 

525.3 

6.5 

6.75 

214.31 

4.861 

2.205    472.6  j    248.06 

5.053 

2.248 

557.6 

6.75 

7. 

224. 

5. 

2.236 

500.9  I 

259. 

5.201 

2.281 

590.8 

7. 

7.25 

233.81 

5.138 

2.267 

530. 

270.06 

5.347 

2.312 

624.4 

7.25 

7.5 

243.75 

5.274 

2.296 

559.7 

281.25 

5.492 

2.344 

659.2 

7.5 

7.75 

253.81 

5.409 

2.325 

590.1 

292.56 

5.635 

2.374 

694.5 

7.75 

8. 

264. 

5.541 

2.354 

621.5 

304. 

5.776 

2.403 

730.5 

8. 

8.25 

274.31 

5.675 

2.382 

653.4 

315.56 

5.917 

2.432 

767.4 

8.25 

8.5 

284.75 

5.806 

2.408 

685.7 

327  .  25 

6.055 

2.460 

805. 

8.5 

8.75      295.31 

5.936 

2.436 

719.4 

339.06 

6.193 

2.488 

843.6 

8.75 

9. 

306. 

6.065 

2.463 

753.7  j!  351. 

6.329 

2.515 

882.8 

9. 

OPEN    AND    CLOSED    CHANNELS. 


63 


TABLE  8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1.  Values 
of  the  factors  a  =  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 
feet,  and  also  \/~  a-11^  «\/F~for  use  in  the  formulae 

v  =  c  X  \/~  X  -v/Tand  Q  =  c  X  ov/T  X  \A~~ 


BED  35  FEET. 

BED  40  FEET. 

Depth 
in 
Feet. 

_ 
a             r 

Vr        a^/r 

a 

r 

vT 

a-v/r 

Depth 
in 

Feet. 

0.75 

23.06    0.621 

.788      18.2 

30.56 

0.726      .852        26. 

0.75 

1. 

36. 

0.952 

.976!     35.1 

41. 

0.957      .978       40.1 

1. 

1.25 

45.31 

1.176 

1.082;     49. 

51.56 

1.184 

1.0881       56.1 

1.25 

1.5 

54.75 

1.395 

i.181!     64.7 

62.25 

1.407 

1.190;       74.1 

1.5 

1.75 

64.30 

1.610 

1.269!     81.6 

73.06 

1.625 

1.275;       93.2 

1.75 

2. 

74. 

1.820 

1.349      99.8 

84. 

1.840 

1.356      113.9 

2. 

2.25 

83.81 

2.026 

1.4231  119.3 

95.06 

2.050 

1.432      136.1 

2.25 

2.5 

93.75 

2.228 

1.493 

140. 

106.25 

2.257 

1.502!     159.6 

2.5 

2.75 

103.81 

2.426 

1.557 

161.6 

117.56 

2.460 

1.568!     184.3 

2.75 

3. 

114. 

2.622 

1.619 

184.6 

129. 

2.661    1.631!     210.4 

3. 

3.25 

124.31    2.815 

1.678 

208.6 

140.56 

2.838    1.685      236.8 

3.25 

3.5 

134.75 

3.001 

1.732 

233.4 

152.25 

3.051    1.747 

266. 

3.5 

3.75 

145.31 

3.197 

1.788 

259.8 

164.06 

3.242 

1.801 

295.5 

3.75 

4. 

156. 

3.368 

1.835 

286.3 

176. 

3.431J   1.852 

326.  . 

4. 

4.25 

166.81 

3.547 

1.883 

314.1 

188.06 

3.615    1.901 

357.5 

4.25 

4.5 

177.75 

3.724 

1.930 

343.1 

200.25 

3.798    1.949 

390.3 

4.5 

4.75 

188.81 

3.898 

1.974 

372.7 

212.56 

3.977    1.994 

423.8 

4.75 

5. 

200. 

4.070 

2.017 

403.4 

225. 

4.155    2.038 

458.6 

5. 

5.25 

211.31 

4.239 

2.059    435.1 

237.56 

4.331    2.081 

494.4 

5.25 

5.5 

222.75 

4.406 

2.099    467.6 

250.25 

4.504!  2.122 

531. 

5.5 

5.75 

234.31 

4.571 

2.138i  501. 

263.06 

4.676    2.162 

567.7 

5.75 

6. 

246. 

4.733 

2.176 

535.3 

276. 

4.844    2.201 

607.5 

6. 

6.25 

257.81 

4.894 

2.212 

570.3 

289.26 

5.015    2.239 

647.7 

6.25 

6.5 

269.75 

5.053 

2.248 

606.4 

j  302.25 

5.1771  2.2',5 

687.6 

6.5 

6.75 

281.81 

5.206 

2.282 

643.1 

315.56 

5.340 

2.311 

729.3 

6.75 

7  . 

294. 

5.365 

2.316 

680.9 

329. 

5.501 

2.343 

770.8 

7. 

7.25 

306.21 

5.517 

2.349 

719.3 

342.56 

5.661 

2.379)     815. 

7.25 

7.5 

318.75 

5.671 

2.381 

758.9 

356.25 

5.830 

2.414      860. 

7.5 

7.75     331.31 

5.821 

2.416 

800.4 

370.06 

5.976 

2.444      904.4 

7.75 

8.          344. 

5.968 

2.443 

840.4 

384. 

6.13-2 

2.4761     950.8 

8. 

8.25 

356.81 

6.117 

2.473 

882.4 

398.06 

6.285 

2.507 

997.9 

8.25 

8.5 

369.75 

6.262 

2.502 

925.1 

412.25 

6.437 

2.537 

1046. 

8.5 

8.75      382.81 

6.4071  2.531 

968.9 

426.56 

6.588 

2.566 

1095. 

8.75 

9.           396. 

6.550 

2.559 

1013. 

441. 

6.737 

2.596 

1145. 

9. 

9.5 

422.75 

6.833 

2.614 

1105. 

470.25 

7.107 

2.666 

1254. 

9.5 

10.          450. 

7.111 

2.666 

1200. 

500. 

7.322 

2.706 

1353. 

10. 

84 


FLOW    OF    WATER    IN 


TABLE  8: 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1.    Values 
of  the  factors  a  =  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 
feet,  and  also  v^aiid  a-^/T^ioT:  use  in  the  formula} 
v  =  c  X  V~  X  -x/JTaiicl  Q  =  c  X 


BED  45  FEKT. 

BED  50  FEET. 

Depth 
in 

a 

r 

x/r  ''•  a\/r 

a 

r 

^/r    a\/r 

Depth 
in 

Feet. 

! 

Feet. 

1.     46. 

0.962 

0.981 

45.1 

51. 

.964 

0.982 

50.1 

1. 

1.5 

69.75 

1.416 

1.19G 

83. 

77.25 

1.424 

1.193 

92.2 

1.5 

1.75 

81.81 

1.638 

1.280 

104.7 

90.56 

1.648 

1.284 

116.3 

1.75 

0 

94. 

1.856 

1.362 

128.1 

104. 

1.868 

1  .  367 

142  .  2 

2. 

2^25 

106.31 

2.071 

1.439 

153. 

117.56 

2.086 

1.444 

169.8 

2.25 

2.5 

118.75 

2.280 

1.510 

179.3 

131.25 

2.300 

1.516 

199. 

2.5 

2.75 

131.31 

2.488 

1.577 

207.1 

145.06 

2.511 

1.584 

229.8 

2.75 

3. 

144. 

2.692 

1.641 

236.3 

159. 

2.719 

1.649 

262.2 

3. 

3.25 

156.81 

2.894 

1.701 

266.7 

173.06 

2.927 

1.711 

296.1 

3.25 

3.5 

169.75 

3.092 

1.758 

298.4 

187.25 

3.126 

1.768 

331.1 

3.5 

3.75 

182.81 

3.288 

1.813 

331.4 

201.56 

3.326 

1.823 

367.4 

3.75 

4. 

196. 

3.481 

1.86G 

365.7 

216. 

3.523 

1.877 

405.4 

4. 

4.25 

209.31 

3.671 

1.916 

401. 

230.56 

3.717  1.928 

444.5 

4.25 

4.5 

222.75 

3.859 

1.964 

437.5 

245.25 

3.910  1.977 

484.8 

4.5 

4.75 

236.31 

4.044 

2.011 

475.2 

2G0.06 

4.100  2.025 

526.6 

4.75 

5. 

250. 

4.227 

2.05G 

514. 

275. 

4.287!  2.070 

569.2 

5. 

5.25 

263.81 

4.408 

2.100 

554. 

290.06 

4.4731  2.115 

613.5 

5.25 

5.5 

277.75 

4.587 

2.142 

594.9 

305.25 

4.656  2.158 

658.7 

5.5 

5.75 

291.81 

4.763 

2.182 

636.7 

320.56 

4.838  2.199 

704.9 

5.75 

6. 

306. 

4.938 

2.222 

679.9 

336. 

5.017-  2.240 

752.6 

6. 

6.25 

320.31 

5.106 

2.260 

723.9 

351.56 

5.195,  2.279 

801.2 

6.25 

6.5 

334.75 

5.281 

2.298 

769.3 

367.25 

5.371  2.317 

850.9 

6.5 

6.  75 

349.31 

5.450 

2.335 

815.6 

383.06 

5.544  2.354 

901.7 

6.75 

7  . 

364. 

5.617 

2.370 

862.7 

399. 

5.716  2.391 

954. 

•  7. 

7.25 

378.81 

5.783 

2.405 

910.3 

415.06 

5.887  2.426 

1007. 

7.25 

7.5 

393.75 

5.947 

2  .  439 

960.4 

431.25 

6.056  2.461 

1061. 

7.5 

7.75 

408.81 

6.109 

2.472 

1011. 

447  .  56 

6.223  2.495 

1117. 

7.75 

8. 

424. 

6.269 

2.504 

1062. 

464. 

6.389  2.527 

1173. 

8. 

8.25 

439.31 

6.429 

2.536 

1114. 

480.56 

6.553  2.560 

1230. 

8.25 

8.5 

454.75 

6.587 

2.566 

1167. 

497.25 

6.716  2.591 

1288. 

8.5 

8.75 

470.31 

6.743 

2.597 

1221  . 

514.06 

6.877!  2.622 

1348. 

8.75 

9. 

486. 

6.898 

2.626 

1276. 

531. 

7.037  2.653 

1409. 

9. 

9.5 

517.75 

7.204 

2.684 

1390. 

565  .  25 

7.353  2.711 

1532. 

9.5 

10. 

550. 

7.505 

2.740 

1507. 

600. 

7.665  2.770 

1662. 

10. 

10.5 

582.75 

7.801 

2.793 

1628. 

635.25 

7.971  2.823 

1793. 

10.5 

11. 

616. 

8.093 

2.845 

1753. 

671. 

8.2731  2.874 

1928. 

11. 

OPEN    AND    CLOSED    CHANNELS. 


65 


TABLE  8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1 .  Values 
of  the  factors  a  =  area  in  square  feet,  and  r  ==  hydraulic  mean  depth  in 
feet,  and  also  ^/r~and  a\/r~for  use  in  the  formula) 

v  =  c  X  V~  X  VJTand  Q  =  c  X  a*/r~  X  •%/•«" 


BED  60  FEET. 

BED  70  FEET. 

Depth 
in 

Feet. 

a 

r 

x/r 

a\/r 

a 

r 

Vr 

a-\/r 

Depth 
in 
Feet. 

1. 

61. 

0.971 

0.985 

60.1 

71. 

0.975 

0.987 

70.1 

1. 

1.5 

92.25 

1.436 

.199 

110.6 

107.25 

1.445 

1.200 

128.7 

1.5 

2. 

124. 

1.889 

.377 

170.7 

144. 

1.903 

1.346 

193.8 

2 

2.25 

140.06 

2.110 

.452 

203.4 

162.56 

2.129 

1.459 

237.2 

2  '.25 

2.5 

156.25 

2.330 

.526 

238.4 

181.25 

2.352 

1.534 

278. 

2.5 

2.75 

172.56 

2.546 

.595 

275.2 

200.06 

2.572 

1.604 

320.9 

2.75 

3. 

189. 

2.760 

.661 

313.9 

219. 

2.790 

1.670 

365.7 

3. 

3.25 

205.56 

2.971 

.724 

355.2 

238.06 

3.006 

1.734 

412.8 

3.25 

3.5 

222.25 

3.180 

1.783 

396.3 

257.25 

3.220 

1.794 

461.5 

3.5 

3.75 

239.06 

3.386 

1.838 

439.4 

276.56 

3.431 

1.852 

512.2 

3.75 

4. 

256. 

3.590 

1.895 

475.1 

296. 

3.640 

1.908 

564.8 

4. 

4.25 

273.06 

3.791 

1.947 

531.6 

315.56 

3.847 

1.961 

618.8 

4.25 

4.5 

290.25 

3.991 

1.998 

579.9 

335.25 

4.052 

2.013 

674.9 

4.5 

4.75 

307.56 

4.188 

2.046 

629.3 

355.06 

4.256 

2.063 

732.5 

4.75 

5. 

325. 

4.384 

2.095 

680.9 

375. 

4.457 

2.111 

791.6 

5. 

5.25 

342.56 

4.577 

2.139 

732.7 

395.06 

4.656 

2.158 

852.5 

5.25 

5.5 

360.25 

4.768 

2.183 

786.4 

415.25 

4.858 

2.204 

915.2 

5.5 

5.75 

378.06 

4.957 

2.226 

841.6 

435.56 

5.049 

2.247 

978.7 

5.75 

6. 

396. 

5.145 

2.268 

898.1 

456. 

5.243 

2.289 

1043.8 

6. 

6.25 

414.06 

5.330 

2.309 

956.1 

476.56 

5.435 

2.331 

1110.9 

6.25 

6.5 

432.25 

5.515 

2.348 

1014.9 

497.25 

5.626 

2.372 

1179.5 

6.5 

6.75 

450.56 

5.697 

2.387 

1075.5 

518.06 

5.815 

2.411 

1249. 

6.75 

7. 

469. 

5.877 

2.424 

1136.8 

539. 

6.002    2.450 

1320.6 

7. 

7.25 

487.56 

6.056 

2.461 

1199.9 

560.06 

6.188 

2.487 

1392.9 

7.25 

7.5 

506.25 

6.234 

2.497 

1264.1 

581.25 

6.373 

2.524 

1467.1 

7.5 

7.75 

525.06 

6.409 

2.531 

1328.9 

602.56 

6.555!  2.560 

1542.6 

7.75 

8. 

544. 

6.584 

2.566 

1396. 

624. 

6.736 

2.596 

1619.9 

8. 

8.25 

563.06 

6.757 

2.599 

1463.4 

645.56 

6.917 

2.630 

1697.8 

8.25 

8.5 

582.25 

6.928 

2.632 

1532.5 

667.25 

7.095 

2.664 

1777.6 

8.5 

8.75 

601.56 

7.098 

2.664 

1602.6 

689.06 

7.272 

2.696 

1857.7 

8.75 

9. 

621. 

7.267 

2.696 

1674.2 

711. 

7.448 

2.729 

1940.3 

9. 

9.5 

660.25 

7.600 

2.759 

1821.6 

755.25 

7.797 

2  '.790 

2107.1 

9.5 

10. 

700. 

7.929 

2.816 

1971.2 

800. 

8.140 

2.853 

2282.4 

10. 

10.5 

740.25 

8.253 

2.873 

2126.7 

845.25 

8.478 

2.912 

2461.4 

10.5 

11. 

781. 

8.572 

2.928 

2286.8 

891. 

8.8121  2.968 

2644.5  11. 

66 


FLOW    OF    WATER    IN 


TABLE  8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1 .  Values 
of  the  factors  a  =  area  in  square  feet,  and  r  —  hydraulic  mean  depth  in 
feet,  and  also  \X~and  a\/r  for  use  in  the  formulae 

v  =  c  X  \/'>~  X  vT~and  Q  =  c  X  a^/T  X  \A~ 


BED  80  FEET. 

BED  90  FEET. 

Depth 
in 

Feet. 

a      r 

v/r 

a^/r 

a 

r 

\/V 

a\/r 

Depth 
in 

Feet. 

1. 

81. 

0.978 

.989 

80.1 

91. 

0.980 

.990 

90.1 

1. 

2. 

164. 

1.915 

1.384J  227.0 

184. 

1.923 

1.387 

255.2 

2. 

2.25 

185.06 

2.143 

1.464 

270.9 

207.56 

2.154 

1.467 

304.5 

2.25 

2.5 

206.25 

2.369 

1.539 

317.4 

231.25 

2.382 

1.543 

356.8 

2.5 

2.75 

227.56 

2.592 

1.610 

366.4 

255.06 

2.609 

1.612 

411.2 

2.75 

3. 

249. 

2.814 

1.678  417.8 

279. 

2.833 

.683 

469.6 

3. 

3.25 

270.56 

3.034 

1.742  471.3 

303.06 

3.055 

.748 

529.7 

3.26 

3.5 

292.25 

3.251 

1.803 

526.9 

327.25 

3.276 

.810 

592.3 

3.5 

3.75 

314.06 

3.466 

1.862 

584.8 

351.56 

3.494 

.869 

657.  J 

3.75 

4. 

336. 

3.680 

1.918 

644.4 

376. 

3.711 

.926 

724.2 

4. 

4.25 

358.06 

3.891 

1.973 

706.5 

400.56 

3.926 

.981 

793.5 

4.25 

4.5 

380.25 

4.101 

2.025 

770. 

425  .  25 

4.139 

2.034 

865. 

4.5 

4.75 

402.56 

4.308 

2.076 

835.7 

450.06 

4.351 

2.086 

938.8 

4.75 

5. 

425. 

4.514 

2.125 

903.1 

475. 

4.562 

2.136 

1015. 

5. 

5.25 

447  .  56 

4.719 

2.172 

972.1 

500.06 

4.769 

2.184 

1092. 

5.25 

5.5 

470.25 

4.921  2.218 

1043. 

525  .  25 

4.976 

2.231 

1172. 

5.5 

5.75 

493.06 

5.122 

2.263 

1116. 

550.56 

5.181 

2.276 

1253. 

5.75 

6. 

516. 

5.321 

2.307 

1190. 

576. 

5.397 

2.320 

1336. 

6. 

6.25 

539.06 

5.519 

2.349 

1266. 

601.56 

5.587 

2.364 

1455. 

6.25 

6.5 

562.25 

5.715 

2.391 

1344. 

627.25 

5.788 

2.406 

1509. 

6.5 

6.75 

585.56 

5.909 

2.431 

1423. 

653.06 

5.986 

2.446 

1597. 

6.75 

7. 

609. 

6.102 

2.470 

1504. 

679. 

6.184 

2.487 

1689. 

7. 

7.25 

632.56 

6.293 

2.508 

1586. 

705.06 

6.380 

2.526 

1781. 

7.25 

7.5 

656.25 

6.484 

2.546 

1671. 

731.25 

6.575 

2.564 

1875. 

7.5 

7.75 

680.06 

6.672 

2.583 

1757. 

757.56 

6.769 

2.602 

1971 

7.75 

8. 

704. 

6.860 

2.619 

1844. 

784. 

6.961 

2.6381  2068. 

8. 

8.25 

728.06 

7.046 

2.654 

1932. 

810.56 

7.152 

2.674 

2167. 

8.25 

8.5 

752.25 

7.230 

2.689 

2023. 

837.25 

7.342 

2.710 

2269. 

8.5 

8.75 

776.56 

7.414 

2.723 

2115. 

864.06 

7.530 

2.744 

2371. 

8.75 

9. 

801. 

7.595 

2.756 

2208. 

891. 

7.717 

2.778 

2475. 

9. 

9.25 

825.56 

7.777 

2.789 

2302. 

918.06 

7.903 

2.811 

2581. 

9.25 

9.5 

850.25 

7.956 

2.821 

2399. 

945.25 

8.088 

2.844 

2688. 

9.5 

9.75 

875.06 

8.134 

2.852 

2496. 

972.56 

8.271 

2.876 

2797. 

9.75 

10. 

900. 

8.312  2.883 

2595. 

1000. 

8.454 

2.907 

2907. 

10. 

10.5 

950.25 

8.663!  2.943 

2797. 

1055.25 

8.816 

2.969 

3133. 

10.5 

11. 

1001. 

9.009!  3.001 

3004. 

1111. 

9.173 

3.028 

3364. 

11. 

12. 

1104. 

9.689  3.113 

3437. 

1224. 

9.876 

3.142 

3846. 

12. 

OPEN    AND    CLOSED    CHANNELS. 


67 


TABLE   8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1 .  Values 
of  the  factors  a  — area  in  square  feet,  and  r=  hydraulic  mean  depth  in 
feet,  and  also  %/~  and  a\/r~  for  use  in  the  formula 

v  =  c  X  \/~  X  \/~  and  Q  =  c  X  ajr   X  -J* 


BED  100  FEET. 

BED  120  FEET. 

Depth 
in 
Feet. 

a 

r 

Vr 

a-v/V 

a 

r 

\/r   a\/r 

Depth 
in 
Feet. 

1. 

101. 

0.982 

0.991 

100.1 

121. 

0.985 

0.992 

120. 

1. 

2. 

204. 

1.931 

1.389 

283.4 

244. 

1.942 

1.393 

339.9 

2. 

2.25 

230.06 

2.163 

1.470 

338.2 

275.06 

2.177 

1.475 

405.7 

2.25 

2.5 

256.25 

2.393 

1.546 

396.2 

306.25 

2.410 

1.552 

475.3 

2.5 

2.75 

282.56 

2.622 

1.619 

457.5 

337.56 

2.642 

1.625 

548.5 

2.75 

3. 

309. 

2.848 

1.687 

521.3 

369. 

2.872 

1.695 

625.5 

3. 

3.25 

335.56 

3.073 

1.752 

587.9 

400.56 

3.101 

1.761 

705.4 

3.25 

3.5 

362.25 

3.296 

1.816 

657.8 

432.25 

3.328 

1.824 

788.4 

3.5 

3.75 

389.06 

3.517 

1.875 

729.5 

464.06 

3.553 

1.885 

874.8 

3.75 

4. 

416. 

3.737 

1.933 

804.1 

496. 

3.777 

1.943 

963.7 

4. 

4.25 

443.06 

3.955 

1.988 

880.8 

528.06 

4. 

2. 

1056. 

4.25 

4.5 

470.25 

4.171 

2.042 

960.3 

560.25 

4.221 

2.054 

1151. 

4.5 

4.75 

497.56 

4.386 

2.094 

1042. 

592.56 

4.441 

2.107 

1249. 

4.75 

5. 

525. 

4.600 

2.145 

1126. 

625. 

4.659 

2.158 

1349. 

5. 

5.25 

552.56 

4.811 

2.193 

1212. 

657.56 

4.876 

2.208 

1452. 

5.25- 

5.5 

580.25 

5.021 

2.241 

1300. 

690.25 

5.092 

2.256 

1557. 

5.5 

5.75 

608.06 

5.230 

2.287 

1391  . 

723.06 

5.306 

2.303 

1665. 

5.75 

6. 

636. 

5.437 

2.331 

1483. 

756. 

5.519 

2.349 

1776. 

6. 

6.25 

664.06 

5.643 

2.375 

1577. 

789.06 

5.731 

2.394 

1889. 

6.25 

6.5 

692.25 

5.848 

2.418 

1674. 

822.25 

5.942 

2.437 

2004. 

6.5 

6.75 

720.56 

6.050 

2.460 

1773. 

855.56 

6.151 

2.480 

2122. 

6.75 

7. 

749. 

6.252 

2.500 

1873. 

889. 

6.359 

2.521 

2241. 

7. 

7.25 

777.56 

6.452 

2.540 

1957. 

922.56 

6.566 

2.562 

2364. 

7.25 

7.5 

806.25 

6.652 

2.579 

2079. 

956.25 

6.772 

2.602 

2488. 

7.5 

7.75 

835.06 

6.849 

2.617 

2185. 

990.06 

6.976 

2.641 

2615. 

7.75 

8. 

864.  i 

7.046 

2.654 

2293. 

1024. 

7.179 

2.679 

2743. 

8. 

8.25 

893.06 

7.241 

2.691 

2403. 

1058.06 

7.382 

2.717 

2875. 

8.25 

8.5 

922.25 

7.435 

2.726 

2514. 

1092.25 

7.583 

2.753 

3007. 

8.5 

8.75 

951.56 

7.628 

2.762 

2628. 

1126.56 

7.783 

2.790 

3143. 

8.75 

9. 

981. 

7.819 

2.796 

2743. 

1161. 

7.982 

2.825 

3280. 

9. 

9.25 

1010.56 

8.010 

2.830 

2860. 

1195.56 

8.180 

2.860 

3419. 

9.25 

9.5 

1040.25 

8.199 

2.863 

2978. 

1230.25 

8.376 

2.894 

3560. 

9.5 

9.75 

1070.06 

8.387 

2.896 

3099. 

1265.06 

8.572 

2.928 

3704. 

9.75 

10. 

1100. 

8.575 

2.928 

3221. 

1300. 

8.767 

2.961 

3849. 

10. 

10.5 

1160.25 

8.946 

2.991 

3470. 

1370.25 

9.153 

3.025 

4145. 

10.5 

11. 

1221. 

9.313 

3.051 

3725. 

1441. 

9.536 

3.088 

4450. 

11. 

11.5 

1282.25 

9.675 

3.110 

3988. 

1512.25 

9.915 

3.149 

4762. 

11.5 

12. 

1344. 

10.03 

3.167 

4256. 

1584. 

10.29 

3.208 

5081. 

12. 

FLOW    OF    WATER    IN 


TABLE  8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1.  Values 
of  the  factors  a  —  area  in  square  feet,  and  r  —  hydraulic  mean  depth  in 
feet,  and  also  -x/~and  a\/r~for  use  in  the  formulae 

v  =  c  X  Vr~  X  \/~and  Q  =  c  X  a->/r~  X  \A~~ 


BED  140  FEET. 

BED  160  FEET. 

Depth 
in 
Feet. 

a 

r 

\/r   a\/r 

a 

r 

V^ 

a\/r 

Depth 
in 
Feet. 

1. 

141. 

0.987 

0.9931  140. 

161. 

0.989 

0.994 

160. 

1. 

2. 

284. 

1.950 

.396   396.5 

324. 

1.956 

1.398 

453. 

2. 

2.25 

320.06 

2.187 

.465   468.9 

365.06 

2.194 

1.481 

540.7 

2.25 

2.5 

356.25 

2  422 

.556 

554.3 

406.25 

2.432 

1.559 

633.3 

2.5 

2.75 

392.56 

2^656 

.630 

639.9 

447  .  56 

2.668 

1.639 

733.6 

2.75 

3. 

429. 

2.889 

.699   728.9 

489.    2.902 

1.704 

833.3 

3. 

3.25 

465.56 

3.121 

.767 

822.6 

530.56  3.136 

1.771 

939.6 

3.25 

3.5 

502  .  25 

3.351 

.831 

906.1 

572.25 

3.368 

1.835 

1050. 

3.5 

3.75 

539.06 

3.579 

.892 

1020. 

614.06 

3.599 

1.897 

1165. 

3.75 

4. 

576. 

3.807 

.951 

1124. 

656. 

3.829  1.957 

1284. 

4. 

4.25 

613.06 

4.033 

2.008 

1231. 

698.06 

4.058 

2.014 

1406. 

4.25 

4.5 

650.25 

4.258 

2.063 

1341. 

740.25 

4.286 

2.070 

1532. 

4.5 

4.75 

687.56 

4.481 

2.117 

1456. 

782.  56i  4.512  2.124 

1662. 

4.75 

5. 

725. 

4.703 

2.169 

1573. 

825. 

4.738  2.177 

1796. 

5. 

5.25 

762.56 

4.924 

2.219 

1692. 

867.56 

4.962  2.228 

1933. 

5.25 

5.5 

800.25 

5.144 

'2.268 

1815. 

910.25 

5.185 

2.277 

2073. 

5.5 

5.75 

838.06 

5.363 

2.315 

1940. 

953.06 

5.407 

2.325 

2216. 

5.75 

6. 

876. 

5.581 

2.362 

2069. 

996. 

5.628 

2.372 

2363. 

6. 

6.25 

914.06 

5.797 

2.408 

2201. 

1039.06 

5.848 

2.418 

2512. 

6.25 

6.5 

952.25 

6.013 

2.452 

2335. 

1082.25 

6.067 

2.463 

2666. 

6.5 

6.75 

990.56 

6.226 

2.495 

2471. 

1125.56 

6.285 

2.507 

2822. 

6.75 

7. 

1029. 

6.439 

2.538 

2612. 

1169. 

6.498 

2.549 

2980. 

7. 

7.25 

1067.56 

6.651 

2.579 

2753. 

1212.56 

6.717 

2.592 

3143.  !  7.25 

7.5 

1106.25 

6.862 

2.620 

2898. 

1256.25 

6.927 

2.632 

3306. 

7.5 

7.75 

1145.06 

7.072 

2.659 

3045. 

1300.06 

7.146 

2.673 

3475. 

7.75 

8. 

1184. 

7.280 

2.700 

3197. 

1344. 

7.359 

2.713 

3646. 

8. 

8.25 

1223.06 

7.488 

2.736 

3346. 

1386.06 

7.561 

2.750 

3812. 

8.25 

8.5 

1262.25 

7.695 

2.774 

3501. 

1432.25 

7.782 

2.790 

3996. 

8.5 

8.75 

1301.56 

7.900 

2.811 

3659. 

1476.56 

7.992 

2.827 

4174. 

8.75 

9. 

1341. 

8.105 

2.847 

3818. 

1521. 

8.201 

2.864 

4356. 

9. 

9.25 

1380.56 

8.289 

2.882 

3979. 

1565.56 

8.410 

2.900 

4540. 

9.25 

9.5 

1420.25 

8.511 

2.917 

4143. 

1610.25 

8.617 

2.936 

4728. 

9.5 

9.75 

1460.06 

8.713 

2  .  952 

4310. 

1655.06 

8.823 

2.970 

4916. 

9.75 

10. 

1500. 

8.912 

2.985 

4478. 

1700. 

9.029 

3.005 

5109. 

10. 

10.5 

1580.25 

9.312 

3.051 

4821. 

1790.25 

9.437 

3.072 

5499. 

10.5 

11. 

1661. 

9.707 

3.116 

5176. 

1881. 

9.843 

3.137 

5901. 

11. 

11.5 

1742.25 

10.098 

3.178 

5537. 

1972.25 

10.24 

3.200 

6311. 

11.5 

12. 

1824. 

10.49 

3.249 

5926. 

2064. 

10.64 

3.262 

6733. 

12. 

13. 

1989. 

11.252 

3.354 

6671. 

2249. 

11.43 

3.381 

7604.  113. 

OPEN    AND    CLOSED    CHANNELS. 


TABLE  8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1.    Values 
of  the  factors  a  =  area  in   square  feet,  and  r  —  hydraulic  mean  depth  in 
feet,  and"  also  \fr~  and  a\/r~ior  use  in  the  formulae 
v  =  c  X  VV~  X  \A~~  and  Q  =  c  X 


BED  180  FEET. 

BED  200  FEET. 

Depth 

Depth 

in                ft 

Feet. 

r 

Vr 

a\/r 

a 

r          Vr 

a\/r 

in 
Feet. 

1. 

181. 

0.990    0.995 

180.1 

201. 

0.991!  0.995 

200. 

1. 

2 

364. 

1.961    1.400 

509.6 

404. 

1.964 

.402 

566.4 

2. 

2^5 

456.25 

2.439    1.562 

712.7 

506.25 

2.445 

.564 

791.8!  2.5 

2.75 

502.56 

2.676    1.636 

822.2 

557.56 

2.683 

.638 

913.3   2.75 

3. 

549. 

2.913    1.706 

936.6 

609. 

2.921 

.709 

1041. 

3. 

3.25 

595.56 

3.148    1.774 

1057. 

660.56 

3.158 

.777 

1174. 

3.25 

3.5 

642.25 

3.382    1.839 

1181. 

712.25 

3.393 

.842 

1312. 

3.5 

3.75 

689.06 

3.615    1.901 

1310. 

764.06 

3.628 

.905 

1456. 

3.75 

4. 

736. 

3.847    1.961 

1443. 

816. 

3.862 

1.965 

1603. 

4. 

4.25 

783.06 

4.078    2.019 

1581. 

868.06 

4.094 

2.023 

1756. 

4.25 

4.5 

830.25 

4.308    2.075 

1723. 

920.25 

4.326 

2.080 

1914. 

4.5 

4.75 

877.56 

4.537 

2.130 

1869. 

972.56 

4.557 

2.134J  2075. 

4.75 

5. 

925. 

4.765 

2.183 

2019. 

1025. 

4.787 

2.1881  2243. 

5. 

5.25 

972.56 

4.991 

2.234 

2173. 

1077.56 

5.015 

2.239J  2413. 

5.25 

5.5 

1020.25 

5.217 

2.284 

2330. 

1130.25 

5.243 

2.290   2588. 

5.5    ' 

5.75 

1068.06 

5.442 

2.333 

2492. 

1183.06 

5.470 

2.339    2767. 

5.75 

6.     . 

1116. 

5.666 

2.380 

2656. 

1236. 

5.697 

2.387!  2950. 

6. 

6.25 

1164.06 

5.889 

2.427 

2825. 

1289.06 

5.921 

2.433    3136. 

6.25 

6.5 

1212.25 

6.111 

2.472 

2997. 

1342.25 

6.146 

2.479!  3327. 

6.5 

6.75 

1200.56 

6.332 

2.516 

3172. 

1395.56 

6.370 

2.524    3522. 

6.75 

7. 

1309. 

6.552 

2.560 

3351. 

1449. 

6.592 

2.567'  3720. 

7. 

7.25 

1357.56 

6.770 

2.602 

3532. 

1502.56 

6.814 

2.610    3922. 

7.25 

7.5 

1406.25 

6.973 

2.641 

3714. 

1556  .  25 

7.035 

2.  6521  4127. 

7.5 

7.75 

1455.06 

7.206 

2.684 

3905. 

1610.06 

7.255 

2.693 

4336. 

7.75 

8. 

1504. 

7.422 

2.724 

4097. 

1664. 

7.474 

2.734 

4549. 

8. 

8.25 

1553.06 

7.638 

2.763 

4291. 

1718.06 

7.693 

2.773 

4764. 

8.25 

8.5 

1602.25 

7.853 

2.802 

4490. 

1772.25 

7.910 

2.812 

4984. 

8.5 

8.75 

1651.56 

8.066 

2.840 

4690. 

1826.56 

8.127 

2.851 

5208. 

8.75 

9. 

1701. 

8.279 

2.877 

4920. 

1881. 

8.343 

2.888 

5432  . 

9. 

9.25 

1750.56 

8.491 

2.914 

5101. 

1935.56 

8.558 

2.925 

5662. 

9.25 

9.5 

1800.25 

8.702 

2.950 

5311. 

1990.25 

8.773 

2.962 

5895. 

9.5 

9.75 

1850. 

8.913 

2.985 

5522. 

12045. 

8.986 

2.997 

6129. 

9.75 

10. 

1900. 

9.122 

3.020 

5738. 

2100. 

9.199 

3.033 

6369. 

10. 

10.5 

2000. 

9.539 

3.089 

6178. 

2210. 

9.622 

3.102 

6855. 

10.5 

11. 

2101. 

9.952 

3.154 

6627. 

2321. 

10.04 

3.169 

7355. 

11. 

11.5 

2202. 

10.36 

3.220 

7091. 

2432. 

10.46 

3.234 

7865. 

11.5 

12. 

2304. 

10.77 

3.282 

7562. 

2544. 

10.87 

3.298 

8390. 

12. 

13. 

2509. 

11.59 

3.406 

8546. 

2769. 

11.69 

3.417 

9462. 

13. 

14. 

2716. 

12.37 

3.517 

9552. 

2996. 

12.50 

3.536 

10594. 

14. 

i 

70 


FLOW    OF    WATER    IN 


TABLE  8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1.  Values 
of  the  factors  a  =  area  in  square  feet,  and  r==  hydraulic  mean  depth  in 
feet,  and  also  -v/^and  a%/r~for  use  in  the  formula) 

v  =  c  X  -\/r~X  \A~and  Q  =  c  X  a^/r~  X  \/~ 


BED  220  FEET. 

BED  240  FEET. 

Depth 
in 

Feet. 

a 

r 

x/r 

a\/r 

a 

r 

Vr 

a\/r 

Depth 
in 
Feet. 

2. 

444. 

1.968 

1.403 

622.9 

484. 

1.970 

1.404 

679.5 

2. 

2.5 

556.25 

2.450 

1  565 

870.5 

606.25 

2.454 

1.567 

950 

2.5 

3. 

669. 

2.928 

1.711 

1145. 

729. 

2.934 

1.713 

1249. 

3. 

3.25 

725.56 

3.166 

1.779 

1291. 

790.56 

3.173 

1.781 

1408. 

3.25 

3.5 

782.25 

3.403 

1.845 

1443. 

852.25 

3.411 

1.847 

1574. 

3.5 

3.75 

839.06 

3.638 

1.907 

1600. 

914.06 

3.647 

1.910 

1746. 

3.75 

4. 

896. 

3.874 

1.968 

1763. 

976. 

3.884 

1.971 

1924. 

4. 

4.25 

953.06 

4.108 

2.027 

1932. 

1038.06 

4.119 

2.030 

2107. 

4.25 

4.5 

1010.25 

4.341 

2.083 

2104. 

1100.25 

4.353 

2.086 

2295. 

4.5 

4.75 

1067.56 

4.573 

2.138 

2282. 

1162.56 

4.587 

2.141 

2489. 

4.75 

5. 

1125. 

4.805 

2.192 

2466. 

1225. 

4.820 

2.195 

2689. 

5. 

5.25 

1182.56 

5.035 

2.244 

2654. 

1287.56 

5.053 

2.248 

2894. 

5.25 

5.5 

1240.25 

5.265 

2.294 

2845. 

1350.25 

5.283 

2.298 

3103. 

5.5 

5.75 

1298.06 

5.494 

2.344 

3043. 

1413.06 

5.514 

2.348 

3318. 

5.75 

6. 

1356. 

5.722 

2.392 

3244. 

1476. 

5.744 

2.397 

3538. 

6. 

6.25 

1414.06 

5.949 

2.439 

3449. 

1539.06 

5.973 

2.444 

3761. 

6.25 

6.5 

1472.25 

6.176 

2.485 

3659. 

1602.25 

6.201 

2.490 

3990. 

6.5 

6.75 

1530.56 

6.402 

2.530 

3872. 

1665.56 

6.429 

2.536 

4224. 

6.75 

7. 

1589. 

6.626 

2.574 

4090. 

1729. 

6.655 

2.580 

4461. 

7. 

7.25 

1647.56 

6.850 

2.617 

4312. 

1792.56 

6.881 

2.623 

4702. 

7.25 

7.5 

1706.25 

7.074 

2.660 

4539. 

1856.25 

7.106 

2.666 

4949. 

7.5 

7.75 

1765.06 

7.296 

2.701 

4767. 

1920.08 

7.331 

2.708 

5199. 

7.75 

8. 

1824. 

7.518 

2.742 

5001. 

1984. 

7.554 

2.748 

5452. 

8. 

8.25 

1883.06 

7.738 

2.782 

5239. 

2048.06 

7.777 

2.789 

5712. 

8.25 

8.5 

1942.25 

7.959 

2.821 

5479. 

2112.25 

8.000 

2.828 

5973. 

8.5 

8.75 

2000.56 

8.178 

2.860 

5722. 

2176.56 

8.221 

2.867 

6240. 

8.75 

9. 

2061. 

8.397 

2.898 

5973. 

2241  . 

8.442 

2.906 

6512. 

9. 

9.25 

2120.56 

8.614 

2.935 

6224. 

2305.56 

8.639 

2.939 

6776. 

9.25 

9.5 

2180.25 

8.832 

2.972 

6480. 

2370.25 

8.882 

2.980 

7063. 

9.5 

9.75 

2240.06 

9.047 

3.007 

6736. 

2435.06 

9.100 

3.017 

7347. 

9.75 

10. 

2300. 

9.264 

3.044 

7001. 

2500. 

9.319 

3.053 

7633. 

10. 

10.5 

2420.25 

9.693 

3.113 

7534. 

2630.25 

9.753 

3.123 

8214. 

10.5 

11. 

2541. 

10.12 

3.181 

8083. 

2761. 

10.18 

3.190 

8808. 

11. 

11.5 

2662.25 

10.54 

3.247 

8644. 

2892.25 

10.61 

3.257 

9420. 

11.5 

12. 

2784. 

10.96 

3.315 

9229. 

3024. 

11.04 

3.323 

10059. 

12. 

13. 

3029. 

11.80 

3.435 

10405. 

3289. 

11.88 

3.44611334. 

13. 

14. 

3276. 

12.62 

3.552 

11636.  |3556.   12.72 

3.56612681. 

14. 

15. 

3525. 

13.46 

3  669 

12933.  3825.  |l3.54 

3.680  14076. 

15. 

16. 

3776. 

14.24 

3.774 

14251. 

4096. 

14.36 

3.789 

15520. 

16 

OPEN    AND    CLOSED    CHANNELS. 


71 


TABLE  8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1.  Values 
of  the  factors  a  =  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 
feet,  and  also  ^/~&nd.  a^/r~ior  use  in  the  formulae 

v  =  c  X  V^X  xA~and  Q  =  c  X  «N/~ X 


BED  260  FEET. 

BED  280  FEET. 

Depth 

in 
Feet. 

a 

r 

\/r 

a^/r 

a      r    v/r   a\/r 

Depth 
in 
Feet. 

2 

524. 

1.972 

1.404!  735.7 

564.    1.974  1.405 

792  A 

2. 

2.5 

656.25 

2.457 

1.567 

1028. 

706.25  2.460  1.568 

1107. 

2.5 

3. 

789. 

2.939 

.714 

1352. 

849.    2.943  1.716 

1457. 

3. 

3.25 

855.56 

3.178 

.783 

1525. 

920.56  3.183  1.784 

1642. 

3.25 

3.5 

922.25 

3.417 

.849 

1705. 

992.25  3.423  1.850 

1836. 

3.5 

3.75 

989.06 

3.655 

.912 

1891. 

1064.06  3.662  1.914 

2037. 

3.75 

4. 

1056. 

3.892 

.973 

2083. 

1136. 

3.900 

1.977 

2246. 

4. 

4.25 

1123.06 

4.129 

2.032 

2282. 

1208.06 

4.136 

2.034 

2457. 

4.25 

4.5 

1190.25 

4.364 

2.089 

2486. 

1280.25  4.373 

2.091 

2677. 

4.5 

4.75 

1257.56 

4.599 

2.145 

2697. 

1352.56 

4.610 

2.147 

2904. 

4.75 

5. 

1325. 

4.833 

2.198 

2912. 

1425. 

4.845 

2.201 

3136. 

5. 

5.25 

1392.56 

5.067 

2.251 

3135. 

1497.56 

5.079 

2.254 

3376. 

5.25 

5.5 

1460.25 

5.299 

2.302 

3361. 

1570.25 

5.313 

2.305 

3619. 

5.5 

5.75 

1528.06 

5.531 

2.352 

3594. 

1643.06 

5.546 

2.355 

3869. 

5.75 

6. 

1596. 

5.762 

2.400 

3830. 

1716. 

5.778 

2.404 

4125. 

6. 

6.25 

1664.06 

5.993 

2.448 

4074. 

1789.06 

6.010 

2.452 

4387. 

6.25 

6.5 

1732.25 

6.223 

2.494 

4320. 

1862.25 

6.241 

2.498 

4652. 

6.5 

6.75 

1800.56 

6.452 

2.541 

4575. 

1835.56 

6.470 

2.544 

4670. 

6.75 

7. 

1869. 

6.680 

2.585 

4831. 

2009. 

6.701 

2.589 

5201. 

7. 

7.25 

1937.56 

6.908 

2.628 

5092. 

2082.56 

6.930 

2.632 

5481. 

7.25 

7.5 

2006.25 

7.134 

2.671 

5359. 

2156.25 

7.159 

2.676 

5770. 

7.5 

7.75 

2075.06 

7.361 

2.713 

5630. 

2230.06 

7.386 

2.718 

6061. 

7.75 

8. 

2144. 

7.586 

2.754 

5905. 

2304. 

7.613 

2.759 

6357. 

8. 

8.25 

2213.06 

7.811 

2.795 

6186. 

2378.06 

7.840 

2.800  6659. 

8.25 

8.5 

2282.25 

8.035 

2.835 

6470. 

2452.25 

8.066 

2.840 

6964. 

8.5 

8.75 

2351.56 

8  .  258 

2.874 

6758. 

2526.56 

8.290 

2.879 

7274. 

8.75 

9. 

2421. 

8.481 

2.912 

7050. 

2601. 

8.515 

2.918 

7590. 

9. 

9.25 

2490.56 

8.703 

2.950 

7347. 

2675.56 

8.739 

2.956 

7909. 

9.25 

9.5 

2560.25 

8.925 

2.987 

7647. 

2750.25 

8.962 

2.993 

8231. 

9.5 

9.75 

2630.06 

9.146 

3.024 

7953. 

2825.06 

9.185 

3.031 

8563. 

9.75 

10. 

2700. 

9.366 

3.060 

8262. 

2900. 

9.407 

3.067 

8894. 

10. 

10.5 

2840.25 

9.804 

3.131 

8893. 

3050.25 

9.849 

3.138 

9572. 

10.5 

11. 

2981. 

10.24 

3.200 

9539. 

3201. 

10.29 

3.203 

10253. 

11. 

11.5 

3122.25 

10.67 

3.266 

10197. 

3352.25 

10.73 

3.276 

10982. 

11.5 

12. 

3264. 

11.10 

3.332 

10876. 

3504. 

11.16 

3.341 

11707. 

12. 

13. 

3549. 

11.96 

3.458 

12272. 

3809. 

12..  02 

3.467 

13206. 

13. 

14, 

3836. 

12.80 

3.578 

13725. 

4116. 

12.88 

3.589 

14772. 

14. 

15. 

4125. 

13.64 

3.693 

15234. 

4425. 

13.72 

3.705 

16395. 

15. 

16. 

4416. 

14.47 

3.804 

16798. 

4736. 

14.56 

3.815 

18068. 

16. 

18. 

5004. 

16.09 

4.012 

20076. 

5364. 

16.21 

4.026 

21595. 

18. 

72 


FLOW    OF    WATER    IN 


TABLE  8. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  to  1.  Values 
of  the  factors  a  =  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 
feet,  and  also  ^/r~  a,nd.  a\/r  for  use  in  the  formulae 

v  =  c  X  Vr~X  -x/«~and  Q  =  c  X  a^/7~X  \/s~ 

BED  300  FEET. 


Depth  in  Feet. 

a 

r 

Vr~ 

a\/r 

2. 

604. 

1.976 

1.405 

846. 

2.5 

756.25 

2.463 

1.569 

1187. 

3. 

909. 

2.947 

1.717 

1561. 

3.25 

985.56 

3.188 

1.777 

1751. 

3.5 

1062.25 

3.428 

1.851 

1966. 

3.75 

1139.06 

3.667 

1.915 

2181. 

4. 

1216. 

3.906 

1.976 

2403. 

4.25 

1293.06 

4.144 

2.035 

2631. 

4.5 

1370.25 

4.382 

2.093 

2868. 

4.75 

1447.56 

4.619 

2.149 

3111. 

5. 

1525. 

4.855 

2.203 

3360. 

5.25 

1602.56 

5.090 

2.256 

3616. 

5.5 

1680.25 

5.325 

2.307 

3876. 

5.75 

1758.06 

5  .  559 

2.358 

4145. 

6. 

1836. 

5.792 

2.406 

4417. 

6.25 

1914.06 

6.025 

2.455 

4699. 

6.5 

1992.25 

6.257 

2.501 

4983. 

6.75 

2070.56 

6.489 

2.547 

5274. 

7. 

2149. 

6.720 

2.592 

5570. 

7.25 

2227.56 

6.950 

2.636 

5872. 

7.5 

2306.25 

7.180 

2.679 

6178. 

7.75 

2385.06 

7.392 

2.719 

6485. 

8. 

2464. 

7.637 

2.764 

6810. 

8.25 

2543. 

7.865 

2.804 

7131. 

8.5 

2622.25 

8.092 

2.845 

7460. 

8.75 

2701.6 

8.319 

2.884 

7791. 

9. 

2781. 

8.545 

2.923 

8129. 

9  25 

2860.6 

8.773 

2.962 

8473. 

9.5 

2940.25 

8.995 

2.999 

8818. 

9.75 

3020. 

9.219 

3.036 

9169. 

10. 

3100. 

9.443 

3.073 

9526. 

10.5 

3260.25 

9.889 

3.144 

10250. 

11. 

3421. 

10.33 

3.214 

10995. 

11.5 

3582.25 

10.77 

3.281 

11753. 

12. 

3744. 

11.21 

3.348 

12535. 

13. 

4069. 

12.08 

3.476 

14144. 

14. 

4396. 

12.94 

3.597 

15812. 

15. 

4725. 

13.80 

3.715 

17553. 

16. 

50.56 

14.64 

3.826 

19344. 

OPEN    AND    CLOSED    CHANNELS. 


73 


TABLE  9. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  £  to  1.    Values 
of  the  factors  a  ~  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 
feet,  and' also  v/~and  a\/r   for  use  in  the  formulae 
v  =  c  X  \/ir  X  v/s"  and  Q  =  c  X  o 


BED  1  FOOT. 

BED  2  FEET. 

Depth 
in 
Feet. 

a 

r 

Vr 

a^/r 

a 

r 

x/F 

a\/r 

Depth 
in 
Feet. 

0.5 

0.62 

0.293 

0.54 

0.34 

1.12 

0.359    0.60 

0.68 

0.5 

0.75 

1.03 

0.385 

0.62 

0.64 

1.78 

0.484    0.69 

1.24 

0.75 

1. 

1.50 

0.464 

0.68 

1.02 

2.50 

0.590 

0.77 

1.92 

1. 

1.25 

2.03 

0.535 

0.73 

1.48 

3.28 

0.684 

0.83 

2.71 

1.25 

1.5 

2.62 

0.602 

0.78 

2.04 

4.12 

0.770 

0.88 

3.62 

1.5 

1.75 

3.28 

0.668 

0.82 

2.69 

5.03 

0.851 

0.92 

4.64 

1.75 

2. 

4.00 

0.731 

0.86 

3.43 

6.00 

0.927 

0.96 

5.78 

2. 

2.25 

7.03 

.000 

1.00 

7.03 

2.25 

2.5 

8.12 

.070 

1.03 

8.41 

2.5 

2.75 

9.28 

.139 

1.07 

9.90 

2.75 

3. 

10.50 

1.217 

1.10 

11.5 

3. 

3.25 

11.78 

.271 

1.13 

13.3 

3.25 

3.5 

13.12 

.337 

1.16 

15.2 

3.5 

3.75 

14.53 

.399 

1.18 

17.2 

3.75 

4. 

16.00 

1.462 

1.21 

19.4 

4. 

BED  3  FEET. 

BED  4  FEET. 

Depih 
iu 
Feet. 

a 

r          \/r 

a-\//* 

a 

, 

v~ 

a\/r 

Depth 
in 
Feet. 

0.5 

1.62 

0.394 

0.63 

1.02 

2.12 

0.411 

0.64 

1.37 

0.5 

0.75 

2.53 

0.541 

0.73 

1.87 

3.28 

0.578 

0.76 

2.50 

0.75 

1. 

3.50 

0.668 

0.82 

2.86 

4.50 

0.722 

0.85 

3.82 

1. 

1.25 

4.53 

0.782 

0.88 

4.00 

5.78 

0.851 

0.92 

5.33 

1.25 

1.5 

5.62 

0.885 

0.94 

5.29 

7.35 

0.969    0.98 

7.01 

1.5 

1.75 

6.78 

0.981 

0.99 

6.72 

8.53 

.078)  1.04 

8.86 

1.75 

2. 

8.00 

.071 

1.03 

8.28 

10.00 

.180 

1.09 

10.9 

2. 

2.25 

9.28 

.156 

1.07 

9.98 

11.53 

.277 

1.13 

13.0 

2.25 

2.5 

10.62 

.237    1.11 

11.8 

13.12 

.369 

1.17 

15.4 

2.5 

2.75 

12.03 

.315    1.15 

13.8 

14.78 

.456 

1.21 

17.8 

2.75 

3. 

13.50 

.391       .18 

15.9 

16.50 

.541 

.24 

20.5 

3. 

3.25 

15.03 

.464!   1.21 

18.2 

18.28 

.623 

.27 

23.3 

3.25 

3.5 

16.62 

1.536      .24 

20.6 

20.12 

.702 

.30 

26.3 

3.5 

3.75 

18.28 

1.606    1.27 

23.2 

22.03 

.779 

.33 

29.4 

3.75 

4. 

20.00 

1.675      .29 

25.9 

24.00 

.854 

.36 

32.7 

4. 

4.25 

21.78 

1.742      .32 

28.8 

26.03 

.957 

.39 

36.2     !  4.25 

4.5 

23.62 

1.809    1.35 

31.8 

28.12 

2.000 

.41 

39.8 

4.5 

5. 

27.50 

1.939    1.39 

38.3 

32.50 

2.1411      .46 

47.6 

5. 

74 


FLOW    OF    WATER    IN 


TABLE  9. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  |  to  1 .  Values 
of  the  factors  a  =  area  in  square  feet,  and  r -- hydraulic  mean  depth  in 
feet,  and  also  -^/^aud  a\/V  for  use  in  the  formulae 

v  =  c  X  ^/r~  X  \A~  and  Q  =  c  X  a^/T X  \S*~~ 


BED  5  FEET. 

BED  6  FEET. 

Depth 
in 
Feet. 

a 

r 

Vr 

a\/r 

a            r         \/r 

a\,/r 

Depth 
in 
Feet. 

05. 

2.625 

.429 

.65 

1.72 

3.125 

.439 

.66 

2.07 

0.5 

0.75 

4.031 

.604 

.77 

3.14 

4.781 

.623 

.78        3.78 

0.75 

1. 

5.500 

.760 

.87 

4.79 

6.500 

.789 

.89 

5.77 

1. 

1.25 

7.031 

.902 

.95 

6.68 

8.281 

.942      .97 

8.04 

1.25 

1.5 

8.625 

1.032 

1.02 

8.76 

10.12 

.082      .04 

10.53 

1.5 

1.75 

10.28 

.156 

.08 

11.04 

12.03 

.214 

.10 

13.31 

1.75 

2. 

12.00 

.267 

.13 

13.51 

14.00 

.337 

.16 

16.19 

2. 

2.25 

13.781 

.374 

.17 

16.16 

16.031 

.453 

.21 

19.33 

2.25 

2.5 

15.625 

.476 

.21 

18.98 

18.125 

.564 

.25 

22.67 

2.5 

2.75 

17.531 

.572 

.25 

21.98 

20.281 

.669 

.29 

26.21 

2.75 

3. 

19.500 

.666 

.29 

25.16 

22  .  500 

.778 

.33 

29.94 

3. 

3.25 

21.531 

.755 

.33 

28.52 

24.781 

.868 

.37 

33.87 

3.25 

3.5 

23.625 

1.834 

.36 

32.06 

27  .  125      .  984 

.40 

37.99 

3.5 

3.75 

25.781 

1.928 

.39 

35.78 

29.231    2.032 

1.43 

42.31 

3.75 

4. 

28.000 

2.008 

.42 

39.68 

32.000    2.223 

1.46 

46.83 

4. 

4.5 

32.625 

2.166 

.47 

48.02 

36.625    2.280 

1.52 

56.45 

4.5 

5. 

37.500 

2.318 

.52 

57.09 

42.5001  2.474!   1.57 

66.85 

5. 

6. 

48.00 

2.606 

.61 

77.28 

54.00      2.781!   1.67 

90.05 

6. 

BED  7  FEET. 

BED  8  FEET. 

Depth 

Depth 

in 

Feet. 

ct 

r 

v*r~ 

a\/r 

a 

r 

v^r 

a\/r 

in 
Feet. 

0.5 

3.62 

0.447 

.67 

2.42 

4.12 

0.452 

.67 

2.77 

0.5 

0.75 

5.53 

0.637J     .79 

4.43 

6.28 

0.649 

.80 

5.06 

0.75 

1. 

7.5 

0.812 

.90 

6.76 

8.5 

0.830 

.91 

7.74 

1. 

1.25 

9.53 

0.973 

.99 

9.40 

10.78 

0.999 

1. 

10.77 

1.25 

1.5 

11.62 

.123 

.06 

12.31 

13.12 

.156 

1.07 

14.11 

1.5 

1.75 

13.78 

.263 

.12 

15.49 

15.53 

.304 

1.14 

17.74 

1.75 

2. 

16.00 

.395 

.18 

18.90 

18.00 

.443 

1.20 

21.63 

2. 

2.25 

18.28 

.519 

.23 

22.54 

20.53 

.576 

1.25 

25.78 

2.25 

2.5 

20.62 

.639 

.28 

26.40 

23.12 

.702 

1.30 

30.17 

2.5 

2.75 

23.03 

.751 

.32 

30.48 

25.78 

.822 

1.35 

34.80 

2.75 

3. 

25.50 

.859 

.36 

34.78 

28.5 

.938 

1.39 

39.67 

3. 

3.25 

28.03 

.965 

.40 

39.29 

31.28 

2.049 

1.43 

44.77 

3.25 

3.5 

30.62 

2.067 

.44 

44.01 

34.12 

2.156 

1.47 

50.10 

3.5 

3.75 

33.28 

2.163 

.47 

48.95 

37.03 

2.260 

1.50 

55.68 

3.75 

4. 

36.0 

2.258 

.50 

54.10 

40. 

2.361 

1.54 

61.47 

4. 

4.5 

41.62 

2.439 

.56 

65.02 

46.12 

2.554 

1.60 

73.71 

4.5 

5. 

47.5 

2.613 

.62 

76.78 

52.50 

2.737 

1.65 

86.86 

5. 

6. 

60.0 

2.939 

.71 

102.85 

66. 

3.081 

1.76 

115.85 

6. 

OPEN    AND    CLOSED    CHANNELS. 


75 


TABLE   9. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  \  to  1.  Values 
of  the  factors  a  =  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 
feet,  and  also  \/7  and  a^/r  for  use  in  the  formulae 

•v  =  c  X  Vr  X  N/Tand  Q  =  c  X  a^/r  X  V* 


BED  9  FEET. 


BED  10  FEET. 


Depth 
in 

n 

Dr 

Feet. 

a 

r 

v/r 

aVr 

Co 

r 

Vr 

a\/r 

Feet. 

0.5 

4.62 

.457 

.676 

3.12 

5.12 

.461 

.68 

3.48 

0.5 

0.75 

7.03 

.659 

.812 

5.71 

7.78 

.666 

.81 

6.37 

0.75 

1. 

9.5 

.845 

.919 

8.73 

10.5 

.858 

'.93 

9.73 

1. 

1.25 

12.03 

1.02 

1.01 

12.15 

13.28 

1.038 

1.02 

13.54 

1.25 

1.5 

14.62 

1.184 

1.09 

15.91 

16.12 

1.192 

1.1 

17.72 

1.5 

1.75 

17.35 

1.344 

.16 

20. 

19.03 

1.367 

.17 

22.26 

1.75 

2 

20. 

1.485 

.22 

24.37 

22. 

1.52 

.23 

27.13 

2. 

2.25 

22.78 

1.624 

.28 

29.03 

25.03 

1.665 

.29 

32.31 

2.25 

2.5 

25.62 

1.756 

.33 

33.96 

28.12 

1.804 

.34 

37.78 

2.5 

2.75 

28.53 

1.883 

.38 

39.15 

31.28 

1.937 

.39 

43.54 

2.75 

3. 

31.5 

2.005 

.42 

44.61 

34.5 

2.065 

.44 

49.57 

3. 

3.25 

34.53 

2.121 

.46 

50.31 

37.78 

2.188 

.48 

55.88 

3.25 

3.5 

37.62 

2.236 

.5 

56.26 

41.12 

2.308 

.52 

62.46 

3.5 

3.75 

40.78 

2.346 

1.54 

62.47 

44.53 

2.422 

.56 

69.31 

3.75 

4. 

44. 

2.446 

1.57 

68.91 

48. 

2.534 

.59 

76.41 

4. 

4.25 

47.28 

2.555 

1.6 

75.59 

51.53 

2.642 

.63 

83.77 

4.25 

4.5 

50.62 

2.656 

1.63 

82.51 

55.12 

2.748 

.66 

91.38 

4.5 

5. 

57.5 

2.849 

1.69 

97.06 

62.5 

3.097 

.72 

107  .  36 

5. 

6. 

72. 

3.212 

1.79 

129.03 

78. 

3.48 

.82 

142.35 

6. 

BED  11  FEET. 

BED  12  FEET. 

Depth 

Depth 

in 

Feet. 

a 

r 

v/r 

a-v/r 

a 

r 

Vr 

a^/r 

in 

Feet. 

0.5 

5.625 

.464      .68 

3.8 

6.12 

.467 

.68 

4.2 

0.5 

0.75 

8.531 

.673 

.81 

7. 

9.28 

.679 

.82 

7.6 

0.75 

1. 

11.5 

.869 

.93 

10.7 

12.5 

.878 

.94 

11.7 

1. 

1.25 

14.531 

1.053 

1.02 

14.9 

15.78 

1.067 

.03 

16.3 

1.25 

1.5 

17.625 

1.228 

1.11 

19.5 

19.1 

.244 

.12 

21.3 

1.5 

1.75 

20.78 

1.393 

1.18 

24.5 

22.5 

.414 

.19 

26.8 

1.75 

2. 

24. 

1.551 

1.25 

29.9 

26. 

.578 

.26 

32.7 

2. 

2,25 

27.281 

1.702 

1.31 

35.6 

29.5 

.732 

.32 

38.9 

2.25 

2.5 

30.625 

1.846 

1.36 

41.6 

33.1 

.882 

.37 

45.5 

2.5 

2.75 

34.031 

1.984 

1.41 

47.9 

36.8 

2.028 

.42 

52.4 

2.75 

3. 

37.5 

2.118 

1.46 

54.6 

40.5 

2.165 

.47 

59.6 

3. 

3.25 

41.03 

2.246 

1.5 

61.5 

44.3 

2.299 

.52 

67.1 

3.25 

3.5 

44.63 

2.372 

1.54 

68.7 

48.1 

2.427 

.56 

75. 

3.5 

3.75 

48.3 

2.492 

1.58 

76.2 

52. 

2.551 

.6 

83.1 

3.75 

4. 

52. 

2.607 

1.61 

84. 

56. 

2.674 

1.64 

91.6 

4. 

4.5 

59.6 

2.83 

1.68 

100.3 

64.1 

2.905 

1.7 

109.3 

4.5 

5. 

67.5 

2.021 

1.74 

117.8 

72.5 

3.128 

1.77 

128.2 

5. 

5.5 

75.6 

3.245 

1.8 

136.2 

81.1 

3.338 

1.83 

148.2 

5.5 

6. 

84. 

3.444 

1.85 

155.8 

90. 

3.541 

1.88 

169.4 

6. 

FLOW    OF    WATER    IN 


TABLE   9. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  \  to  1.  Values 
of  the  factors  a  —  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 
feet,  and  also  ^/r  and  a^/r  for  use  in  the  formulae 

v  =  c  X  Vr   X  v'a"  and  Q  =  c  X  a\/r  X  \/$ 


BED  13  FEET. 


Depth 
in 
Feet. 

a 

r 

VV 

a\/r 

0.5 

6.62 

.469 

.68 

4.5 

0.75 

10. 

6.682 

.82 

8.5 

1. 

13.5 

.886 

.94 

12. 

1.25 

17. 

1.076 

.03 

17.7 

1.5 

20.6 

1.26 

.12 

23.2 

1.75 

24.3 

1.437 

.2 

29.2 

2. 

28. 

1.603 

.27 

35.4 

2.25 

31.8 

1.764 

.33 

42.2 

2.5 

35.6 

1.915 

.38 

49.3 

2.75 

39.5 

2.063 

.44 

56.8 

3. 

43.5 

2.207 

.49 

64.6 

3.25 

47.5 

2.344 

.53 

72.8 

3.5 

51.6 

2.479 

.57 

81.3 

3.75 

55.8 

2.609 

.61 

90.1 

4. 

60. 

2.734 

.65 

99.2 

4.5 

68.6 

2.975 

.73 

118.4 

5. 

77.5 

3.189 

.79 

138.7 

5.5 

86.6 

3.423 

1.85 

160.3 

6. 

96. 

3.634 

1.91 

183. 

BED  14  FEET. 


a 

r 

v^ 

a\/r 

Depth 
in 
Feet. 

7.12 

All 

.69 

4.9 

0.5 

10.8 

.689 

.83 

8.9 

0.75 

14.5 

.893 

.94 

13.7 

1. 

18.3 

.09 

1.05 

19.1 

1.25 

22.1 

.273 

1.13 

25.0 

1.5 

26. 

.451 

.2 

31.4 

1.75 

30. 

.624 

.27 

38.2 

2 

34. 

.787 

.33 

45.5 

2.25 

38.1 

.945 

.39 

53.2 

2.5 

42.3 

2.099 

.45 

61.2 

2.75 

46.5 

2.246 

.5 

69.7 

3. 

50.8 

2.388 

.55 

78.5 

3.25 

55.1 

2.526 

.59 

87.6 

3.5 

59.5 

2.658 

.63 

97.1 

3.75 

64. 

2.79 

.67 

106. 

4. 

73.1 

3.038 

.74 

127.5 

4.5 

82.5 

3.276 

.81 

149.3 

5. 

92.1 

3.502 

.87 

172.4 

5.5 

102. 

3.72 

.93 

196.7 

6. 

BED  15  FEET. 


BED  16  FEET. 


Depth 
in 

Feet. 

a 

f 

Vr 

a\/r 

a 

r 

Vr 

a\/r 

Depth 
in 

Feet. 

0.5 

7.62 

.473 

.69 

5.2 

8.12 

.474 

.69 

5.6 

0.5 

0.75 

11.5 

.689 

.83 

9.6 

12.3 

.696 

.83 

10.2 

0.75 

1. 

15.5 

.899 

.95 

14.7 

16.5 

.905 

.95 

15.7 

1. 

1.25 

19.5 

1.096 

1.05 

20.5 

20.8 

.161 

.05 

21.8 

1.25 

1.5 

23.6 

1.289 

1.13 

26.8 

25.1 

.297 

.14 

28.6 

1.5 

1.75 

27.8 

1.47 

1.21 

33.7 

29.5 

.482 

.22 

37. 

1.75 

2. 

32. 

1.643 

1.28 

41. 

34. 

.661 

.29 

43.8 

2. 

2.25 

36.3 

1.812 

1.34 

49.2 

38.5 

.831 

.35 

52.6 

2.25 

2.5 

40.6 

1.972 

1.4 

57.1 

43.1 

.996 

.41 

60.9 

2.5 

2.75 

45. 

2.128 

1.46 

65.7 

47.8 

2.158 

.47 

70.2 

2.75 

3. 

49.5 

2.28 

1.51 

74.7 

52.5 

2.312 

.52 

79.8 

3. 

3.25 

54. 

2.425 

1.56 

84.2 

57.3 

2.463 

.57 

89.9 

3.25 

3.5 

58.6 

2.568 

1.6 

93.9 

62.1 

2.608 

.61 

100.3 

3.5 

3.75 

63.3 

2.707 

1.65 

104.1 

67. 

2.748 

.66 

111.1 

3.75 

4. 

68. 

2.84 

1.69 

114.6 

72. 

2.887 

.  7 

122.3 

4. 

4.5 

77.6 

3.096 

1.76 

136.3 

82.1 

3.15 

•  .78 

145.8 

4.5 

5. 

87.5 

3.342 

1.83 

160. 

92.5 

3.403 

.84 

170.6 

5. 

5.5 

97.6 

3.575 

1.89 

184.6 

103.1 

3.643 

.91 

196.9 

5.5 

6. 

108. 

3.801 

1.95 

210.5 

114. 

3.875 

.97 

224.4 

6. 

OPEN    AND    CLOSED    CHANNELS. 


77 


TABLE  9. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  -J  to  1.  Values 
of  the  factors  a  =  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 
feet,  and  also  A/?7  and  a^/r  for  use  in  the  formulae 

v  =  c  X  Vr  X  Vs  and  Q  =  c  X  a^/r  X  V* 


BED  17  FEET. 


BED  18  FEET. 


Depth 
in 

Feet. 

a 

r 

V~ 

a^/r 

a 

r 

x/r 

a\/r 

Depth 
in 
Feet. 

0.75 

13.031 

.696 

.84 

10.9 

13.8 

.701 

.84 

11.5 

0.75 

1. 

17.5 

.915 

.95 

16.7 

18.5 

.914 

.96 

17.7 

1. 

1.25 

22.031 

.113 

1.05 

23.2 

23.3 

1.125 

1.06 

24.6 

1.25 

1.5 

26.625 

.308 

1.14 

30.4 

28.1 

1.316 

1.15 

32.3 

1.5 

1.75 

31.281 

.496 

1.22 

38.3 

33. 

1.506 

1.23 

40.6 

1.75 

2. 

36. 

.677 

1.29 

46.6 

38. 

1.691 

1.3 

49.4 

2. 

2.25 

40.8 

.852 

1.36 

55.5 

43. 

1.867 

1.37 

58.8 

2.25 

2.5 

45.6 

2.019 

1.42 

64.8 

48.1 

2.039 

1.43 

68.7 

2.5 

2.75 

50.5 

2.182 

1.48 

74.7 

53.3 

2.207 

1.49 

79.1 

2.75 

3. 

55.5 

2.341 

1.53 

84.9 

58.5 

2.368 

1.54 

90. 

3. 

3.25 

60.5 

2.493 

1.58 

95.6 

63.8 

2.525 

1.59 

101.3 

3.25 

3.5 

65.6 

2.643 

1.63 

106.7 

69.1 

2.677 

1.64 

113.1 

3.5 

3.75 

70.8 

2.789 

1.67 

118.2 

74.5 

2.824 

1.68 

125.3 

3.75 

4. 

76. 

2.93 

1.71 

130.1 

80. 

2.969 

1.72 

137.9 

4. 

4.5 

86.6 

3.2 

1.79 

155. 

91.1 

3.246 

1.80 

164.2 

4.5 

5. 

97.5 

3.46 

1.86 

181.4 

102.5 

3.513 

1.87 

192.1 

5. 

5.5 

108.6 

3.707 

1.93 

209.2 

114.1 

3.766 

1.94 

221.5 

5.5 

6. 

120. 

3.945 

1.99 

238.3 

126. 

4.014 

2 

252.3 

6. 

7. 

143.5 

4.395 

2.09 

300. 

150.5 

4.472 

2^11 

318.3 

7. 

BED  19  FEET. 


BED  20  FEET. 


Depth 
iu 


0.5 

0.75 

1. 

1.25 

1.5 

1.75 

2. 

2.25 

2.5 

2.75 

3. 

3.25 

3.5 

3.75 

4. 

4.25 

4.5 

5. 

5.5 

6. 

7. 

8. 


a 

T 

v/r 

a\/r 

a 

r 

</? 

a\/r 

Depth 
in 
Feet. 

9.62 

.478 

.69 

6.7 

10.1 

.478 

.69 

7 

0.5 

14.5 

.701 

.84 

12.2 

15.3 

.706 

.84 

13 

0.75 

19.5 

.918 

.96 

18.7 

20.5 

.922 

.96 

20 

1. 

24.5 

1  .  124 

.06 

26. 

25.8 

1.132 

1.06 

27 

1.25 

29.6 

1  .  324 

.15 

34.1 

31.1 

1.332 

1.15 

36 

1.5 

34.8 

1.519 

.23 

42.9 

36.5 

1.527 

1.23 

45 

1.75 

40. 

1.704 

.31 

52  2 

42. 

1.716 

1.31 

55 

2. 

45.3 

1.885 

.37 

62.2 

47.5 

1.898 

1.38 

66 

2.25 

50.62 

2.059 

.43 

72.6 

52.6 

2.056 

1.44 

77 

2.5 

56. 

2.227 

.49 

83.6 

58.8 

2.249 

1.5 

88 

2.75 

61.5 

2.392 

.55 

95.1 

64.5 

2.415 

1.55 

100 

3. 

67. 

2.551 

.6 

107.1 

70.3 

2.578 

1.6 

113 

3.25 

72.6 

2.707 

.65 

119.5 

76.1 

2.736 

1.65 

126 

3.5 

78.3 

2.859 

.7 

132.4 

82. 

2:889 

1.7 

139 

3.75 

84. 

3.006 

.74 

145.6 

88. 

3.04 

1.74 

153 

4. 

89.8 

3.151 

.78 

159.3 

94. 

3.186 

1.79 

168 

4.25 

95.6 

3.29 

.81 

173.5 

100.1 

3.36 

1.83 

183 

4.5 

107.5 

3.629 

.89 

202.9 

112.5 

3.608 

1.9 

214 

5. 

119.6 

3.963 

.96 

233.9 

125.1 

3.873 

1.97 

246 

5.5 

132. 

4.294 

2.02 

266.4 

138. 

4.13 

2.03 

280 

6. 

157.5 

4.545 

2.13 

335.8 

164.5 

4.614 

2.15 

353 

7. 

184. 

4.988 

2.23 

410.9 

192. 

5.068 

2.25 

432 

8. 

78 


FLOW    OF    WATER    IN 


TABLE  9. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  -J  to  1.  Values 
of  the  factors  a  =  area  in  sqiiare  feet,  and  r  =  hydraulic  mean  depth  in 
feet,  and  also  ^/r  and  a\/r  for  use  in  the  formula 

v  =  c  X  V'r  X  V^  and  Q  ~  c  X  a-^/r  X  -\A 


JJ.CiJJ 

^tj      JJ  .C 

J-/JL.J- 

'       9J\J        A'    JC. 

Depth 

Depth 

in 

Feet. 

a 

r 

V'r 

a\/r 

a 

r 

V~ 

a\/r 

in 

Feet. 

0.5 

12.12 

.464 

.7 

9 

15.1 

.485 

.7 

11 

0.5 

0.75 

19.03 

.713 

.85 

16 

22.8 

.72 

.85 

19 

0.75 

1. 

25.5 

.936 

.97 

25 

30.5 

.946 

.97 

30 

1. 

1.25 

32.03 

1.152 

1.08 

34 

38.3 

.168 

.08 

41 

1.25 

1.5 

38.62 

1  .  362 

1.17 

45 

46.1 

.382 

.18 

54 

1.5 

1.75 

45.28 

1.566 

1.25 

57 

54. 

.592 

.26 

68 

1.75 

2. 

52. 

1.764 

1.33 

69     1 

62. 

.798 

.34 

83 

2. 

2.25 

58.78 

1.957 

.4 

82     i 

70. 

.998 

.41 

91 

2.25 

2.5 

65.62 

2.145 

.46 

96 

78.1 

2.194 

.48 

116 

2.5 

2.75 

72.53 

2.329 

.52 

111 

86.3 

2.387 

.54 

133 

2.75 

3. 

79.5 

2.507 

.58 

126 

94.5 

2.574 

.6 

152 

3. 

3.25 

86.53 

2.681 

.64 

142 

102.8 

2.758 

.66 

171 

3.25 

3.5 

93.62 

2.853 

.69 

158 

111.1 

2.938 

.71 

190 

3.5 

3.75 

100.78 

3.019 

.74 

175 

119.5 

3.113 

.76 

211 

3.75 

4. 

108. 

3.182 

.78 

193 

128. 

3.287 

.81 

232 

4. 

4.25 

115.28 

3.341 

.83 

211 

136.5 

3.455 

.86 

254 

4.25 

4.5 

122.62 

3.497 

.87 

229 

145.1 

3.622 

.9 

276 

4.5 

4.75 

130.03 

3.654 

.91 

248 

153.8 

3.786 

1.95 

299 

4.75 

5. 

137.5 

3.8 

.95 

268 

162.5 

3.946 

1.99 

323 

5. 

5.25 

145.03 

3.948 

.99 

288 

171.3 

4.104 

2.03 

347 

5.25 

5.5 

152.62 

4.092 

2.02 

309 

180.1 

4.258 

2.06 

372 

5.5 

5.75 

160.28 

4.234 

2.06 

330 

189. 

4.41 

2.1 

397 

5.75 

6. 

168. 

4.373 

2.09 

351 

198. 

4.561 

2.14 

423 

6. 

6.25 

175.78 

4.510 

2.12 

373 

207. 

4.707 

2.17 

449 

6.25 

6.5 

183.62 

4.645 

2.15 

396 

216.1 

4.852 

2.2 

476 

6.5 

6.75 

191.53 

4.777 

2.19 

419 

225.2 

4.994 

2.24 

504 

6.75 

7. 

199.5 

4.908 

2.22 

442 

234.5 

5.137 

2.27 

531 

7. 

7.25 

207.53 

5.036 

2^25 

466 

243.8 

5.275 

2.3 

560 

7.25 

7.5 

215.62 

5.162 

2.27 

490 

253.1 

5.412 

2.33 

589 

7.5 

7.75 

223.78 

5.287 

2.30 

515 

262.5 

5.546 

2.36 

618 

7.75 

8. 

232. 

5.409 

2.33 

540 

272. 

5.68 

2.38 

648 

8. 

8.25 

240.28 

5.53 

2.36 

565 

281.5 

5.81 

2.41 

679 

8.25 

8.5 

248.62 

5.65 

2.38 

591 

291.1 

5.94 

2.44 

710 

8.5 

8.75 

247.03 

5.678 

2.4 

617 

300.8 

6.069 

2.47 

741 

8.75 

9. 

235.5 

5.844 

2.43 

644 

310.5 

6.195 

2.49 

773 

9. 

OPEN    AND    CLOSED    CHANNELS. 


79 


TABLE  9. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  J  to  1.  Values 
of  the  factors  a  =  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 
feet,  and  also  v/r  and  a\/r  for  use  in  the  formulae 

v  =  c  X  Vr   X  V~s  and  Q  =  c  X  aVr  X  \A~ 


BED  35  FEET. 

BED  40  FEET. 

Depth 
in 
Feet. 

a 

r 

Vr 

a\/r 

a 

r 

\/r     i    a^/r 

Depth 
in 

Feet. 

0.75 

26.53      .723 

.85 

23 

40.37 

.727      .85 

26 

0.75 

1. 

35  .  25      .  947 

.98 

35 

40.50 

.959 

.98 

40 

1. 

1.25 

44.53 

1.178 

1.09 

48 

50.78 

1.187 

.09 

55 

1.25 

1.5 

53.62 

1.398 

1.18 

63 

61.02 

1.408 

.19 

73 

1.5 

1.75 

62.78 

1.613 

1.27 

80 

71.58 

1.630 

.28 

91 

1.75 

2. 

72.00 

1.824 

1.35 

97 

82. 

1.844 

.36 

111 

2. 

2.25 

81.28 

2.030 

1.42 

116 

92.53 

2.055 

.43 

133 

2.25 

2.5 

90.62 

2.233 

1.49 

135 

103.2 

2.264 

.50 

155 

2.5 

2.75 

100.03 

2.431 

1.56 

156 

113.8 

2.466 

.57 

179 

2.75 

3. 

109  .  50 

2.625 

1.62 

177 

124.5 

2.665      .63 

203 

3. 

3.25 

119.03 

2.816 

1.68 

200 

135.3 

2.862 

.69 

229 

3.25 

3.5 

128.62 

3.004 

1.73 

223 

146.1 

3.055 

.75 

255 

3.5 

3.75 

138.28 

3.187 

1.79 

247 

157. 

3.245 

.80 

283 

3.75 

4. 

148.00 

3.368 

1.84 

272 

168. 

3.433      .85 

311 

4. 

4.25 

157.78 

3.545 

1.89 

297 

179. 

3.617    1.90 

340 

4.25 

4.5 

167.62 

3.720 

1.93 

323 

190.1 

3.797    1.95 

371 

4.5 

4.75 

177.53 

3.891 

1.97 

350 

201.3 

3.977    2.00 

401 

4.75 

5. 

187.50 

4.060 

2.01 

378 

212.5 

4.152    2.04 

433 

5. 

5.25 

197.53 

4.226 

2.05 

406 

223.8 

4.326    2.08 

465 

5.25 

5.5 

207.62 

4.390 

2.10 

435 

235.1 

4.495    2.12 

499 

5.5 

5.75 

217.78 

4.551 

2.14 

465 

246.5 

4.664    2.16 

532 

5.75 

6. 

228.00 

4.709 

2.17 

495 

258.0 

4.826    2.20 

567 

6. 

6.25 

238.28 

4.865 

2.21 

526 

269.5 

4.993    2.24 

602 

6.25 

6.5 

248  .  62 

5.019 

2.24 

557 

281.1 

5.155    2.27 

638 

6.5 

6.75 

259.03 

5.171 

2.28 

589 

292.8 

5.315    2.31 

675 

6.75 

7. 

269.50 

5.321 

2.31 

622 

304.5 

5.472    2.34 

712 

7. 

7.25 

280.03 

5.468 

2.34 

655 

316.3 

5.627    2.37 

750 

7.25 

7.5 

290.62 

5.614 

2.37 

689 

328.1 

5.779   2.40 

789 

7.5 

7.75 

301.28 

5.756 

2.40 

723 

340. 

5.931;  2.44 

828 

7.75 

8. 

312.00 

5.900 

2.43 

758 

352. 

6.081    2.47 

868 

8. 

8.25 

322.78 

6.039 

2.46 

793 

364. 

6.228   2.50 

908 

8.25 

8.5 

333.62 

6.177 

2.49 

829 

376.1 

6.376    2.52 

950 

8.5 

8.75 

344.53 

6.314 

2.52 

866 

388.3 

6.519   2.55 

991 

8.75 

9. 

355.50 

6.449 

2.54 

903 

400.5 

6.661 

2.58 

1034 

9. 

9.5 

377.62 

6.714 

2.59 

979 

425.1 

6.941    2.63 

1120 

9.5 

10. 

400.00 

6.974 

2.64 

1056 

450. 

7.216 

2.69 

1209 

10. 

80 


FLOW    OF    WATER    IN 


TABLE  9. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  £to  1.  Values 
of  the  factors  a  =  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 
feet,  and  also  v">  and  a*/r  for  use  in  the  formulae 

v  =  c  X  \/r  X  <\/«~  and  Q  =  c  X  o\/r   X  \/?~ 


BED  45  FEET. 


BED  50  FEET. 


Depth 
in 
Feet. 

a 

r 

Vr 

a\/r 

a 

r 

Vr 

(i\/r 

Depth 
in 
Feet. 

0.50 

22.62 

.490 

.70 

16 

25.37! 

.490 

.700 

17.8 

0.50 

0.75 

34.03 

.729 

.85 

29 

38.34 

.728 

.853 

32.7 

0.75 

1. 

45.50 

.953 

.98 

45 

51.50 

.961 

.980 

50.5 

1. 

1.25 

57.03 

1.193 

.09 

62 

64.84 

1.190 

1.091 

70.7 

1.25 

1.50 

68.62 

1.419 

.19 

82 

76.12 

1.427 

1.19 

91. 

1.50 

1.75 

80.28 

1.641 

.28 

103 

89.03 

1.651 

1.28 

114. 

1.75 

2. 

92.00 

1.860 

.36 

125 

102. 

1.873 

.37 

140. 

2. 

2.25 

103.78 

2.074 

.44 

150 

115. 

2.090 

.45 

166. 

2.25 

2.5 

115.62 

2.285 

.51 

175 

128.1 

2.305 

.52 

194. 

2.5 

2.75 

127.53 

2.493 

.58 

201 

141.3 

2.517 

.59 

224. 

2.75 

3. 

139.5 

2.698 

.64 

229 

154.5 

2.723 

.65 

255. 

3. 

3.25 

151.53 

2.899 

.70 

258 

167.8 

2.930 

.71 

287. 

3.25 

3.5 

163.62 

3.098 

.76 

288 

181.1 

3.132 

.77 

320. 

3.5 

3.75 

175.78 

3.293 

.82 

319 

194.5 

3.331 

.83 

355. 

3.75 

4. 

188. 

3.485 

.87 

351 

208. 

3.529 

.88 

391. 

4. 

4.25 

200.28 

3.675 

1.92 

384 

221.5 

3.722 

1.93 

427. 

4.2o 

4.5 

212.62 

3.861 

1.96 

418 

235.1 

3.914 

1.98 

465. 

45 

4.75 

225.03 

4.046 

2.01 

453 

248.8 

4.104 

2.03 

504. 

4.75 

5. 

237.50 

4.228 

2.06 

488 

262.5 

4.291 

2.07 

544. 

5. 

5.25 

250.03 

4.407 

2.10 

525 

276.3 

4.475 

2.12 

585. 

5.25 

5.5 

262.62 

4.583 

2.14 

562 

290.1 

4.657 

2.16 

626. 

5.5 

5.75 

275.28 

4.758 

2.18 

600 

304. 

4.836 

2.20 

669. 

5.  7o 

6. 

288. 

4.930 

2.22 

639 

318. 

5.015 

2.24 

712. 

6. 

6.25 

300.78 

5.100 

2.26 

679 

332. 

5.190 

2.28 

756. 

6.25 

6.5 

313.62 

5.268 

2.30 

720 

346.1 

5.360 

2.32 

802. 

6.5 

6.75 

326.53 

5.434 

2.34 

761 

360.3 

5.535 

2.36 

848. 

6.75 

7. 

339.50 

5.598 

2.37 

803 

374.5 

5.704 

2.39 

894. 

7. 

7.25 

352.53 

5.759 

2.40 

725 

388.8 

5.872 

2.43 

942. 

7.25 

7.5 

365.62 

5.9H 

2.43 

890 

403.1 

6.037 

2.46 

990. 

7.5 

7.75 

378.78 

6.077 

2.47 

934 

417.5 

6.156 

2.49 

1040. 

7.75 

8. 

392. 

6.233 

2.50 

979 

432. 

6.363 

2.52 

1090. 

8. 

8.25 

405.28 

6.388 

2.53 

1024 

446.5 

6.523 

2.55 

1141. 

8.25 

8.5 

418.62 

6.540 

2.56 

1071 

461.1 

6.682 

2.58 

1192. 

8.5 

8.75 

432.03 

6.691 

2.59 

1118 

475.8 

6.840 

2.61 

1244. 

8.75 

9. 

445.5 

6.842 

2.62 

1165 

490.5 

6.995 

2.64 

1295. 

9. 

9.5 

472.62 

7.135 

2.67 

1262 

520.1 

7.300 

2.70 

1405. 

9.5 

10. 

500. 

7.423 

2.72 

1362 

550. 

7.601 

2.76 

1516. 

10. 

10.5 

527.62 

7.705 

2.78 

1465 

580.1 

7.809 

2.81 

1630. 

10.5 

11. 

555.50 

7.982 

2.83 

1569 

610.5 

8.184 

2.86 

1746. 

11, 

OPEN    AND    CLOSED    CHANNELS. 


81 


TABLE  9. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  J  to  1.  Values 
of  the  factors  a  =  area  in  square  feet,  and  r  —  hydraulic  mean  depth  in 
feet,  and  also  ^/r  and  a\/r  for  use  in  the  formulae 

v  =  c  X  Vr   X  \/8  and  Q  =  c  X  a^/r  X  \/a~ 

BED  60  FEET. 


Depth  iu  Feet. 

a 

r 

Vr 

a^/r 

1. 

60.50 

.972 

.99 

60 

1.5 

91.12 

1.438 

1.20 

109 

1.75 

106.53 

1.667 

1.29 

137 

2. 

122. 

1.892 

1.38 

168 

2.25 

137.53 

2.115 

1.46 

200 

2.5 

153.12 

2.334 

1.53 

234 

2.75 

168.78 

2.552 

1.60 

270 

3. 

184.50 

2.781 

1.66 

307 

3.25 

200.28 

2.977 

1.73 

346 

3-5 

216.12 

3.188 

1.79 

386 

3.75 

232.03 

3.378 

1.84 

427 

4. 

248. 

3.597 

1.90 

470 

4.25 

264  .  03 

3.799 

1.96 

515 

4.5 

280.12 

3.998 

2. 

560 

4.75 

296.28 

4.195 

2.05 

607 

5. 

312.50 

4.390 

2.10 

655 

5.25 

328.78 

4.583 

2.15 

704 

5.5 

345.12 

4.774 

2.18 

754 

5  75       361.53 

4.962 

2.23 

805 

6. 

378. 

5.149 

2.27 

858 

6.25       394.53 

5.333 

2.31 

911 

6.5 

411.12 

5.516 

2.35 

965 

6.75 

427  .  78 

5.697 

2.39 

1021 

7. 

444.50 

5.876 

2  42 

1077 

7.25 

461.28 

6.053 

2^46 

1135 

7.5 

478.12 

6.228 

2.50 

1193 

7.75 

495.03 

6.363 

2.53 

1252 

8. 

512. 

6.574 

2.56 

1313 

8.25 

529.03 

6.744 

2.59 

1374 

8.5 

546.12 

9.912 

2.63 

1436 

8.75 

563.28 

7.079 

2.66 

1499 

9. 

580.50 

7.245 

2.69 

1563 

9.5 

615.12 

7.571 

2.75 

1693 

10. 

650. 

7.892 

2.81 

1826 

10.5 

685.12 

8.271 

2.86 

1963 

11. 

720.50 

8.517 

2.92 

2103 

82 


FLOW    OF    WATER    IN 


TABLE    10. 


Sectional  areas,  in  square  feet,  of  trapezoidal  channels,  with  side  slopes 
of  Jto  1. 

Depth 
in 
Feet. 

BED  WIDTH 

70  feet 

80  feet. 

90  feet. 

100  feet. 

120  feet. 

1. 

70.50 

80.50 

90.50              100.50 

120.50 

1.5 

106.12 

121.12 

136.12 

151.12 

181.12 

2. 

142. 

162.                  182. 

202. 

242. 

2.25 

160.03 

182.53 

205  .  03 

227.53 

272.r,:; 

2.5 

178.12 

203.12 

228.12 

253.12 

303.1-2 

2.75 

196.28              224.78 

252.28 

278.78 

333.78 

3. 

214.50              244.50 

274.50 

304.50 

364.50 

3.25 

232.78              265.28 

297.78 

330.28 

395.28 

3.5 

251.12              286.12 

321.12 

356.12 

426.12 

3.75 

269.53              307.03              344.53 

382.03 

457.03 

4. 

288.                  328.                  368. 

408. 

488. 

4.25 

306.53              349.03             391.53 

43*.  03 

519.03 

4.5 

325.12              370.12             415.12 

460.12 

550.12 

4.75 

343.78 

391.28             438.78 

486.28 

581.28 

5. 

362.50 

412.50             462.50 

512.50 

612.50 

5.25 

381.28 

433.78             486.28 

538.78 

663.78 

5.5 

400.12 

455.12 

510.12 

565.12 

675.12 

5.75 

419.03 

476.53 

534.03 

591.53 

706.53 

6. 

438. 

498.                  558. 

618. 

738. 

6.25 

457.03 

519.53 

582.03 

644.53 

769.53 

6.5 

476.12 

541  .  12 

606.12 

671.12 

801.12 

6.75 

495.28 

562.78 

630.28 

697.78 

832.78 

7. 

514.50 

584.50 

654.50 

724.50 

864  .  50 

7.25 

533.78 

606.28 

678.78 

751.28 

896  .  28 

7.5 

553.12 

628  .  12 

703.12 

778.12 

928.12 

7.75 

572.53 

650.03 

727.53 

805.03 

960.03 

8. 

592. 

672. 

752. 

832. 

992. 

8.25 

611.53 

694.03 

776.53 

859.03 

1024.03 

8.5 

631.12 

716.12 

701  .  12 

886.12 

1056.12 

8.75 

650.78 

738.28 

825.78 

913.28 

1088.28 

9. 

670.50 

760.50 

850.50 

940.50 

1120.50 

9.25 

690.28 

782.78 

875.28 

967.78 

1152.78 

9.5 

710.12 

805.12 

900.12 

995.12 

1185.12 

9.75 

730.03 

827.53 

925.03 

1022.53 

1117.53 

10. 

750. 

850. 

950. 

1050. 

1250. 

10.5 

790.12 

895.12 

1000.12 

1105.12 

1315.12 

11. 

830.50 

940.50 

1050.50 

1160.50 

1380.50 

11.5 

871.12 

986.12 

1101.12 

1216.12 

1446.12 

12. 

912. 

1032. 

1152. 

1272. 

1512. 

OPEN    AND    CLOSED    CHANNELS. 


83 


TABLE    10. 

Sectional  areas,  in  square  feet,  of  trapezoidal  channels,  with  side  slopes 
of  }  to  1. 


Depth 


BED  WIDTH 


ill 

Feet. 

140  feet. 

160  feet. 

180  feet. 

200  feet. 

220  feet. 

1.        140.50 

160.50 

180.50 

200.50 

220.50 

2.        282. 

322. 

362. 

402. 

442. 

2.5       353.12 

403.12 

453.12 

503.  10 

553.12 

2.75      388.78 

443.78 

498.78 

553.78 

608.78 

3. 

424.50 

484.50 

544.50 

604.50 

664.50 

3.25 

460.28 

525  .  28 

590.28 

655.28 

720.28 

3.5 

496.12 

566.12 

636.12 

706.12 

776.12 

3.75 

532.03 

607.03 

682.03 

757.03 

832.03 

4. 

568. 

648. 

728.  . 

808. 

888.80 

4.25 

604.03 

689.03 

774.03 

859.03 

944.03 

4.5 

640.12 

730.12 

820.12 

910.12 

1000.12 

4.75 

676.28 

771.28 

866.28 

961.28 

1056.28 

5. 

712.50 

812.50 

912.50 

1012.50 

1112.50 

5.25 

748.78 

853.78 

958.78 

1063.78 

1168.78 

5.5 

785.12 

895.12 

1005.12 

1115.12 

1225.12 

5.75 

821.53 

936.53 

1051.53 

1166.53 

1281.53 

6. 

858. 

978. 

1098. 

1218. 

1338. 

6.25 

894.53 

1019.53 

1144.53 

1269  53 

1394.53 

6.5 

931.12 

1061.12 

1191.12 

1321.12 

1451.12 

6.75 

967.78 

1102.78 

1237.78 

1372.78 

1507.78 

7. 

1004.50 

1144.50 

1284.50 

1424.50 

1564.50 

7.25 

1041.28 

1186.28 

1331.28 

1476.28 

1621.28 

7.5 

1078.12 

1228.12 

1378.12 

1528.12 

1678.12 

7.75 

1115.03 

1270.03 

1425.03 

1580.03 

1735.03 

8. 

1152. 

1312. 

1472. 

1632. 

1792. 

8.25 

1189.03 

1354.03 

1519.03 

1684.03 

1849.03 

8.5 

1226.12 

1396.12 

1566.12 

1736.12 

1906.12 

8.75 

1263.28 

1438.28 

1613.28 

1788.28 

1963.28 

9. 

1300.50 

1480.50 

1660.50 

1840.50 

2020.50 

9.25 

1337.78 

1522.78 

1707.78 

1892.78 

2077.78 

9.5 

1375.12 

1565.12 

1755.12 

1945.12 

2135.12 

9.75 

1412.53 

1607.53 

1802.53 

1997.53 

2192.53 

10. 

1450. 

1650. 

1850. 

2050. 

2250. 

10.5 

1525.12 

1735.12 

1945.12 

2155.12 

2365.12 

11. 

1600.50 

1820.50 

2040.50 

2260.50 

2480.50 

11.5 

1676.12 

1906.12 

2136.12 

2366.12 

2596.12 

12. 

1752. 

1992. 

2232. 

2472. 

2712. 

13. 

1904.50 

2164.50 

2424.50 

2684.50 

2944.50 

14. 

2058. 

2338. 

2618. 

2898. 

3178. 

15. 

2212.50 

2512.50 

2812.50 

3112.50     3412.50 

16. 

2368. 

2688. 

3008. 

3328.       3648. 

84 


FLOW    OF    WATER    IN 


TABLE    10. 

Sectional  areas,  in  square  feet,  of  trapezoidal  channels,  with  side  slopes 
of  ito  1. 


Depth 


BED  WIDTH 


111 

Feet. 

240  feet. 

260  feet. 

280  feet. 

300  feet. 

1. 

240.50 

260.50 

280.50 

300.50 

2. 

482. 

522. 

562. 

602. 

2.5 

603.12 

653.12 

703.12 

753.12 

2.75 

663.78 

718.78 

773.78 

828.78 

3. 

724.50 

784.50 

844.50 

904  .  50 

3.25 

785.28 

850.28 

915.28 

980.28 

3.5 

846.12 

916.12 

986.12 

1056.12 

3.75 

907.03 

982.03 

1057.03 

1132.03 

4. 

968. 

1048. 

1128. 

1208. 

4.25 

1029.03 

1114.03 

1199.03 

1284.03 

4.5 

1090.12 

1180.12 

1270.12 

1360.12 

4.75 

1151.28 

1246.28 

1341.28 

1436.28 

5. 

1212.50 

13  J  2.  50 

1412.50 

1512.50 

5.25 

1273.78 

1378.78 

1483.78 

1588.78 

5.5 

1335.12 

1445.12 

1555.12 

1665.12 

5.75 

1396.53 

1511.53 

1626.53 

1741.53 

6. 

1458. 

1578. 

1698. 

1818. 

6.25 

1519.53 

1644.53 

1769.53 

1894.53 

6.5 

1581.12 

1711.12 

1841.12 

1971.12 

6.75 

1642.78 

1777.78 

1912.78 

2047.78 

7. 

1704.50 

1844.50 

1984.50 

2124.50 

7.25 

1766.28 

1911.28 

2056.28 

2201.28 

7.5 

1828.12 

1978.12 

2128.12 

2278.12 

7.75 

1890.03 

2045.03 

2200.03 

2355  .  03 

8. 

1952. 

2112. 

2272. 

2432. 

8.25 

2014.03 

2179.03 

2344.03 

2509.03 

8.5 

2076.12 

2246.12 

2416.12 

2586.12 

8.75 

2138.28 

2313.28 

2488.28 

2663.28 

9. 

2200.50 

2380.50 

2560.50 

2740.50 

9.25 

2262.78 

2447.78 

2632.78 

2817.78 

9.5 

2325.12 

2515.12 

2705.12 

2895.12 

9.75 

2387.53 

2582.53 

2777.53 

2972.53 

10. 

2450. 

2650. 

2850. 

3050. 

10.5 

2575.12 

2785.12 

2995.12 

3205.12 

11. 

2700.50 

2920.50 

3140.50 

3360.50 

11.5 

2826.12 

3156.12 

3486.12 

3816.12 

12. 

2952. 

3192. 

3432. 

3672. 

13. 

3204.50 

3464.50 

3724.50 

3984.50 

14. 

3458. 

3738. 

4018. 

4298. 

15. 

3712.50 

4012.50 

4312.50 

4412.50 

16. 

3968. 

4288. 

4608. 

4928. 

OPEN    AND    CLOSED    CHANNELS. 


85 


TABLE  11. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1|  to  1.  Values 
of  the  factors  a  —  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 
feet,  and  also  \/r  and  a\/r  for  use  in  the  formulae 

v  =  c  X  -\/r~  X  -s/s"  and  also  Q  =  c  X  a\/r  X  \A' 


BED  1  FOOT. 

BED  2  FEET. 

Depth 

Depth 

in 
Feet. 

a 

r 

Vr 

a\/r 

a 

r 

\/r 

a\/r 

in 
Feet. 

0.5 

.87 

.312 

.56 

.49 

1.375 

.362 

.60 

.83 

0.5 

0.75 

1.59 

.452 

.65 

1.04 

2.344 

.499      .71 

1.66 

0.75 

1. 

2.5 

.542 

.74 

1.84 

3.5 

.624      .79 

2.76 

1. 

1.25 

3.59 

.652 

.81 

2.89 

4.844 

.744 

.86 

4.17 

1.25 

1.5 

4.87 

.761|     .87 

4.24 

!     6.37 

.860 

.93 

5.93 

1.5 

1.75 

6.34 

.868      .93 

5.9 

8.09 

.974 

.99 

8. 

1.75 

2. 

8. 

.974 

.99 

7.9 

10. 

1.086 

1.04 

10.4 

2. 

2.25 

9.84 

1.081 

1.04 

10.2 

12.09 

1.196 

1.09 

13.2 

2.25 

2.5 

11.87 

1.186 

1.09 

12.9 

14.37 

1.294 

1.14 

16.4 

2.5 

2.75 

14.09 

1.280 

1.14 

16.1 

16.84 

1.414 

1.19 

20. 

2.75 

3. 

J6.5 

1.397 

1.18 

19.5 

19.50 

1.521 

1.23 

24. 

3. 

3.25 

22.34 

1.629 

1.28 

28.5 

3.25 

3.5 

25.37 

1.736 

1.32 

33.4 

3.5 

3.75 

28.6 

1.842 

1.36 

38.8 

3.75 

4. 

32. 

1.949 

1.39 

44.4 

4. 

BED  3  FEET. 

BED  4  FEET. 

Depth 
iu 
Feet. 

a 

r 

vT 

a\/r 

a 

i 
r      !    vT" 

a^/r 

Depth 
in 
Feet. 

0.5 

1.875 

.499 

.63 

1.17 

2.37 

.409      .64        1.51 

0.5 

0.75 

3.094 

.543 

.73 

2.29 

3.84 

.574      .76 

2.92 

0.75 

1. 

4.50 

.681 

.83 

3.71 

5.5 

.723      .85       4.67 

1. 

1.25 

6.09 

.811 

.90 

5.48 

7.34 

.863i     .93 

6.83 

1.25 

1.5 

7.87 

.935 

.97 

7.62 

9.37 

.996 

9.38 

1.5 

1.75 

9.84 

1.057 

1.03 

10.1 

11.59 

1.125 

.06 

12.3 

1.75 

2. 

12. 

1.175 

1.08 

13. 

14. 

1.248 

.12 

15.7 

2. 

2.25 

14.34 

1.291 

1.14 

16.4 

16.59 

1.370 

.17 

19.4 

2.25 

2.5 

16.87 

1.405 

.19 

20.1 

19.37 

1.489 

.22 

23.6 

2.5 

2.75 

19.59 

1.518 

.23 

24.1 

22.34 

1.607 

.27 

28.4 

2.75 

3. 

22.50 

1.628 

.28 

28.8 

25.50 

1.721 

.31 

33.4 

3. 

3.25 

25.60 

1.739 

.32 

33.8 

28.84 

1.835 

.36 

39.2 

3.25 

3.5 

28.87 

1.848 

.36 

39.3 

32.37 

1.947 

.40 

45.3 

3.5 

3.75 

32.34 

1.958 

.40 

45.3 

36.09 

2.060 

.44 

52. 

3.75 

4. 

36. 

2.067 

.44 

51.8 

40. 

2.171 

.47 

59. 

4. 

4.25 

39.84 

2.175 

1.48 

59. 

44.09 

2.282 

1.51 

66.6 

4.25 

4.5 

43.87 

2.283 

1.51 

66.3 

48.37 

2.392 

1.55 

75. 

4.5 

5. 

52.5 

2.497 

1.58 

83. 

57.50 

2.610 

1.62 

92.9 

5. 

86 


FLOW    OF    WATER    IN 


TABLE   11. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1 J  to  1.  Values 
of  the  factors  a  =  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in 
feet,  and  also  */r  and  a\/r  for  use  in  the  formulae 

v  -.=  c  X  \/r  X  \/s  and  Q  =  c  X  a^/r  X  V* 


BED  5  FEET. 

BED  6  FKET. 

Depth 

Depth 

in 

Feet. 

a 

r 

VT 

a\/r 

a 

r 

Vr 

u\/r 

in 
Feet. 

0.5 

2.875 

.423 

.64 

1.87 

3.37 

.433 

.66 

2.23 

0.5 

0.75 

4.59 

.597 

.77 

3.54 

5.34 

.614 

.78 

4.17 

0.75 

1. 

6.5 

.755 

.87 

5.64 

7.5 

.780 

.89 

6.62 

1  . 

1.25 

8.59 

.904 

.95 

8.17 

9.84 

.937 

.97 

9.55 

1.25 

1.5 

10.87 

1.045 

1.02 

11.09 

12.37 

1.084 

1.04 

12.9 

1.5 

1.75 

13.34 

1.179 

1.09 

14.54 

15.09 

1.226 

1.11 

16.8 

1.75 

2. 

16. 

1.310 

1.15 

18.24 

18. 

1.362 

.17 

21. 

2. 

2.25 

18.84 

1.437 

1.20 

22.61 

21.09 

1.495 

.23 

26. 

2.25 

2.5 

21.87 

1.560 

1.25 

27  .  33 

24.37 

1.623 

.28 

31.2 

2.5 

2.75 

25.09 

1.683 

1.30 

32.62 

27.84 

1.750 

.33 

37] 

2.75 

3. 

28.5 

1.802 

1.34 

38.20 

31.5 

1.873 

.37 

43.2 

3. 

3.25 

32.09 

1.919 

1.39 

44.61 

35.34 

1.995 

.41 

49.8 

3.25 

3.5 

35.87 

2.036 

1.43 

51.30 

39.37 

2.114 

.45 

57.1 

3.5 

3.75 

39.84 

2.153 

1.47 

58.57 

43.59 

2.233 

.49 

65. 

3.75 

4. 

44. 

2.266 

1.51 

66.40 

48. 

2.350 

.53 

73.6 

4. 

4.5 

52.87 

2.491 

1.58 

83.54 

57.37 

2.581 

.60 

91.8 

4.5 

5. 

62.50 

2.713 

1.64 

103. 

67.50 

2.808 

1.67 

113.1 

5. 

6. 

84. 

3.153 

1.78 

149.5 

90. 

3.256 

1.81 

162.9 

6. 

BED  7  FEET. 

BED  8  FEET. 

Depth 

Depth 

in 

Feet. 

a 

r 

Vr 

a^T 

a 

r 

Vr 

aVr 

in 
Feet. 

0.5 

3.87 

.440 

.67 

2.57 

4.37 

.446 

.67 

2.92 

0.5 

0.75 

6.09 

.623 

.79 

4.81 

6.84 

.640 

.80 

5.48 

0.75 

1. 

8.5 

.801 

.89 

7.61 

9.5 

.818 

.90 

8.58 

1. 

1.25 

11.09 

.965 

.98 

10.87 

12.34 

.987 

.99 

12.2 

1.25 

1.5 

13.87 

.119 

1.06 

14.71 

15.37 

1.146 

.07 

16.5 

1.5 

1.75 

16.84 

1.266 

1.12 

18.90 

18.59 

1.299 

.14 

21.2 

1.75 

2. 

20. 

1.407 

1.18 

23.70 

22. 

1.446 

.20 

26.5 

2. 

2.25 

23.34 

.545 

1.24 

29. 

25.59 

1.589 

.26 

32.3 

2.25 

2.5 

26.87 

.679 

1.30 

34.9 

29.37 

1.726 

.31 

38.5 

2.5 

2.75 

30.59 

.809 

1.35 

41.3 

33.34 

i.862 

.36 

45.4 

2.75 

3. 

34.50 

.936 

1.39 

48. 

37.50 

1.993 

.41 

52.9 

3. 

3.25 

38.59 

2.062 

1.44 

55.6 

41.84 

2.125 

.46 

61.1 

3.25 

3.5 

42.87 

2.184 

1.48 

63.4 

46.37 

2.248 

.50 

69.6 

3.5 

3.75 

47.34 

2.307 

1.52 

72. 

51.09 

2.374 

.54 

78.7 

3.75 

4. 

52. 

2.427 

1.56 

81.1 

56. 

2.497 

.58 

88.5 

4. 

4.5 

61.87 

2.664 

1.63 

100.9 

66.37 

2.739 

.65 

109.5 

4.5 

5. 

72.50 

2.897 

1.70 

123.3 

77.50 

2.976 

.72 

133.3 

5. 

6. 

96. 

3.353 

1.83 

175.8 

102. 

3.442 

.85 

189.2 

6. 

OPEN    AND    CLOSED    CHANNELS. 


87 


TABLE   11. 

Channels  naving  a  trapezoidal  section,  with  side  slopes  of  1 J  to  1.  Values 
of  the  factors  a  =  area  in  square  feet;  r  =  hydraulic  mean  depth  in  feet, 
and  alsa  ^/r  and  a\/r  for  use  in  the  formulae 

v  =  c  X  \/r  X  Vs  and  Q  =  c  X  a\/r   X  -s/s 


BED  9  FEET. 

BED  10  FEET. 

Depth 

Depth 

m 
Feet. 

a 

r 

N/r 

a\/r 

a 

r 

Vr 

a\/r 

in 

Feet. 

0.5 

4.875 

.451 

.68 

3.28 

5.375 

.456 

.68 

3.63 

0.5 

0.75 

7.59 

.649 

.81 

6.15 

8.344 

.657 

.81 

6.15 

0.75 

1. 

10.5 

.833 

.91 

9.58 

11.5 

.845 

.92 

10.58 

1. 

1.25 

13.594 

1.006 

13.6 

14.844 

1.023 

.01 

15. 

1.25 

1.5 

16.875 

1.170 

!os 

18.3 

18.375 

.192 

.09 

20. 

1.5 

1.75 

20.344 

1.329 

.15 

23.4 

22.094 

.355 

.16 

25.6 

1.75 

2. 

24. 

1.480 

.22 

29.3 

26. 

.510 

.23 

32. 

2. 

2.25 

27.844 

1.623 

.28 

35.5 

30.094 

.662 

.29 

38.8 

2.25 

2.5 

31.875 

1.769 

.33 

42.4 

34.375 

.807 

.34 

46.2 

2.5 

2.75 

36.094 

1.909 

.38 

49.8 

38.844 

.951 

.39 

54. 

2.75 

3. 

40.5 

2.044 

.43 

57.9 

43.5 

2.090 

.44 

62.6 

3. 

3.25 

45.094 

2.176 

.48 

66.7 

48  .  344 

2.223 

.49 

72. 

3.25 

3.5 

49.875 

2.306 

.52 

75.8 

53.375 

2.358 

.54 

82.2 

3.5 

3.75 

54.844 

2.440 

.56 

85.6 

58.594 

2.491 

.58 

92.6 

3.75 

4. 

60. 

2.561 

.60 

96. 

64. 

2.620 

.62 

103.6 

4. 

4.25 

65.344 

2.687 

.64 

107.2 

69.594 

2.749 

.66 

115.5 

4.25 

4.5 

70.875 

2.810 

.68 

118.8 

75.375 

2.873 

.70 

128.1 

4.5  - 

5. 

82.5 

3.052 

.75 

144.4 

87.5 

3.121 

.77 

154.6 

5. 

6. 

108. 

3.525 

.877 

202.7 

114. 

3.604 

.9 

216.6 

6. 

BED  11  FEET. 

BED  12  FEET. 

Depth 

Depth 

in 
Feet. 

a 

r 

VT 

a\/r 

a 

r 

Vr 

a\/r 

in 

Feet. 

0.5 

5.87 

.459 

.68 

3.99 

6.37 

.462 

.68 

4.33 

0.5 

0.75 

9.094 

.664 

.81 

7.37 

9.844 

.670 

.82 

8.07 

0.75 

1. 

12.5 

.856 

.93 

11.63 

13.5 

.865 

.93 

12.55 

1. 

1.25 

16.094 

1.038 

1.02 

16.42 

17  .  344 

1.051 

1.02 

17.7 

1.25 

1.5 

19.875 

1.211 

1.10 

21.86 

21.375 

1.228 

1.11 

23.7 

1.5 

1.75 

23  .  844 

.377 

1.17 

27.90 

25.594 

1.398 

1.18 

30.2 

1.75 

2 

28. 

.537 

1.24 

34.7 

30. 

1.561 

1.25 

37.5 

2. 

2^25 

32.344 

.693 

1.30 

42. 

34.594 

1.720 

1.31 

45.3 

2.25 

2.5 

36.875 

.842 

1.36 

50.2 

39.375 

1.874 

1.37 

53.9 

2.5 

2.75 

41.594 

.989 

1.41 

58.6 

44.344 

2.024 

1.42 

63. 

2.75 

3. 

46.5 

2.132 

1.46 

67.9 

49.5 

2.170 

1.47 

72.9 

3. 

3.25 

51.594 

2.271 

1.51 

77.9 

54.844 

2.312 

1.52 

83.4 

3.25 

3.5 

56  .  875 

2.407 

1.55 

88.2 

60.375 

2.452 

1.57 

94.8 

3.5 

3.75 

62.344 

2.543 

1.59 

99.1 

66.094 

2.590 

1.61 

106.4 

3.75 

4. 

68. 

2.675 

1.64 

111.5 

72. 

2.725 

1.65 

118.9 

4. 

4.5 

79.875 

2.933 

1.71 

136.6 

84.375 

2.990 

1.73 

146. 

4.5 

5. 

92.5 

3.186 

1.78 

164.6 

97.5 

3.247 

1.80 

175.5 

5. 

5.5 

105.875 

3.434 

1.85 

196.2 

111.375 

3.499 

1.87 

208.3 

5.5 

6. 

120. 

3.676 

1.92 

230.4 

126. 

3.746 

1.94 

244. 

6. 

88 


FLOW    OF    WATER    IN 


TABLE   11. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1£  to  1.  Values 
of  the  factors  a  =  area  in  square  feet;  r  =•  hydraulic  mean  depth  in  feet, 
and  also  ^/r  and  a-^/r  for  use  in  the  formulas 

v  =  c  X  Vr  X  V*  and  Q  =  c  X  a^/r  X  N/«~ 


BED  13  FEET. 

BED  14  FEET. 

Depth 

Depth 

in 

Feet. 

a 

r 

Vr 

a\/r 

a 

r 

Vr 

a\/r 

in 

Feet. 

0.5 

6.87 

0.464 

0.681 

4.68 

7.37 

0.467 

0.68 

5.03 

0.5 

0.75 

10.594 

0.675 

0.82 

8.69 

11.34 

0.679 

0.82 

9.30 

0.75 

1. 

14.5 

0.873 

0.93 

13.49 

15.50 

0.880 

0.93 

14.5 

1. 

1.25 

18.594 

1.061 

1.03 

19.15 

19.84 

1.072 

.04 

20.6 

1.25 

1.5 

22.875 

1.242 

1.11 

25.4 

24.37 

1.256 

.12 

27.3 

1.5 

1.75 

27.344 

1.416 

1.19 

32.5 

29.09 

1.433 

.20 

34.9 

1.75 

2. 

32. 

1.583 

1.26 

40.3 

34. 

1.602 

.26 

43. 

2. 

2.25 

36.844 

1.745 

1.32 

48.6 

39.09 

1.768 

.33 

52. 

2.25 

2.5 

41.875 

1.902 

.38 

57.8 

44.37 

1.928 

.39 

61.7 

2.5 

2.75 

47.094 

2.056 

.43 

67.3 

49.84 

2.085 

.44 

71.8 

2.75 

3. 

52.5 

2.204 

.48 

77.7 

55.50 

2.236 

.50 

83.3 

3. 

3.25 

58.094 

2.350 

.53 

89.0 

61.34 

2.382 

.55 

95.1 

3.25 

3.5 

63.875 

2.492 

.58 

100.9 

67.37 

2.530 

.59 

107.1 

3.5 

3.75 

69.844 

2.634 

1.62 

113.1 

73.59 

2.674 

1.64 

120.7 

3.75 

4. 

76. 

2.771 

1.66 

126.2 

80. 

2.814 

1.68 

134.3 

4. 

4.5 

88.875 

3.040 

1.74 

154.6 

93.37 

3.089 

1.76 

164.5 

4.5 

5. 

102.5 

3.303 

1.82 

186.6 

107.5 

3.356 

1.83 

196.7 

5. 

5.5 

116.875 

3.561 

1.89 

220.9 

122.37 

3.617 

1.90 

232.5 

5.5 

6. 

132. 

3.811 

1.95 

257.4 

138. 

3.872 

1.97 

271.9 

6. 

BED  15  FEET. 

BED  16  FEET. 

Depth 

Depth 

in 
Feet. 

a 

r 

N/r 

a\/r 

a             r      '    \/r 

a\/r 

in 
Feet. 

0.5 

7.87 

0.463 

0.68 

5.3 

8.37   0.470   0.69 

5.8 

0.5 

0.75 

12.09 

0.683 

0.83 

10. 

12.84 

0.687    0.83 

10.7 

0.75 

1. 

16.500 

0.886 

0.94 

15.5 

17.5 

0.892;  0.94 

16.5 

1. 

1.25 

21.094 

1.081 

.04 

22. 

22.34 

1.089:   1.04 

23.2 

1.25 

1.5 

25.875 

1.267 

.12 

29.1 

27.37 

1.279 

1.13 

30.9 

1.5 

1.75 

30.84 

1.447 

.20 

37. 

32.59 

1.461 

1.21 

39.4 

1.75 

2 

36. 

1.620 

.28 

46.1 

38. 

1.637 

1.28 

48.6 

2 

2^25 

41.344 

1.789 

.34 

55.4 

43.59 

1.808 

1.34 

58.4 

2  '.25 

2.5 

46.875 

1.951 

.39 

65.6 

49.37 

1.974 

1.40 

69.1 

2.5 

2.75 

52.594 

2.111 

.45 

76.3 

55.34 

2  136 

.46 

80.8 

2.75 

3. 

58.500 

2.266 

.51 

88.3 

61.50 

2.293 

.51 

92.9 

3. 

3.25 

64.594 

2.417 

1.56 

100.8 

67.84 

2.447 

.56 

105.8 

3.25 

3.5 

70.875 

2.565 

1.60 

113.4 

74.37 

2.599 

.61 

119.7 

3.5 

3.75 

77.344 

2.711 

1.65 

127.3 

81.09 

2.747 

.66 

134.6 

3.75 

4. 

84. 

2.855 

1.69 

142. 

88. 

2.892      .70 

149.6 

4. 

4.5 

97.875 

3.134 

1.77 

173.2 

102.37 

3.176      .78 

182.2 

4.5 

5. 

112.500 

3.405 

1.85 

207.7 

117.50 

3.453    1.86 

218.6 

5. 

5.5 

127.875 

3.677 

1  .  92 

245.5 

133.37 

3.722    1.93 

257.4 

5.5 

6. 

144. 

3.930 

1.98 

285.1 

150. 

3.9811  2. 

300. 

6. 

OPEN    AND    CLOSED    CHANNELS. 


89 


TABLE  11. 

Channels  having  a  trapezodial  section,  with  side  slopes  of  1J  to  1.  Values 
of  the  factors  a  --=  area  in  square  feet;  r  =  hydraulic  mean  depth  in.  feet, 
and  also  ^/r  and  a^/'r  for  use  in  the  formulae 

v  =  c  X  \/r  X  >/«" and  also  Q  =  c  X  a^/7  X 


BED  17  FEET. 

BED  18  FEET. 

Depth 

Depth 

in 
Feet. 

a 

r          V 

a\/r 

a 

r 

V?      °V*       rlet. 

0.75 

13.59 

.690      .83        11.3 

14.34 

.693      .83 

11.9 

0.75 

1.            18.50 

.897 

.95 

17.6 

19.5 

.902 

.95 

18.5 

1. 

1.25       23.59 

1.097 

.05 

24.8 

24.84 

1.104 

1.05 

26.1 

1.25 

1.5          28.87 

1.288 

.13 

32.6 

30.37 

1.297 

1.14 

34.6 

1.5 

1.75       34.34    1.473 

.21 

41.6 

36.09 

1.485 

1.22 

44. 

1.75 

2.            40.      1  1.652 

.29 

51.6 

42. 

1.665 

1.29 

54.2 

2 

2.25        45.84!  1.810 

.35 

61.9 

48.09 

1.842 

1.36 

65.3 

2^25 

2.5          51.87    1.993J      .41 

73.1 

54.37 

2.013 

1.42 

77.2 

2.5 

2.75  i     58.09;  2.159 

1.47 

85.4 

60.84 

2.180 

1.48 

90. 

2.75 

3.            64.50   2.318 

1.52 

98. 

67.50 

2.342|  1.53 

106.3 

3. 

3.25 

71.09    2.475 

1.57 

111.6 

74.34 

2.501 

1.58 

117.5 

3.25 

3.5         77.87    2.6281   1.62      126.2 

81.37 

2.658J   1.63 

132.6 

3.5 

3.75        84.84    2.780 

1.67      141.7 

88.59 

2.811J   1.68 

148.8 

3.75 

4. 

92. 

2.927 

1.71      157.3 

96. 

2.961i   1.72 

165.2 

4. 

4.5 

106.87 

3.216    1.79      191. 

111.37 

3.254 

1.80 

200.8 

4.5 

5. 

122.50    3.496    1.87 

229. 

127.50 

3.539 

1.88 

239.7 

5. 

5.5 

138.87    3.771!   1.94     269. 

144.37 

3.816 

1.95 

281.5 

5.5 

6. 

156.        4.037    2.01      314. 

182. 

4.087 

2.02 

327.4 

6.      • 

7. 

192.  50J  4.557!  2.135    411. 

199.50 

4.614 

2.15 

428  .  9 

7.  . 

BED  19  FEET. 

BED  20  FEET. 

Depth  i 

Depth 

F^t.i        - 

r 

\/r        a\/r 

a 

r 

v~ 

a\/r 

in 

Feet  . 

0.75        15.09 

0.695 

0.834:     12.6 

15.80 

.698 

.  835 

13.2 

0.75 

1. 

20.5 

0.906 

0.952      20.5 

21.50 

.910 

.95 

20.4 

1 

1.25 

26.09 

1.1 

1.053      27.5 

27.34 

1.116 

1.05 

28.7 

1^25 

1  .  o 

31.87 

1.305 

1.142      36.3 

33.37 

1.313 

.15 

38.4 

1.5 

1.75 

37.84 

1.459 

1.223;     46.3 

39.59 

1.505 

.23 

48.7 

1.75 

2. 

44. 

1  .  678 

1.295      57. 

46. 

1.690 

.30 

59.8 

2. 

2.25 

50.34 

1.857 

1.363      68.6 

52.59 

1.871      .37 

72.1 

2.25 

2.5 

56.87 

2.03 

1.425      81. 

59.37 

2.046 

.43 

85.5 

2.5 

2.75 

63.59 

2.199 

1.4831     94.3 

66.34 

2.218 

.49 

98.9 

2.75 

3. 

70.5 

2.364 

1.538]   108.4 

73.50 

2  386 

.54      113.2 

3. 

3.25 

77.59 

2.526 

1.589;   123.3 

80.84 

2.549 

.60 

129.4 

3.25 

3.5 

84.87 

2.683 

1.64 

139.2 

88.37 

2.708 

1.65 

145.8 

3.5 

3.75 

92.34 

2.839 

1.685 

155.6 

96.09 

2.867 

1.69 

162.4 

3.75 

4. 

100. 

2.992 

1.709 

170.9 

104. 

3.021 

1.73 

179.9 

4. 

4.25 

107.84 

3.142 

1.772 

191.1 

112.09 

3.174 

1.78 

199.5 

4.25 

4.5 

115.87 

3.289 

1.813 

210. 

120.37 

3.322 

1.82 

219.1 

4.5 

5. 

132.5 

3.577 

1.892 

250.5 

137.5 

3.615 

1.90 

261.7 

5. 

5.5 

149.87 

3.855 

1.964 

294.3 

155.37 

3.901 

1.97 

306. 

5.5 

6. 

168. 

4.134 

2.033 

341.5 

174. 

4.179 

2.04      355. 

6. 

7.       1  206.5 

4.668 

2.16 

446. 

213.5 

4.719 

2.17      463.7 

7  . 

8.        I  248. 

5.183 

2.277 

564.7 

256. 

5.241 

2.28      583.7 

8. 

90 


FLOW    OF    WATER    IN 


TABLE   11. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1|  to  1.  Values 
of  the  factors  a —  area  in  square  feet;  r  —  hydraulic  mean  depth  in  feet, 
and  also  \/r  and  a\/r  for  use  in  the  formulae 

v  —  c  X  V>  X  Vs  and  Q  =  c  X  «A/r  X  \A 


BED  25  FEET. 


BED  30  FEET. 


Depth 

Depth 

in 

Feet. 

a 

r 

Vr 

a^/r 

a 

r 

\/r 

a^/r 

in 
Feet. 

0.5 

12.87 

.480 

.693 

8.92 

15.37 

.483 

.695 

10.69 

0.5 

0.75 

19.59 

.707 

.841 

16.5 

23.34 

.714 

.845 

19.7 

0.75 

1. 

26.50 

.926 

.962 

25.5 

39.06 

.937 

.968 

37.8 

1. 

1.25 

33.59 

1.138 

1.067 

35.8 

47.81 

1.132 

1.064 

50.9 

1.25 

1.5 

40.87 

1.344 

1.16 

47.4 

48.37 

1.366 

1.17 

56.3 

1.5 

1.75 

48.34 

1.544 

1.24 

60. 

57.09 

1  .572 

1.25 

71.4 

1.75 

2. 

56. 

1.733 

1.32 

73.9 

66. 

1.774 

1.33 

87.8 

2. 

2.25 

63.844 

1.922 

1.39 

88.7 

75.09 

1.970 

1.40 

105.1 

2.25 

2.5 

71.875 

2.107 

1.45 

104.3 

84.37 

2.167 

1.47 

124.3 

2.5 

2.75 

80.094 

2.294 

1.51 

120.9 

93.84 

2.351 

1.53 

143.6 

2.75 

3. 

88.5 

2.471 

1.57 

139. 

103.59 

2.536 

1.59 

165.2 

3. 

3.25 

97.094 

2.645 

1.63 

158. 

113.34 

2.717 

.65 

187. 

3.25 

3.5 

105.875 

2.814 

1.68 

177. 

123.37 

2.895 

.70 

209.7 

3.5 

3.75 

114.844 

2.982 

1.73 

199. 

133.59 

3.070 

.75 

233.8 

3.75 

4. 

124. 

3.146 

1.78 

221. 

144. 

3.242 

.80 

259.2 

4. 

4.25 

133.344 

3.307 

1.82 

243. 

154.59 

3.411 

.85 

286. 

4.25 

4.5 

142.875 

3.466 

1.86 

266. 

165.37 

3.578 

.89 

312.6 

4.5 

4.75 

152.594 

3.623 

1.90 

290. 

176.34 

3.743 

.93 

340.3 

4.75 

5. 

162.5 

3.776 

1.94 

315. 

187.50 

3.904 

.97 

371. 

5. 

5.25 

172.594 

3.929 

1.98 

342. 

198.84 

4.060 

2.01 

400. 

5.25 

5.5 

182.875 

4.079 

2.02 

369. 

210.37 

4.222 

2.05 

431. 

5.5 

5.75 

193.3 

4.228 

2.06 

398. 

222. 

4.377 

2.09 

460. 

5.75 

6. 

204. 

4.374 

2.C9 

426. 

234. 

4.532 

2.13 

498. 

6. 

6.25 

214.8 

4.519 

2.126 

457. 

246.10 

4.684 

2.16 

533. 

6.25 

6.5 

225.9 

4.663 

2.109 

490. 

258.37 

4.835 

2.20 

568. 

6.5 

6.75 

237.1 

4.806 

2.192 

520. 

270.84 

4.985 

2.23 

605. 

6.75 

7. 

248.5 

4.946 

2.224 

553. 

283.50 

5.132 

2.27 

641. 

7. 

7.25 

260.1 

5.086 

2.255 

587. 

296.34 

5.279 

2.30 

681. 

7.25 

7.5 

271.9 

5.224 

2.285 

621. 

309.37 

5.424 

2.33 

721. 

7.5 

7.75 

283.4 

5.354 

2.314 

656. 

322.60 

5.567 

2.36 

761. 

7.75 

8. 

296. 

5.497 

2.344 

694. 

336. 

5.710 

2.39 

803. 

8. 

8.25 

307.3 

5.614 

2.369 

728. 

349.60 

5.851 

2.42 

846. 

8.25 

8.5 

320.9 

5.776 

2.403 

771. 

363.4 

5.992 

2.45 

890. 

8.5 

8.75 

333.6 

5.899 

2.429 

810. 

377.3 

6.130 

2.48 

934. 

8.75 

9. 

346.5 

6.031 

2.456 

851. 

391.5 

6.269 

2.50 

980. 

9. 

OPEN    AND    CLOSED    CHANNELS. 


91 


TABLE   11. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  H  to  1 .  Values 
of  the  factors  a  =  area  in  square  feet;  r --  hydraulic  mean  depth  in  feet, 
and  also  \/r  and  a\/r  for  use  in  the  formulae 

v  =  c  X  Vr  X  V*  and  Q  =  c  X  ci^/r   X 


BED  35  FEET. 

BED  40  FEET. 

Depth 
in 
Feet. 

a 

r 

Vr 

a\/r 

a             r 

Vr 

a\/r 

Depth 
in 
Feet. 

0.75 

27.09 

.719 

.847 

22.95 

30.84 

.722 

.85 

26.2 

0.75 

1. 

36.50 

.945 

.972 

35.5 

41.5 

.952 

.976 

40.5 

1. 

1.25 

46.11 

1.167 

1.080 

49.8 

52.3 

1.176 

1.084 

56.7 

1.25 

1.5 

55.87 

1  .  383 

1.176 

65.7 

63.4 

1.396 

1.181 

74.9 

1.5 

1.75 

65.844 

1.594 

1.26 

83.4 

76.34 

1.648 

1.28 

97.7 

1.75 

2. 

76. 

1.801 

1.34 

101.8 

86. 

1.822 

1.35 

115. 

2. 

2.25 

86.344 

2.003 

.41 

121.7 

97.59 

2.029 

1.42 

138.6 

2.25 

2.5 

96.875 

2.201 

.48 

143.2  ''    109.37 

2.232 

1.49 

163. 

2.5 

2.75 

107.594 

2.396 

.55 

166.8       121.34 

2.431 

1.56 

189.3 

2.75 

3. 

118.5 

2.587 

.61 

190.8       133.50 

2.627 

1.62 

216.3 

3. 

3.25 

129.594 

2.774 

.67 

216.4 

145.84 

2.839 

1.68 

245. 

3.25 

3.5 

140.875 

2.958 

.72 

242  .  4 

158.37 

3.010 

1.73 

274. 

3.5 

3.75 

152.344 

3.140 

.77 

269.6 

171.09 

3.197 

1.79 

306. 

3.75 

4. 

164. 

3.318 

.82 

298.5 

184. 

3.399 

1.84 

338. 

4. 

4.25 

175.844 

3.495 

.87 

329. 

197.09 

3.563 

1.89 

373. 

4.25 

4.5 

187.875 

3.668 

.91 

359. 

210.37 

3.742 

1.93 

406. 

4.5 

4.75 

200.094 

3.839 

.96 

392. 

223.84 

3.919 

1.98 

443. 

4.75 

5. 

212.5 

4.007 

2. 

425. 

237.50 

4.094 

2.03 

481. 

5. 

5.25 

225.094 

4.174 

2.04 

459. 

251.34 

4.265 

2.07 

520. 

5.25 

5.5 

237.875 

4.338 

2.08 

495. 

265.37 

4.435 

2.11 

560. 

5.5 

5.75 

250.8 

4.501 

2.12 

535.3 

279.6 

4.604 

2.15 

601. 

5.75 

6. 

264. 

4.661 

2.16 

570. 

294. 

4.770 

2.18 

641. 

6. 

6.25 

277.3 

4.820 

2.19 

608.7 

308.6 

4.935 

2.22 

685. 

6.25 

6.5 

290.9 

4.977 

2.23 

649. 

323.4 

5.097 

2.26  !     731. 

6.5 

6.75 

304.6 

5.133 

2.26 

689.9 

338.3 

5.259 

2.29  !     776. 

6.75 

7. 

318.5 

5.287 

2.30 

732.2 

353.5 

5.418 

2.33       823. 

7. 

7.25 

332.6 

5.440 

2.33 

775.6 

368.8 

5.577 

2.36        871. 

7.25 

7.5 

346.9 

5.591 

2.36 

820.4 

384.4 

5.733 

2.39        920. 

7.5 

7.75 

351.3 

5.741 

2.39 

841.7 

400.1 

5.889 

2.43        970. 

7.75 

8. 

376. 

5.889 

2.42 

912.2 

416. 

6.043 

2.46      1023. 

8, 

8.25 

390.8 

6.037 

2.45 

960.2 

432.1 

6.195 

2.49  i   1075. 

8.25 

8.5 

405.9 

6.183 

2.48 

1009. 

448.4 

6.347 

2.52 

1130. 

8.5 

8.75 

421.1 

6.327 

2.51 

1059. 

464.8 

6.497 

2.55 

1185. 

8.75 

9. 

436.5 

6.471 

2.54 

1110. 

481.5 

6.646 

2.58 

1241. 

9. 

9.5 

467.9 

6.756 

2.60 

1216. 

515.4 

6.941 

2.64 

1358. 

9.5 

10.         500. 

7.037 

2.65 

1327. 

550. 

7.232 

2.69 

1479.   JlO. 

92 


FLOW    OF    WATER    IN 


TABLE  11. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1  £  to  1.  Values 
of  the  factors  a  =  area  in  square  feet;  r  =  hydraulic  mean  depth  in  feet, 
and  also  \/r  and  a\/r  for  use  in  the  formula 

v  =  c  X  V~r   X\/s  and  Q  =  c  X  a^/r  X  \/~* 


BED  45  FEET. 

BED  50  FEET. 

Depth 
in 

Feet. 

a             r 

i 

Vr 

a\/r 

a 

r 

x/r 

a\/r 

Depth 
in 

Feet. 

0.5 

22.87 

.490      .700      16. 

25.37      .490 

.700!       17.8 

0.5 

0.75 

34.59 

.725 

.852      29.5 

38.34      .728 

.85?        32.7 

0.75 

1. 

46.50 

.957 

.977     45.4 

51.50      .961 

.980 

50.5 

1. 

1.25 

58.57 

1.183 

1.084 

63.5 

64.841  1.190 

1.091        70.7 

1.25 

1.5 

70.88 

1.406 

1.190      84.3 

78.37    1.415 

.190       93.3 

1.5 

1.75 

83.34 

1.624 

1.274    106.2 

92.09    1.635 

.28 

118. 

1.75 

2 

96. 

1.839 

.356    130.2 

106.         1.853 

.36 

138. 

2. 

2.25 

108.8 

2.049 

.43 

156. 

120.09    2.067      .44 

173. 

2.25 

2.5 

121.9 

2.257 

.50 

183. 

134.37    2.277 

.51 

202. 

2.5 

2.75 

135.1 

2.460 

.57 

212. 

148.84    2.484 

.58 

235. 

2.75 

3. 

148.5 

2.660 

.63 

242. 

163.50   2.688      .64 

268. 

3. 

3.25 

162.1 

2.858 

.69 

274. 

178.34    2.890      .70 

303. 

3.25 

3.5 

175.9 

3.052 

.75 

308. 

193.37    3.088 

.76 

340. 

3.5 

3.75 

189.8 

3.244 

.80 

342. 

208.  59j  3.284 

.81 

378. 

3.75 

4. 

204. 

3.433 

.85 

377. 

224. 

3.477 

.86 

417. 

4. 

4.25 

218.3 

3.620 

1.90     415. 

239.59   3.6681     .92 

460. 

4.25 

4.5 

232.9 

3.804 

1.95 

454. 

255.37    3.856 

.96 

501. 

4.5 

4.75 

247.6 

3.985 

2. 

495. 

271.34   4.043 

2.01 

545. 

4.75 

5. 

262.5 

4.165 

2.04 

536. 

287.50   4.226 

2.05 

591. 

5. 

5.25 

277.6 

4.342 

2.08 

577. 

303.841  4.408 

2.10 

638. 

5.25 

5.5 

292.88    4.518 

2.13 

624. 

320.4 

4.588 

2.14 

686. 

5.5 

5.75 

308.34    4.683 

2.16 

667.2 

337.1 

4.766 

2.18 

735. 

5.75 

6. 

324. 

4.862 

2.20 

713. 

354. 

4.941 

2.22 

786. 

6. 

6.25 

339.84 

5.032 

2.25 

763.6 

371.1 

5.116 

2.26 

839. 

6.25 

6.5 

355.99 

5.200 

2.28 

811. 

388.4     5.288 

2.30 

893. 

6.5 

6.75 

372.1 

5.366    2.31 

861.8 

405.8 

5.461 

2.33 

948. 

6.75 

7. 

388.5 

5.531 

2.35 

913. 

423.5 

5.628 

2.37 

1005. 

7. 

7  25 

405.7 

5.703 

2.39 

968.8 

441.3 

5.799    2.40 

1063. 

7.25 

7.5 

421.9 

5.856 

2.42    1021. 

459.4 

5.9631  2.44 

1122. 

7.5 

7.75 

438.8 

6.016 

2.45 

1076. 

477.6 

6.128 

2.47 

1182. 

7.75 

8. 

456. 

6.175 

2.48 

1133. 

496. 

6.291 

2.50 

1244. 

8. 

8.25 

473.3 

6.333 

2.51 

1191. 

514.6 

6.453 

2.54 

1307. 

8.25 

8.5 

490.9 

6.489 

2.55 

1250. 

533.4 

6.613 

2.57 

1371. 

8.5 

8.75 

508.6 

6.644 

2.58 

1311. 

552.3     6.773 

2.60 

1437. 

8.75 

9. 

526.5 

6.798   2.61 

1373. 

571.5 

6.931 

2.63 

1503. 

9. 

9.5 

562.9 

7.102!  2.66  11500. 

610.4 

7.244 

2.69 

1642. 

9.5 

10. 

600. 

7.414    2.72  '1633. 

650. 

7  .  5f>3 

2.75 

1786. 

10. 

10.5 

637.9 

7.869;  2.78  i!773. 

690.4 

7.858 

2.80      1933. 

10.5 

11. 

676.5  1  7.991!  2.83  11912. 

731.5 

8.158 

2.86      209.2 

11. 

OPEN    AND    CLOSED    CHANNELS. 


93 


TABLE  11. 

Channels  having  a  trapezoidal  section,  with  side  slopes  of  1 J  to  1.  Values 
of  the  factors  a  =  area  in  square  feet;  r  =  hydraulic  mean  depth  in  feet, 
and  also  ^/r  and  a\/r  for  use  in  the  formulae 

r"  X  \AT  and  Q  =  c  X  a^/r  X  \A 


BED  60  FEET. 


BED  70  FEET. 


Depth 

- 



y  

Depth 

iu 

a 

r 

\/T 

a\/r 

a 

r 

-v//* 

a^/r 

in 

feet. 

feet. 

1. 

61.50 

.951 

.978 

59.2 

71.5 

.9713 

.98 

70. 

1. 

1.5 

91.12 

1.393 

.180 

107.5 

108.37 

1.437 

.J9 

129. 

1.5 

1.75 

109.59 

1.647 

.29 

141.4 

127.09 

1.666 

.29 

164. 

1.75 

2. 

126. 

1.875 

.37 

172.6 

146. 

1.891 

.37 

200. 

2. 

2.25 

142.60 

2.094 

.45 

206.8 

165.09 

2.114 

.45 

239. 

2.25 

25 

159.38 

2.309 

.52 

242.3 

184.37 

2.334 

.53 

282. 

2.5 

2.75 

176.34 

2  522 

59 

280.4 

203.84 

2.551 

.60 

326. 

2.75 

3. 

193.50 

2.732 

.65 

320. 

223.5 

2.765 

.66 

371. 

3. 

3.25 

210.84 

2.940 

1.71 

360. 

243  34 

2.978 

.73 

421. 

3.25 

3.5 

228.37 

3.145 

1.77 

404. 

263.37 

3.188 

.79 

471. 

3.5 

3.75 

246.09 

3.347 

1.83 

450. 

283.59 

3.396 

.84 

522. 

3.75 

4. 

264. 

3.547 

1.88 

496. 

304. 

3.601 

.90 

578. 

4. 

4.25 

282.09 

3.745 

1.94 

547. 

324.59 

3.804 

.95 

633. 

4  25 

4.5 

300.37 

3.941 

1.99 

598. 

345.38 

4.006 

2. 

691. 

4.5 

4.75 

318.84 

4.134 

2.03 

647. 

366.34 

4.205 

2.05 

751. 

4.75 

5. 

337.50 

4.325 

2.08 

702. 

387.5 

4.402 

2.10 

814. 

5.       - 

5.25 

356.34 

4.515 

2.12 

755. 

408.8 

4.597 

2.14 

875. 

5.25 

5.5 

375.37 

4.702 

2.17 

815. 

430.4 

4.791 

2.19 

943. 

5.5 

5.75 

394.59 

4.888 

2.21 

872. 

452.09 

4.983 

2.23 

1008. 

5.75 

6. 

414. 

5.071 

2.25 

932. 

474. 

5.172 

2.27 

1076. 

6. 

6.25 

433.59 

5.253 

2  29 

993. 

496.09 

5.361 

2.32 

1151. 

6.25 

6.5 

453.37 

5  434 

2.33 

1056. 

518.4 

5.548 

2.36 

1223. 

6.5 

6.75 

473.34 

5.612 

2.37 

1122. 

540.84 

5  733 

2.39 

1293. 

6.75 

7. 

493.50 

5.789 

2.40 

1188. 

563.5 

5.916 

2.43 

1369. 

7. 

7.25 

513.84 

5.965 

2.44 

1255. 

586.34 

6.099 

2.47 

1448. 

7.25 

7.5 

534.37 

6.139 

2.47 

1325. 

609.4 

6.279 

2.51 

1527. 

7.5 

7.75 

555.09 

6.312 

2.51 

1394. 

632.59 

6.459 

2.54 

1607. 

7.75 

8. 

576. 

6.483 

2.54 

1466. 

656. 

6.636 

2.57 

1686. 

8. 

8.25 

597.09 

6.605 

2.58 

1546. 

679.59 

6.813 

2.61 

1774. 

8.25 

8.5 

618.37 

6.822 

2.61 

1615. 

703.4 

6.988 

2.64 

1859. 

8.5 

8.75 

639.84 

6.989 

2.64 

1690. 

727.34 

7.162 

2.68 

1949. 

8.75 

9. 

661.50 

7.155 

2.67 

1770. 

751.5 

7.335 

2.71 

2036. 

9. 

9.5 

705.37 

7.484 

2.73 

1929. 

800.4 

7.677 

2.77 

2218. 

9.5 

10. 

750. 

7.808 

2.79 

2096. 

850. 

8.014 

2.83 

2406. 

10. 

10.5 

795.37 

8.128 

2.85 

2268. 

900.4 

8.347 

2.90 

2601. 

10.5 

11. 

841.5 

8.444 

2.90 

2445. 

951.5 

8.676 

2.94 

2802. 

11. 

94 


FLOW    OF    WATER    IN 


TABLE    12. 

Sectional  areas,  in  square  feet,  of  trapezoidal  channels,  with  side  slopes 
of  11  to  1. 


Depth 
in 
Feet. 

BED  WIDTH 

70  feet. 

80  feet. 

90  feet.     100  feet. 

120  feet. 

1. 

71.50 

81.50 

91.50 

101.50 

121.50 

1.5 

108.37 

123.37 

138.37 

153.37 

183.37 

2. 

146. 

166. 

186. 

206. 

246. 

2.25 

165.09 

187.59 

210.09 

232.59 

277.59 

2.5 

184.37 

209.37 

234.37 

259.37 

309.37 

2.75 

203.84 

231.34 

258.84 

286.34 

313.84 

3. 

223.50 

253.50 

283.5 

313.50 

373.50 

3.25 

243.34 

275.84 

308.34 

340.84 

405.84 

3.5 

263.37 

298.37 

333  37 

368.37 

438  ,37 

3.75 

283.59 

321.09      358.59 

396.09 

471.09 

4. 

304. 

344. 

384. 

424. 

504. 

4.25 

324.59 

367.09 

409.59 

452.09 

537  .  09 

4.5 

345.37 

390.37 

435.37 

480.37 

570.37 

4.75 

366.34 

413.84 

461.34 

508  .  84 

603.84 

5. 

387.50 

437.50 

487  .  50 

537.50 

637.50 

5.25 

408.84 

461.34 

513.84 

566.34 

671.34 

5.5 

430.37 

485.37 

540.37 

595/37 

705.37 

5.75 

452.09 

509.59 

567.09 

624.59 

739.59 

6. 

474. 

534. 

594. 

654. 

774. 

6.25 

496.09 

558.59 

621.09 

683.59 

808.59 

6.5 

518.37 

583.37 

648.37 

713.37 

843.37 

6.75 

540.84 

608.34 

675.84 

743.34 

878.34 

7. 

563  .  50 

633.50 

703.50 

773.50 

913.50 

7.25 

586.34 

658.84 

731.34 

803.84 

948.84 

7.5 

609.37 

684.37 

759.37 

834.37 

984.37 

7.75 

632.59 

710.09 

787.59 

865.09 

1020.09 

8. 

656. 

736. 

816. 

896. 

1056. 

8.25 

679.59 

762.09 

844.59 

927.09 

1092.09 

8.5 

703.37 

788.37 

873.37 

958  .  37 

1128.37 

8.75 

727.34 

814.84 

902.34 

989.84 

1164.84 

9. 

751.50 

841.50 

931.50 

1021.50 

1201.50 

9.25 

775.84 

868.34 

960.84 

1053.34 

1238.34 

9.5 

800.37 

895.37 

990.37 

985.35 

1275.35 

9.75 

825.09 

922  .  59 

1020.09 

1117.59 

1312.59 

10. 

850. 

950. 

1050. 

1150. 

1350. 

10.5 

900.37 

1005.37 

1110.37 

1215.37 

1425.37 

11. 

951.50 

1061.50 

1171.50 

1281.50 

1501.50 

11.5 

1003.37 

1118.37 

1233.37 

1348.37 

1578.37 

12. 

1056. 

1176. 

1296. 

1416. 

1656. 

OPEN    AND    CLOSED    CHANNELS. 


95 


TABLE    12. 

Sectional  areas,  in  square  feet,  of  trapezoidal  channels,  with  side  slopes 


of 


Depth 
in 
Feet 

BED  WIDTH 

140  feet. 

160  feet. 

180  feet. 

200  feet. 

220  feet. 

1. 

141.50 

161.50 

181.50 

201.50 

221.50 

2. 

286. 

326. 

366. 

406. 

446. 

2.5 

359.37 

409.37 

459.37 

509.37 

559.37 

2.75 

368.84 

423.84 

478.84 

533.84 

588.84 

3. 

433.50 

493.50 

553.50 

613.50 

673.50 

3.25 

470.80 

535.80 

600.80 

665.80 

730.80 

3.5 

508.37 

578.37 

648.37 

718.47 

788.47 

3.75 

546.09 

621.09 

696.09 

771.09 

846.09 

4. 

584. 

664. 

744. 

824. 

904. 

4.25 

622  .  09 

707.09 

792.09 

877.09 

962.09 

4.5 

660.37 

750.37 

840.37 

930.37 

1020.37 

4.75 

698.84 

793.84 

888.84 

983.84 

1078.84 

5. 

737.50 

837.50 

937.50 

1037.50 

1137.50 

5.25 

776.34 

881.34 

986.34 

1091.34 

1196.34 

5.5 

815.37 

925.37 

1035.37 

1145.37 

1255.37 

5.75 

854.59 

969.59 

1084.59 

1199.59 

1314.59 

6. 

894. 

1014. 

1134. 

1254. 

1374. 

6.25 

933.59 

1058.59 

1183.59 

1308.59 

1433.59 

6.5 

973.37 

1103.37 

1233.37 

1363.37 

1493.37 

6.75 

1013.34 

1148.34 

1283.34 

1418.34 

1553.34 

7. 

1053.50 

1193.50 

1333.50 

1473.50 

1613.50 

7.25 

1093.84 

1238.84 

1383.84 

1528.84 

1673.84 

7.5 

1134.37 

1284.37 

1434.37 

1584.37 

1734.37 

7.75 

1175.09 

1330.09 

1485.09 

1640.09 

1795.09 

8. 

1216. 

1376. 

1536. 

1696. 

1856. 

8.25 

1257.09 

1422.09 

1587.09 

1752.09 

1917.09 

8.5 

1298.37 

1468.37 

1638.37 

1808.37 

1978.37 

8.75 

1339.84 

1514.84 

1689.84 

1864.84 

2039.84 

9. 

1381.50 

1561.50 

1741.50 

1921.50 

2101.50 

9.25 

1423.34 

1608.34 

1793.34 

1978.34 

2163.34 

9.5 

1465.35 

1655.35 

1845.35 

2035.35 

2225.35 

9.75 

1507.59 

1702.59 

1897.59 

2092.59 

2287.59 

10. 

1550. 

1750. 

1950. 

2150. 

2350. 

10.5 

1635.37 

1845.37 

2055.37 

2265.37 

2475.37 

11. 

1721.50 

1941.50 

2161.50 

2381.50 

2601.50 

11.5 

1808.37 

2038.37 

2268.37 

2498.37 

2728.37 

12. 

1896. 

2136. 

2376. 

2616. 

2856. 

13. 

2073.50 

2333.50 

2593.50 

2853.50 

3113.50 

14. 

2254. 

2534. 

2814. 

3094. 

3374. 

15. 

2437.50 

2737.50 

3037.50 

3337.50 

3637.50 

16. 

2624. 

2944. 

3264. 

3584. 

3904. 

i 

FLOW    OF    WATER    IN 


TABLE    12. 

Sectional  areas,  in  square  feet,  of  trapezoidal  channels,  with  side  slopes 
of  H  to  1. 


Depth 

BED  i 

VlDTH 

in 

Feet. 

240  feet. 

260  feet. 

280  feet. 

300  feet. 

2 

486. 

526. 

566. 

606. 

2.5 

609  .  37 

659.37 

709.37 

759.37 

3. 

733.50 

793.50 

853.50 

913.50 

3.25 

795.80 

860.80 

925  .  80 

990.80 

3.5 

858.47 

928.47 

998.47 

1068.47 

3.75 

921.09 

996.09 

1071.09 

1146.09 

4. 

984. 

1064. 

1144. 

1224. 

4.25 

1047.09 

1132.09 

1217.09 

1302.09 

4.5 

1110.37 

1200.37 

1290.37 

1380.37 

4.75 

1173.84 

1268  .  84 

1363.84 

1458.84 

5. 

1237.50 

1337.50 

1437.50 

1537.50 

5.25 

1301.34 

1406.34 

1511.34 

1616.34 

5.5 

1365.37 

1475.37 

1585.37 

1695.37 

5.75 

1429.59 

1544.59 

1659.59 

1774.59 

6. 

1494. 

1614. 

1734. 

1854. 

6.25 

1558.59 

1683.59 

1808.59 

1933.59 

6.5 

1623.37 

1753.37 

1883.37 

2013.37 

6.75 

1688.34 

1823.34 

1958.34 

2093.34 

7. 

1753.50 

1893.50 

2033.50 

2173.50 

7.25 

1818.84 

1963.84 

2108.84 

2253.84 

7.5 

1884.37 

2034.37 

2184.37 

2334.37 

7.75 

1950.09 

2105.09 

2260.09 

2415.09 

8. 

2016. 

2176. 

2336. 

2496. 

8.25 

2181.09 

2346.09 

2511.09 

2676.09 

8.5 

2148.37 

2318.37 

2488.37 

2658.37 

8.75 

2214.84 

2389.84 

2564  .  84 

2739.84 

9. 

2281.50 

2461.50 

2641.50 

2821.50 

9.25 

2348.34 

2533.34 

2718.34 

2903.34 

9.5 

2415.35 

2605.35 

2795.35 

2985.35 

9.75 

2482.59 

2677.59 

2872.59 

3067.59 

10. 

2550. 

2750. 

2950. 

3150. 

10.5 

2685.37 

2895.37 

3105.37 

3315.37 

11.0 

2821.50 

3041.50 

3261.50 

3481.50 

11.5 

2958.37 

3188.37 

3418.37 

3648  .  37 

12. 

3096. 

3336. 

3576. 

3816. 

13. 

3373.50 

3633.50 

3893.50 

3153.50 

14. 

3654. 

3934. 

4214. 

4494. 

15. 

3937.50 

4237.50 

4537.50 

4837.50 

16. 

4224. 

4544. 

4864. 

5184. 

OPEN    AND    CLOSED    CHANNELS. 


97 


TABLE  13. 

Channels  having  a  rectangular  cross-section.  Values  of  the  factors 
a  =  area  in  square  feet;  r  =  hydraulic  mean  depth  in  feet,  and  also  ^/r 
and  a\/r  for  use  in  the  formulae 

'o  =  c^Jrs  and  Q  —  c  X  a\/r  X 


BED  1  FOOT. 

BED  2  FEET. 

Depth 
in 
Feet. 

a 

r 

v~ 

a\/r 

a 

r 

VT 

a\/r 

Depth 
in 
Feet. 

0.25 

.25 

.167 

.408 

.102 

.5 

.200 

.447 

.224      0.25 

0.5 

.5 

.250 

.500 

.250 

1. 

.333 

.557 

.557 

0.5 

0.75 

.75 

.300 

.548 

.411 

1.5 

.429 

.655 

.982     0.75 

1. 

1. 

.333 

.577 

.577 

2. 

.500 

.707 

1.414 

1. 

1.25 

1.25 

.357 

.598 

.747 

2.5 

.555 

.744 

1.860 

1.25 

1.5 

1.5 

.375 

.612 

.918 

3. 

.600 

.775 

2.325 

1.5 

1.75 

3.5 

.636 

.798 

2.793 

1.75 

2 

4. 

.666 

.816 

3.264 

2 

2~25 

4.5 

.692 

.832 

3.744 

2.25 

2.5 

5. 

.714 

.843 

4.215 

2.5 

2.75 

5.5 

.733 

.856 

4.708 

2.75 

3. 

6. 

.750 

.866 

5.196 

3. 

3.25 

6.5 

.765 

.874 

5.681 

3.25 

3.5 

7. 

.777 

.882 

6.174 

3.5 

BED  3  FEET. 

BED  4  FEET. 

Depth 
in 
Feet. 

a             r 

v'r 

a\/  r 

a            r 

\/r        a\/r 

Depth 
in 
Feet. 

0.25 

.75 

.214 

.463 

.347 

1.             .222 

.471 

.471 

0.25 

0.5 

1.50 

.375 

.612 

.918 

2 

.400 

.632 

1.264 

0.5 

0.75 

2.25 

.500 

.707 

1.591 

3. 

.545 

.738 

2.214 

0.75 

1. 

3. 

.600 

.774 

2.322 

4. 

.666 

.816 

3.264 

1. 

1.25 

3.75 

.682 

.825 

3.094 

5. 

.769 

.877 

4.385 

1.25 

1.5 

4.50 

.750 

.866 

3.897 

6. 

.857      .926 

5.556 

1.5 

1.75 

5.25 

.808 

.899 

4.720 

7. 

.933 

.965 

6.755 

1.75 

2. 

6. 

.857 

.926 

5.556 

8. 

1. 

1. 

8. 

2. 

2.25 

6.75 

.900      .948 

6.399 

9. 

1.058 

1.028 

9.252 

2.25 

2.5 

7.50 

.937 

.967 

7.252 

10. 

1.111 

1.054 

10.540 

2.5 

2.75 

8.25 

.971 

.989 

8.159 

11. 

1.158 

1.076 

11.836 

2.75 

3. 

9. 

1. 

1. 

9. 

12. 

1.200 

1.095 

13.140 

3. 

3.5 

10.5 

1.05 

1.024 

10.752 

14. 

1.273 

1.128 

15.792 

3.5 

4. 
4.5 

12. 
13.5 

1.091 
1.125 

1.044 
1.067 

12.528 
14.404 

16. 

18. 

1.333 
1.384 

1.154 
1.185 

18.464   4. 
21.330   4.5 

5. 

15. 

1.154 

1.074 

16.110 

20. 

1.428 

1.195 

23.900   5. 

98 


FLOW    OF    WATER    IN 


TABLE    13. 

Channels  having  a  rectangular  cross-section.  Values  of  the  factors 
a  =  area  in  square  feet;  r  =  hydraulic  mean  depth  in  feet,  and  also  ^/r 
and  a\/r  for  use  in  the  formulae 

v  =  c\frs  and  Q  —  c  X 


BED  5  FEET. 

BED  6  FEET. 

Depth  i 

Depth 

in 
Feet. 

a 

r         Vr 

a\/r 

a 

r 

V> 

a\/r 

in 
Feet. 

0.5 

2.5 

.416      .645 

1.612 

3. 

.428 

.654 

1.962 

0.5 

0.75 

3.75 

.577 

.759 

2.846  ! 

4.5 

.600 

.775 

3.487 

0.75 

1. 

5. 

.714      .845 

4.225  ! 

6. 

.750 

.866 

5.196 

1. 

1.25 

6.25 

.833      .913 

5.706  j 

7.5 

.882 

.939 

7.042 

1.25 

1.5 

7.5 

.937      .968 

7.260  ! 

9. 

1. 

9. 

1.5 

1.75 

8.75 

.029 

1.014 

8.872 

10.5 

!l06 

1.051 

11.035 

1.75 

2. 

10. 

.111 

1.054 

10.540 

12. 

2 

1.095 

13.140 

2. 

2.25 

11.25 

.184 

1.088 

12.240 

13.5 

'.286 

1.134 

15.309 

2.25 

2.5 

12.5 

.250 

1.118 

13.975 

15. 

.364 

1.168 

17.520 

2.5 

2.75 

13.75 

.309 

1.144 

15.730 

16.5 

.436 

1.198 

19.767 

2.75 

3. 

15. 

.364 

.168 

17.520 

18. 

1.5 

1.225 

22.050 

3. 

3.25 

16.25 

.413 

.187 

19.289 

19.5 

1.56 

1.250 

24.375 

3.25 

3.5 

17.5 

.458 

.208 

21.140 

21. 

1.615 

1.278 

26.838 

3.5 

3.75 

18.75 

.500 

.225 

22.969 

22.5 

1.666 

1.298 

29.205 

3.75 

4. 

20. 

1.538 

.241 

24!  820 

24. 

1.714 

1.309 

31.416 

4. 

4.25 

21.25 

1.574 

.   .254 

26.647 

25.5 

1.759 

1.326 

33.8 

4.25 

4.5 

22.5 

1.607 

.268 

28.530 

27. 

1.8 

1.341 

36.207 

4.5 

5. 

25. 

1.686 

.290 

32.250 

30. 

1.875 

1.377 

41.310 

5 

BED  7  FEET. 

BED  8  FEET. 

Depth 

Depth 

in 

Feet. 

a 

r 

Vr~ 

a\/r 

<&            r 

VT 

a\Jr 

in 
Feet. 

0.5 

3.5 

.438 

.661 

2.313 

4. 

.444 

.667 

2.668 

0.5 

0.75 

5.25 

.618 

.786 

4.126 

6. 

.632 

.795 

3.792 

0  75 

1. 

7. 

.778 

.882 

6.174 

8. 

.800 

801 

6.408 

1. 

1.25 

8.75 

.921 

.960 

8.400 

10. 

.857 

.826 

8  260 

1.25 

1.5 

10.50 

.050 

1.025 

10.762 

12. 

.091 

1.044 

12.528 

1.5 

1.75 

12.25 

.167 

1.080 

13.230 

14. 

.218 

1.104 

15.456 

1.75 

2. 

14. 

.273 

1.128 

15.792 

16. 

.333 

1.153 

18.448 

2. 

2.25 

15.75 

.367 

1.170 

18.427 

18. 

440 

1.200 

21.600 

2  25 

2.5 

17.50 

.458 

1.208 

21.140 

20. 

.538 

1  240 

24.800 

2.5 

2.75 

19.25 

.540 

.241 

23.889 

22. 

.628 

1.276 

28.072 

2.75 

3. 

21. 

.615 

.271 

26.691 

24. 

.714 

1.309 

31.416 

3. 

3.25 

22.75 

.685 

.298 

29.5 

26. 

.794 

1.340 

34.840 

3.25 

3.5 

24.50 

.750 

.323 

32.413 

28. 

.866 

1.366 

38.248 

3.5 

3.75 

26.25 

.810 

.345 

35.3 

30. 

.938 

1  .  392 

41.760 

3.75 

4. 

28. 

.866 

.366 

38.2 

32. 

2. 

1.414 

45.248 

4. 

4.25 

29.75 

.919 

.385 

41.2 

34. 

2.061 

1.436 

48.824 

4.25 

4.5 

31.50 

1.969 

.403 

44.1 

36. 

2.117 

1  .  455 

52.380 

4.5 

4.75 

33.25 

2.015 

.419 

47.2 

38. 

2.171 

1.473 

55.974 

4.75 

5. 

35. 

2.059 

.435 

50.2 

40. 

2.222 

1.490 

59.600 

6. 

OPEN    AND    CLOSED    CHANNELS. 


99 


TABLE    13. 

Channels  having  a  rectangular  cross-section.  Values  of  the  factors 
a  =  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in  feet,  and  also 
•x/Fand  a\/r  for  use  in  the  formulae 

v  =  c  X  Vr  X  Vs  and  Q  =  c  X  a^/r   X  V» 


BED  10  FEET. 

BED  12  FEET. 

Depth 

1 

Depth 

in 
Feet. 

a 

r 

Vr 

a\/r 

a 

r 

x/r 

a\/r 

in 
Feet. 

1. 

10. 

.833 

.913 

9.130 

12. 

.857 

.926 

11.112 

1. 

1.25 

12.5 

1. 

1. 

12.50 

15. 

1.035 

1.017 

15.255 

1.25 

1.5 

15. 

1.154 

1.074 

16.11 

18. 

1.2 

1.095 

19.710 

1.5 

1.75 

17.5 

1.295 

1.138 

19.91 

21. 

1.357 

.165 

24.465 

1.75 

2. 

20. 

1.429 

1.195 

23.90 

24. 

1.5 

.224 

29.376 

2. 

2.25 

22.5 

1.553 

1.246 

28.03 

27. 

1.636 

.278 

34.506 

2.25 

2.5 

25. 

1.666 

1.290 

32.25 

30. 

1.764 

.328 

39.840 

2.5 

2.75 

27.5 

1.777 

1.333 

36.66 

33. 

1.887 

.374 

45.342 

2.75 

3. 

30. 

1.875 

1.369 

41.07 

36. 

2. 

.414 

50.904 

3. 

3  25 

32.5 

1.970 

1.404 

45.63 

39. 

2.106 

.451 

56.589 

3.25 

3.5 

35. 

2.058 

.434 

50.19 

42. 

2.209 

.484 

62.328 

3.5 

3.75 

37.5 

2.143 

.463 

54.86 

45. 

2.304 

.517 

68.265 

3.75 

4. 

40. 

2.222 

.490 

59  .  60 

48. 

2.4 

.549 

74.352 

4. 

4.25 

42.5 

2.297 

515 

64  4 

51. 

2.488 

.578 

80.5 

4.25 

4.5 

45. 

2.367 

.538 

69.21 

54. 

2.571 

.603 

86.562 

4.5 

4.75 

47.5 

2.436 

.561:  74.1 

57. 

2.651 

1.628 

92.8 

4.75 

5. 

50. 

2.5 

1.581!  79.05 

60. 

2.727 

1.651 

99.060 

5. 

6. 

60. 

2.727 

1.651!  99.1 

72. 

3.000 

1.732 

124.7 

6.  ' 

BED  14  FEET. 

BED  16  FEET. 

Depth 

Depth 

in 
Feet 

« 

r 

Vr 

a-\/r 

a 

r 

V'r 

a\/r 

in 
Feet. 

1 

14. 

.875 

.935 

13.090 

16. 

.888 

.942 

15.072 

1. 

1.5 

21. 

1  .  244 

1.115 

23.415 

24. 

1.262 

.123 

26.952 

1.5 

1.75 

24.5 

1.397 

1.182 

28.959 

28. 

1.434 

.197 

33.516 

1.75 

2. 

28. 

1.555 

1.246 

34.888 

32. 

1.600 

.265 

40.480 

2. 

2.25 

31.5 

1.701 

1.304 

41.076 

36. 

1.757 

.325 

47.700 

2.25 

2.5 

35. 

1.841 

1.357 

47.495 

40. 

1.904 

.379 

55.160 

2.5 

2.75 

38.5 

1.971 

1.404 

54.054 

44. 

2.050 

.432 

63.008 

2.75 

3. 

42. 

2.1 

1.450 

60.900 

48. 

2.182 

.455 

69  840 

3. 

3.25 

45  5 

2.23 

1.493 

67.931 

52. 

2.311 

.520 

79.040 

3.25 

3.5 

49. 

2.333 

1.527 

74.823 

56. 

2.346 

.532 

85.792 

3.5 

3.75 

52.5 

2.447 

1.564 

82.110 

60. 

2.556 

.599 

95.940 

3.75 

4. 

56 

2.545 

1.595 

89.320 

64. 

2.666 

.632 

104.448 

4. 

4.25 

59.5 

2.644 

1.626 

96.747 

68. 

2.774 

.665 

113.220 

4.25 

4.5 

63. 

2.741 

.655 

104.265 

72. 

2.880 

.697 

122.184 

4.5 

4.75 

66.5 

2.833 

.683 

111.919 

76. 

2.979 

.726 

131.176 

4.75 

5. 

70. 

2.917 

.708 

119.560 

80. 

3.080 

.755 

140.400 

5. 

5.5 

77.- 

3.080 

.755 

135.135 

88. 

3.256 

.804 

158  752 

5.5 

6. 

84. 

3.230 

.797 

150.948 

96. 

3.429 

.852 

177.792 

6. 

6.5 

91. 

3.367 

.835 

166.985 

104. 

3.588 

.894 

196.976 

6.5 

7. 

98. 

3.500 

.870J183.260 

112. 

3.733 

.932 

216.384 

7. 

100 


FLOW    OF    WATER    IN 


TABLE  13 

Channels  having  a  rectangular  cross-section.  Values  of  the  factors 
a  =  area  in  square  feet,  and  r  =  hydraulic  mean  depth  in  feet,  and  also 
vV"and  a\fr  for  use  in  the  formulae 

v  =  c  X  V~r  X  vT  and  Q  =  c  X  a^/r  X  V* 


BED  18  FEET. 

BED  20  FEET. 

Depth 

Depth 

in 
Feet. 

a 

r 

\/r        a\/r 

a 

r 

v/r 

a-v/r 

in 
Feet. 

0.5 

9. 

.526 

.725 

6.525 

10. 

.476 

.690 

6.9001  0  5 

1. 

18. 

.900 

.948 

17.064 

20 

.909 

.953 

19.060    1. 

1.5 

27. 

1.286 

1  .  134 

30  .  620 

30. 

1.305 

1.142 

34.260    1.5 

2. 

36. 

1.636 

1.279 

46.044 

40. 

1.666 

1.290 

51.600   2. 

2.25 

40.5 

1.800 

1  341 

54.310 

45. 

1.836 

.355 

60.975 

2  25 

2.5 

45. 

1.953 

1.397 

62.865 

50. 

2. 

.414 

70.700 

2  5 

2.75 

49.5 

2.109 

1.452 

71.874 

55. 

2.156 

.468 

80.740 

2.75 

3. 

54. 

2.250 

1.500 

81. 

60. 

2.307 

.518 

91.080 

3. 

3.25 

58.5 

2.387 

1.545 

90.382 

65. 

2.457 

.567 

101  .  855 

3.25 

3.5 

63. 

2.520 

1.587 

99.981 

70. 

2.590 

.609 

112  630 

3.5 

3.75 

67.5 

2.646 

1.626 

109.755 

75. 

2.727 

.651 

123.825 

3  75 

4. 

72. 

2.768 

1.663 

119.736 

80. 

2.857 

.690 

135.200 

4. 

4.25 

76.5 

2.892 

1.700 

130  050 

85. 

2.975 

.725 

146.625!  4.25 

4.5 

81. 

3. 

1  .  732 

140.292 

90. 

3.105 

.762 

158.580 

4.5 

4.75 

85.5 

3.109 

1.760 

150.480 

95. 

3.211 

.792 

170.240 

4.75 

5. 

90. 

3.214 

1.792 

161.280 

100. 

3.333 

.825 

182  500 

5. 

5.5 

99. 

3.416 

1.848 

182.952 

110. 

3.553 

.885 

207  .  350 

5.5 

6. 

108. 

3.600 

1.897 

204.876 

120. 

3.750 

.937 

232.440 

6. 

6.5 

117. 

3.779 

1.944 

227  448 

130. 

3.939 

1.984  257.  920J  6.5 

7. 

126. 

3.938 

1.984 

249.984 

140. 

4.116 

2  029 

284.060J  7. 

BED  25  FEET. 

BED  30  FEET. 

Depth 

Depth 

in 
Feet. 

a 

r 

\/r 

ax/?* 

a 

r 

Vr 

a\Jr 

in 

Feet. 

1. 

25. 

.925 

.961 

24.025 

30. 

.938 

.968 

29.040 

1 

1.5 

37.5 

1.338 

1.156 

43.350 

35. 

1.364 

1.170 

40.950 

1.5 

2. 

50. 

1.725 

1.313 

65  650 

60. 

1.764 

.328 

79.680 

2. 

2.25 

56.25 

1.901 

.380 

77.625 

67.5 

1.957 

.391 

93.892 

2.25 

2.5 

62.5 

2.083 

.443 

90.187 

75. 

2.143 

.464 

109.800 

2.5 

2.75 

68.75 

2.255 

.500 

103.  125 

82.5 

2.326 

.525 

125.812 

2.75 

3. 

75. 

2.422 

.556 

116.700 

90. 

2.500 

.581 

142.290 

3. 

3.25 

81.25 

2.579 

.606 

130.487 

97.5 

2.672 

.634 

159.315 

3.25 

3.5 

87.5 

2.734 

.653 

144.637 

105. 

2.835 

.683 

176.715 

3.5 

3.75 

93.75 

2.884 

.699 

159.281 

112  5 

3. 

.732 

194.850 

3.75 

4. 

100. 

3.030 

.746 

174.600 

120. 

3.156 

.776 

213.120 

4. 

4.25 

106.25 

3.166 

.779 

189.019 

127.5 

3.312 

.820 

232.050 

4.25 

4.5 

112.5 

3.308 

.818 

204.525 

135. 

3.456 

1.860 

251.100 

4.5 

4.75 

118.75 

3  327 

.824 

216.600 

142.5 

3.608 

1.899 

270.607 

4.75 

5. 

125. 

3.571 

.890 

236.250 

150. 

3.750 

1.936 

290  400 

5. 

5.5 

137  5 

3.820 

.954 

268.675 

165. 

4.026 

2.006 

330.990 

5.5 

6. 

150. 

4.050 

2.019 

302.850 

180. 

4.286 

2.072 

372.960 

6. 

6.5 

162.5 

4.274 

2.057 

334.262 

195. 

4.544 

2.131 

415.545 

6.5 

7. 

175. 

4.480 

2.117 

370.475 

210. 

4.773 

2.184 

458.640 

7. 

7.5 

187.5 

4.687 

2.165 

405.937 

225. 

5. 

2.235 

502.875 

7.5 

8 

200. 

4.880 

2.209 

441  .  800 

240. 

5.22 

2.284 

548.160 

8. 

OPEN    AND    CLOSED    CHANNELS. 


101 


TABLE    13. 

Channels  having  a  rectangular  cross-section.  Values  of  the  factors 
a  =  area  in  square  feet,  and  r=  hydraulic  mean  depth  in.  feet,  and  also 
\/jr  and  a\/r  for  use  in  the  formulae 

v  =  c  X  V~r  X  \/s  and  Q  =  c  X  a^/r   X  vT 


BED  35  FEET. 


BED  40  FEET. 


Depth 
in 
Feet. 

a 

r 

\/r 

a\/r 

a 

r 

V~ 

Depth 

*VF  &. 

1. 

35. 

.945 

.972 

34. 

40. 

.952 

.975 

39. 

1. 

1.5 

52.5 

1.382 

1.176 

61.7 

60. 

1.398 

1.182 

70.9 

1.5 

2. 

70. 

1  792 

1.338 

93.7 

80. 

1  818 

1.348 

107.8 

2. 

2.25 

78.75 

1.994 

1.412 

111  2 

90. 

2.023 

1.422 

128. 

2  25 

2.5 

87.5 

2.187 

1.482 

129.7 

100. 

2.222 

1.490 

149. 

2.5 

2.75 

96.25 

2.377 

1  542 

148.4 

110. 

2.418 

1.555 

171. 

2.75 

3. 

105. 

2.562 

1.600 

168. 

120. 

2.610 

1.615 

193.8 

3. 

3.25 

113.75 

2.741 

1.655 

188.3 

130. 

2.795 

1.672 

217.4 

3.25 

3.5 

122.5 

2.919 

1.709 

209.4 

140. 

2.982 

1.727 

241.8 

3.5 

3.75 

131  25 

3.071 

1.752 

229.9 

150. 

3.099 

1.760 

264. 

3.75 

4. 

140. 

3.162 

1.778 

248.9 

160 

3.333 

1.826 

292.2 

4. 

4.25 

148.75 

3.421 

1.849 

275. 

170. 

3.505 

1.872 

318.2 

4.25 

4.5 

157.5 

3.579 

1.892 

298 

180. 

3.672 

1.916 

344  .  9 

4  5 

4.75 

166.25 

3.737 

1.933 

321.4 

190. 

3.838 

1.959 

372.2 

4.75 

5. 

175 

3.944 

1.986 

347.6 

200. 

4. 

2. 

400. 

5. 

5.25 

183.75 

4  038 

2.009 

369.2 

210. 

4.158 

2.039 

428.2 

5.25 

5.5 

192.5 

4.177 

2.044 

389. 

220. 

4.314 

2.077 

456.9 

5.5 

5.75 

201.25 

4.328 

2.080 

418.6 

230. 

4.466 

2.113 

486. 

5.75 

6. 

210. 

4.468 

2.114 

444  1 

240. 

4.614 

2.148 

515.5 

6. 

6.25 

218.75 

4.605 

2.146 

469  4 

250. 

4.762 

2  182 

545.5 

6.25 

6.5 

227  5 

4.739 

2.177 

495.3 

260. 

4.906 

2  215 

575.9 

6.5 

6.75 

236.25 

4.871 

2.203 

520.5 

270. 

5.047 

2.246 

606  4 

6.75 

7. 

245. 

5. 

2.236 

547.8 

280. 

5.180 

2.276 

637.3 

7.    • 

7.25 

253.75 

5.126 

2.264 

574.5 

290. 

5.321 

2.306 

668.7 

7.25 

7.5 

262.5 

5  250 

2.291 

601.4 

300. 

5.455 

2.335 

700.5 

7.5 

7.75 

271.25 

5  372 

2.318 

628.8 

310 

5.586 

2.360 

731.6 

7.75 

8. 

280 

5  491 

2.343 

656. 

320. 

5  714 

2.394 

766.1 

8. 

9. 

315. 

5.943 

2.438 

768. 

360. 

6.207 

2.491 

896.8 

9. 

102 


FLOW    OF    WATER    IN 


TABLE   13 

Channels  having  a  rectangular  section.    Values  of  the  factors  a  =  urea  in 
square  feet,  and  r  =  hydraulic  mean  depth  in  feet,  and  also  ^/r  and 
for  use  in  the  formulae 

v  =  c  X  \/r  X  \A~  and  Q  =  c  X  «V>   X  \A' 


BED  50  FEET. 

BED  60  FEET. 

Depth 
in 
Feet. 

a 

T 

Vr 

a^/r 

a 

r 

\/r        a\/r 

Depth 
in 

Feet. 

1. 

50. 

.962 

.980 

49. 

60. 

.968!      .984 

59. 

1. 

2. 

100. 

1.852 

1.360 

136. 

120. 

1.875    1.369 

164.3 

2. 

2.25 

112.5 

2  063 

1.436 

161.5 

135. 

2.093    1.446 

195  2 

2.25 

2.5 

125. 

2.273 

1.507 

188.4 

150. 

2.3081      .519 

227.8 

2.5 

2.75 

137.5 

2.477 

1.574 

216.4 

165. 

2.519 

.587 

261.8 

2.75 

3. 

150. 

2.679 

1.637 

245.5 

180. 

2.727 

.651 

297.2 

3. 

3.25 

162.5 

2.876 

1.696 

275.6 

195. 

2.932 

.712 

333.8 

3.25 

3.5 

175. 

3.069 

1.751 

306.4 

210. 

3.134 

.770 

371.7 

3.5 

3.75 

187.5 

3.261 

1.806 

338.6 

225. 

3.333 

.825 

410.6 

3.75 

4. 

200. 

3.448 

1.857 

371.4 

240. 

3.529 

878 

450.7 

4. 

4.25 

212.5 

3.632 

1.906 

405. 

255. 

3.722 

.929 

491.9 

4.25 

4.5 

225. 

3.814 

1.953 

439.4 

270. 

3.913 

1.978 

534.1 

4.5 

4.75 

237.5 

3.991 

1.997 

474.3 

285. 

4.101 

2.025 

577.1 

4.75 

5. 

250. 

4.167 

2.041 

510.2 

300. 

4.286 

2.073 

621.9 

5. 

5.25 

262.5 

4.339 

2.083 

546.8 

315. 

4.468 

2.114 

665.9 

5.25 

5.5 

275. 

4.507 

2.123 

583.8 

330. 

4.646 

2.155 

711.1 

5.5 

5.75 

287.5 

4.675 

2.162 

621.6 

345. 

4.825 

2.196 

757.6 

5.75 

6. 

300. 

4.839 

2.200 

660. 

360. 

5. 

2.236 

805 

6. 

6.25 

312.5 

5 

2.236 

698.7 

375. 

5.172 

2.274 

852  7 

6.25 

6.5 

325. 

5.158 

2.271 

738.1 

390. 

5.343 

2.311 

901.3 

6.5 

6.75 

337.5 

5.315 

2.305 

777.9 

405. 

5.510 

2.347 

950.5 

6.75 

7. 

350. 

5.470 

2.339 

818.6 

420. 

5.676 

2.382 

1000.4 

7. 

7.25 

362.5 

5.620 

2.350 

851.9 

435. 

5.839 

2.416 

1051. 

7.25 

7.5 

375. 

5.767 

2.401 

900.4 

450. 

6. 

2.450 

1102.5 

7.5 

7.75 

387.5 

5.916 

2.432 

942.4 

465. 

6.158 

2.481 

1153.7 

7.75 

8. 

400. 

6.060 

2.461 

984.4 

480. 

6.316 

2.513 

1206.2 

8. 

8.25 

412.5 

6.103 

2.470 

1018.9 

495. 

6.471 

2.544 

1259.3 

8.25 

8.5 

425. 

6.345 

2.519 

1070.6 

510. 

6.624 

2.574 

1312.7 

8.5 

8.75 

437.5 

6.481 

2.546 

1113.9 

525. 

6.775 

2.603 

1366.6 

8.75 

9. 

450. 

6.619 

2.573 

1157.8 

540. 

6.923 

2  .  633 

1421.8 

9. 

9.25 

462.5 

6.752 

2.598 

1201.6 

555. 

7.010 

2.648 

1475.7 

9.25 

9.5 

475. 

6.883 

2.623 

1245.9 

570. 

7.216 

2.686 

1531  . 

9.5 

9.75 

487.5 

7.014 

2.648 

1290.9 

585. 

7.358 

2,712 

1586.5    9.75 

10. 

500. 

7.145 

2.673 

1336.5 

600. 

7.500 

2.738 

1642.8 

10. 

10.5 

525. 

7.394 

2.719 

1427 

630. 

7.7781  2.789 

1757. 

10.5 

11. 

550. 

7.639 

2.764 

1520. 

660. 

S.049i  2.837 

1872.4 

11. 

12. 

600. 

8.108 

2.847 

1708. 

720. 

8.571i  2.927 

2107  4 

12. 

OPEN    AND    CLOSED    CHANNELS. 


103 


TABLE  14.     V-SHAPED  FLUME,  EIGHT-ANGLED  CKOSS-SECTION. 

Based  on  Kutter's  formula,  with  n—  .013.     Giving  values  of  a,  r  and  c, 
and  also  the  values  of  the  factors  c-y/r  and  ac\/r  for  use  in  the  formulae 
v  =  c\/r  X  -\/s  and  Q  —  ac\/r  X  \/s 

The  constant  factors  c\/r  and  ac\/r  given  in  table  are  substantially 
correct  for  all  slopes  up  to  1  in  2640,  or  2  feet  per  mile. 

These  factors  are  to  be  used  only  where  the  value  of  n,  that  is  the  co- 
efficient of  roughness  of  lining  of  channel  =  .013,  as  in  ashlar  and  well- 
laid  brickwork;  ordinary  metal;  earthenware  and  stoneware  pipe,  in  good 
condition  but  not  new;  cement  and  terra  cotta  pipe,  not  well  jointed  nor 
in  perfect  order,  and  also  plaster  and  planed  wood  in  imperfect  or  inferior 
condition,  and  generally  the  materials  mentioned  with  n  =  .01  when  in 
imperfect  or  inferior  condition 


Depth  of 
water  in  feet. 

a  =  area  in 
square  feet. 

r  =  hydraulic 
mean  depth 
in  feet. 

For  velocity 
c^ 

For  discharge 
ac\/r 

.40 

.16 

.141 

27.07 

4.33 

.5 

25 

.177 

32.54 

8.14 

.6 

.36 

.212 

37.44 

13.48 

.7 

.49 

.247 

42.16 

20.66 

.75 

.56 

.265 

44.55 

24.95 

.8 

.64 

.283 

46.76 

29.92 

.9 

.81 

.318 

51.10 

41.39 

1. 

_ 

.354 

55.63 

55.63    ' 

1.1 

]21 

.389 

59.47 

72. 

1.2 

.44 

.424 

63.28 

91.12 

1.25 

.56 

.442 

65.30 

101.9 

1.3 

.69 

.459 

66.40 

112  2 

1.4 

.96 

.494 

70.93 

139. 

1.5 

2.25 

.530 

74.55 

167.7 

1.6 

2.56 

.566 

78.06 

199.8 

1.7 

2.89 

.601 

81.53 

235.6 

1.75 

3.06 

.618 

83.24 

254.7 

1.8 

3.24 

.636 

85.15 

275.9 

1.9 

3.61 

.672 

90.47 

326.6 

2. 

4. 

.707 

91.50 

366. 

2.1 

4.41 

.743 

94.73 

417.8 

2.2 

4.84 

.778 

97.90 

473.8 

2.25 

5.06 

.795 

99.46 

503.3 

2.3 

5.29 

.813 

101.02 

534.4 

2.4 

5.76 

.849 

104. 

598.9 

2.5 

6.25 

.884 

106.9 

668. 

2.6 

6.76 

.919 

109.9 

742.9 

2.7 

7.29 

.955 

112.7 

821.9 

2.75 

7.56 

.972 

114.2 

863.2 

2.8 

7.84 

.990 

116.2 

910.9 

2.9 

8.41 

1.025 

118.4 

995.8 

3. 

9. 

1.061 

121.2 

1091. 

104 


FLOW    OF    WATER    IN 


TABLE  15. 

Based  on  Kutter's  formula,  with  n  =  .009.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulas 

v  =  c^/rs  =  cX  \/r~  X  \/s~  =  c^/r~  X  \/s~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  fcGt 

1  in  20000=0.264  ft.  per  mile 

1  in  15840=0.3333  ft.  per  mile 

Vr 

s  =  .00005 

s  =  .000063131 

diff. 

diff. 

diff. 

diff. 

in  1661 

c 

.01 

cVr 

.01 

c 

.01 

cV~ 

.01 

.4 

93.4 

1.49 

37.4 

1.68 

97.8 

1.49 

39.1 

1.72 

.4 

.5 

108.3 

1.29 

54.2 

1.85 

112.7 

1.27 

56.3 

1.89 

.5 

.6 

121.2 

1.13 

72.7 

2. 

125.4 

1.10 

75.2 

2.03 

.6 

.7 

132.5 

.99 

92.7 

2.12 

136.4 

.95 

95.5 

2.13 

.7 

.8 

142.4 

.88 

113.9 

2.22 

145.9 

.85 

116.8 

2.21 

.8 

.9 

151.2 

.78 

136.1 

2.29 

154.4 

.75 

138.9 

2.30 

.9 

1. 

159. 

.71 

159. 

2.37 

161.9 

.67 

161.9 

2.35 

1. 

1.1 

166.1 

.64 

182.7 

2.43 

168.6 

.60 

185.4 

2.41 

1.1 

1.2 

172.5 

.58 

207. 

2.48 

174.6 

.54 

209.5 

2.45 

1.2 

1.3 

178.3 

.53 

231.8 

2.52 

180. 

.49 

234. 

2.49 

1.3 

1.4 

183.6 

.48 

257. 

2.57 

184.9 

.45 

258.9 

2.53 

1.4 

1.5 

188.4 

.45 

282.7 

2.59 

189.4 

.42 

284.2 

2.55 

1.5 

1.6 

192.9 

.41 

308.6 

2.63 

193.6 

.38 

309.7 

2.58 

1.6 

1.7 

197. 

.38 

334.9 

2.66 

197.4 

.35 

335.5 

2.60 

1.7 

1.8 

200.8 

.35 

361.5 

2.68 

200.9 

.32 

361.5 

2.63 

1.8 

1.9 

204.3 

.33 

388.3 

2.70 

204.1 

.30 

387.8 

2.64 

1.9 

2. 

207.6 

.31 

415.3 

2.72 

207.1 

.28 

414.2 

2.65 

2. 

2.1 

210.7 

.29 

442.5 

2.74 

209.9 

.26 

440.7 

2.67 

2.1 

2.2 

213.6 

.27 

469.9 

2.75 

212.5 

.24 

467.4 

2.69 

2.2 

2.3 

216.3 

.25 

497.4 

2.77 

214.9 

.23 

494.3 

2.70 

2.3 

2.4 

218.8 

.24 

525.1 

2.78 

217.2 

.21 

521.3 

2.70 

2.4 

2.5 

221.2 

.22 

552.9 

2.79 

219.3 

.20 

548.3 

2.72 

2.5 

2.6 

223.4 

.21 

580.8 

2.81 

221.3 

.20 

575.5 

2.73 

2.6 

2.7 

225.5 

.20 

608.9 

2.81 

223.3 

.17 

602.8 

2.73 

2.7 

2.8 

227.5 

.19 

637. 

2.83 

225. 

.17 

630.1 

2.75 

2.8 

2.9 

229.4 

.18 

665.3 

2.83 

226.7 

.16 

657.6 

2.74 

2.9 

3. 

231.2 

693.6 

228.3 

685. 

3. 

OPKX    AND    CLOSED    CHANNELS. 


105 


TABLE   15. 

Based  011  Kutter's  formula,  with  n  =  .009.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  —  c\/rs  .---  c  X  \//'    X  \A  =  c\/r   X  \A' 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  10000=0.528  ft.  per  mile 

1  in  7500  =  0.704  ft.  per  mile 

\/r 
iia  feet 

8  =  .0001 

s  =  .000133,333 

c 

diff. 
.01 

CVT 

diff. 
.01 

$ 

diff. 
.01 

cVr 

<Lff. 
.01 

.4 

105.5 

1.47 

42.2 

1.79 

109.5 

1.45 

43.8 

1.82 

.4 

.5 

120.2 

1.22 

60.1 

1.93 

124. 

1.20 

62. 

1.96 

.5 

.6 

132.4 

1.25 

79.4 

2.06 

136. 

1.01 

81.6 

2.07 

.6 

.7 

142.9 

.77 

100. 

2.15 

146.1 

.87 

102.3 

2.15 

.7 

.8 

151.9 

.90 

121.5 

2.22 

154.8 

.74 

123.8 

2.22 

.8 

.9 

159.6 

.69 

143.7 

2.28 

162.2 

.65 

146. 

2.27 

.9 

1. 

166.5 

.60 

166.5 

2.33 

168.7 

.57 

168.7 

2.32 

1.1 

172.5 

.54 

189.8 

2.41 

174.4 

.51 

191.9 

2.35 

:  .1 

1.2 

177.9 

.48 

213.9 

2.37 

179.5 

.45 

215.4 

2.39 

.2 

1.3 

182.7 

.44 

237.6 

2.43 

184. 

.41 

239.3 

2.40 

.3 

1.4 

187.1 

.39 

261.9 

2.46 

188.1 

.37 

263.3 

2.44 

.4 

1.5 

191. 

.36 

286.5 

2.49 

191.8 

.33 

287.7 

2.45 

.5 

1.6 

194.6 

.33 

311.4 

2.50 

195.1 

.31 

312.2 

2.47 

.6 

1.7 

197.9 

.30 

336.4 

2.52 

198.2 

.27 

336.9 

2.48 

.7 

1.8 

200.9 

.29 

361.6 

2.54 

200.9 

.26 

361.7 

2.49 

.8 

1.9 

203.8 

.24 

387. 

2.55 

203.5 

.23  i  386.6 

2.51 

.'9 

2. 

206.2 

.24 

412.5 

2.56 

205.8 

.22     411.7 

2.51 

2. 

2.1 

208.6 

.22 

438.1 

2.57 

208. 

.20  i  436.8 

2.53 

2.1 

2.2 

210.8 

.21 

463.8 

2.58 

210. 

.19 

462.1 

2.53 

2.2 

2.3 

212.9 

.19 

489.6 

2.59 

211.9 

.18 

487.4 

2.54 

2.3 

2.4 

214.8 

.18 

515.5 

2.59 

213.7 

.16 

512.8 

2.55 

2.4 

2.5 

216.6 

.17 

541.4 

2.61 

215.3 

.15 

538.3 

2.55 

2.5 

2.6 

218.3 

.15 

567.5 

2.61 

216.8 

.15 

563.8 

2.56 

2.6 

2.7 

219.8 

.15 

593.6 

2.61 

218.3  |      .14 

589.4 

2.56 

2.7 

2.8 

221.3 

.14 

619.7 

2.63 

219.7  !      .12 

615. 

2.57 

2.8 

2.9 

222.7 

.14 

646. 

2.66 

220.9  S      .12 

640.7 

2.57 

2.9 

3.          224.1 

672.6 

i 

222.1  i 

666.4 

3. 

100 


FLOW    OF    WATER    IN 


TABLE  15. 

Based  on  Kutter's  formula,  with  n  =  .009.     Values  of  the  factors  c  and 
for  use  in  the  formula} 

v  =  c\/rs  —  c  X  V'?"   X  V  s  ==  C's/f   X  \A' 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


x/F 

in  feet 

1  in  5000=1.056  ft.  per  mile 

1  in  3333.3=1.584  ft.  per  mile 

xA 

in  feet 

s=.0002 

a  =  .0003 

diff. 

diff. 

diff. 

diff. 

c 

.01 

cVr 

.01 

c           .01 

c^/r 

.0!     1 

.4 

114.1 

1.42 

45.6 

1.86 

117.5 

1.40 

47. 

1.88 

.4 

.5 

128.3 

1.17 

64.2 

1.98 

131.5 

1.14 

65.8 

2. 

.5 

.6 

140. 

.97 

84. 

2.08 

142.9 

.95 

85.8 

2.08 

.6 

.7 

149.7 

.83 

104.8 

2.16 

152.4 

.79 

106.6 

2.16 

.7 

.8 

158. 

.70 

126.4 

2.21 

160.3 

.67 

128.2 

2.21 

.8 

.9 

165. 

.62 

148.5 

2.27 

167. 

.59 

150.3 

2.26 

.9 

1. 

171.2 

.53 

171.2 

2.30 

172.9 

.51 

172.9 

2.29 

1. 

1.1 

176.5 

.47 

194.2 

2.33 

178. 

.44 

195.8 

2.31 

1.1 

1.2 

181.2 

.42 

217.5 

2.36 

182.4 

.40 

218.9 

2.34 

1.2 

1.3 

185.4 

.38 

241.1 

2.38 

186.4 

.35 

242.3 

2.36 

1.3 

1.4 

189.2 

.34 

264.9 

2.40 

189.9 

.32 

265.9 

2.38 

1.4 

1.5 

192.6 

.30 

288.9 

2.41 

193.1 

.29 

289.7 

2.39 

1.5 

1.6 

195.6 

.28 

313. 

2.43 

196. 

.26 

313.6 

2.40 

1.6 

1.7 

198.4 

.26 

337.3 

2.44 

198.6 

.24 

337.6 

2.42 

1.7 

1.8 

201. 

.23 

361.7 

2.45 

201. 

.21 

361.8 

2.42 

1.8 

1.9 

203.3 

.21 

386.2 

2.47 

203.1 

.20 

386. 

2.43 

1.9 

2. 

205.4 

.20 

410.9 

2.46 

205.1 

.19 

410.3 

2.44 

2. 

2.1 

207.4 

.18 

435.5 

2.48 

207. 

.17 

434.7 

2.44 

2.1 

2.2 

209.2 

.17 

460.3 

2.49 

208.7 

.16 

459.1 

2.45 

2.2 

2.3 

210.9 

.16 

485.2 

2.49 

210.3 

.14 

483.6 

2.45 

2.3 

2.4 

212.5 

.15 

510.1 

2.49 

211.7 

.14 

508.1 

2.46 

2.4 

2.5 

214. 

.14 

535. 

2.50 

213.1 

.13 

532.7 

2.46 

2.5 

2.6 

215.4 

.13 

560. 

2.50 

214.4 

.12 

557.3 

2.47 

2.6 

2.7 

216.7 

.12 

585. 

2.51 

215.6 

.11 

582. 

2.47 

2.7 

2.8 

217.9 

.11 

610.1 

2.51 

216.7 

.11 

600.  7 

2.48 

2.8 

2.9 

219. 

.11 

635.2 

2.52 

217.8 

.09 

631.5 

2.47 

2.9 

3. 

220.1 

660.4 

218.7 

656.2 

3. 

OPEN    AND    CLOSED    CHANNELS. 


107 


TABLE   15. 

Based  on  Kutter's  formula,  with  n  =  .009.     Values  of  the  -factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c\/rs  =  c  X  \/f   X  \/a  =  v\/  r   X  \A' 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 

in  feet 

1  in  2500=2.114  ft.  per  mile 

1  in  1000  =  5.28  ft.  per  mile 

•s/r 
in  feet 

s=.0004 

5^.001 

c 

diff. 
.01 

cVr 

diff. 
.01 

c 

diff. 
.01 

cVr 

diff. 
.01 

.4 

119.3 

1.39 

47.7 

1.89 

122.8 

1.37 

49.1 

1.91 

.4 

.5 

133.2 

1.13 

66.6 

1.99 

136.5 

1.09 

68.2 

2.02 

.5 

.6 

144  .  5 

.92 

86.7 

2.09 

147.4 

.89 

88.4 

2.10 

.6 

.7 

153.7 

.78 

107.6 

2.16 

156.3 

.75 

109.4 

2.16 

.7 

.8 

161.5 

.66 

129.2 

2.21 

163.8 

.62 

131. 

2.20 

.8 

.9 

168.1 

.57 

151.3 

2.25 

170. 

.54 

153.        2.24 

.9 

1. 

173.8 

.49 

173.8 

2.28 

175.4 

.47 

175.4 

2  27 

1. 

1.1 

178.7 

.44 

196.6 

2.31 

180.1 

.41 

198.1 

2i29 

1.1 

1.2 

183.1 

.38 

219.7 

2.33 

184.2 

.36 

221. 

2.31 

1.2 

1.3 

186.9 

.34 

243. 

2.35 

187.8 

.32 

244.1 

2.33 

1.3 

1.4 

190.3 

.31 

266.5 

2.36 

191. 

.29 

267.4 

2.34 

1.4 

1.5 

193.4 

.28 

290.1 

2.38 

193.9 

.26 

290.8 

2.36 

1.5 

1.6 

196.2 

.25 

313.9 

2.39 

196.5 

.23 

314.4 

2.36 

1.6 

1.7 

198.7 

.23 

337.8 

2.40 

198.8 

.22 

338. 

2.38 

1.7 

1.8 

201. 

.21 

361.8 

2.40 

201. 

.19 

361.8 

2.37 

1.8 

1.9 

203.1 

.19 

385.8 

2.42 

202.9 

.18 

385.5 

2.39 

1.9' 

2. 

205. 

.18 

410. 

2.42 

204.7 

.16 

409.4 

2.33 

2 

2.1 

206.8 

.16 

434.2 

2.43 

206.3 

.15 

433.2 

2.40 

2^1 

2.2 

208.4 

.15 

458.5 

2.43 

207.8 

.14 

457.2 

2.40 

2.2 

2.3 

209.9 

.14 

482.8 

2.44 

209.2 

.13 

481.2 

2.40 

2^3 

2.4 

211.3 

.13 

507.2 

2.44 

210.5 

.13 

505.2 

2.42 

2.4 

2.5 

212.6 

.12 

531.6 

2.44 

211.8 

.11 

529.4 

2.41 

2.5 

2.6 

213.8 

.12 

556. 

2.45 

212.9 

.11 

553.5 

2.42 

2.6 

2.7 

215. 

.11 

580.5 

2.45 

214. 

.10 

577.7 

2.42 

2.7 

2.8 

216.1 

.10 

605. 

2.46 

215. 

.09 

601.9 

2.42 

2.8 

2.9 

217.1 

.09 

629.6 

2.45 

215.9 

.09 

626.1 

2.42 

2.9 

3. 

218. 

654.1 

1 

216.8 

650.3 

3. 

108 


FLOW    OF    "WATER    IN 


TABLE  16. 

Based  on  Kutter's  formula,  with  n=.Ql.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c\/rs  —  c  X  \/r   X  \A  =  c\/r   X  \/s~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-emcieiit  as  1  in  1000. 


-v/r 

in  feet 

1  in  20000=.  264  ft.  per  mile 

1  in  15840=.  3333  ft.  per  mile 

Vr 
in  feet 

a  =  .00005 

s=.  000063131 

c 

diff. 
.01 

cVr 

diff. 
.01 

c 

diff. 
.01 

cVr 

diff. 
.01 

.4 

81. 

1.34 

32.4 

1.48 

84.8 

1.34 

33.9 

.52 

.4 

.5 

94.4 

1.16 

47.2 

1.64 

98.2 

1.15 

49.1 

.67 

.5 

.6 

106. 

1.03 

63.6 

1.78 

109.7 

1.01 

65.8 

.81 

.6 

.7 

116.3 

.92 

81.4 

1.90 

119.8 

.89 

83.9 

.91 

.7 

.8 

125.5 

.82 

100.4 

1.99 

128.7 

.79 

103. 

.99 

.8 

.9 

133.7 

.73 

120.3 

2.07 

136.6 

.70 

122.9 

2.07 

.9 

1. 

141. 

.66 

141. 

2.14 

143.6 

.63 

143.6 

2.13 

1. 

1.1 

147.6 

.61 

162.4 

2.20 

149.9 

.57 

164.9 

2.18 

1.1 

1.2 

153.7 

.55 

184.4 

2.25 

155.6 

.51 

186.7 

2.23 

1.2 

1.3 

159.2 

.50 

206.9 

2.30 

160.7 

.47 

209. 

2.26 

1.3 

1.4 

164.2 

.46 

229.9 

2.33 

165.4 

.44 

231.6 

2.30 

1.4 

1.5 

168.8 

.43 

253.2 

2.38 

169.8 

.39 

254.6 

2.33 

1.5 

1.6 

173.1 

.40 

277. 

2.40 

173.7 

.37 

277.9 

2.36 

1.6 

1.7 

177.1 

.36 

301. 

2.43 

177.4 

.33 

301.5 

2.38 

1.7 

1.8 

180.7 

.34 

325.3 

2.45 

180.7 

.32 

325  .  3 

2.41 

1.8 

1.9 

184.1 

.32 

349.8 

2.48 

183.9 

.29 

349.4 

2.42 

1.9 

2. 

187.3 

.30 

374.6 

2.50 

186.8 

.27 

373.6 

2.44 

2 

2.1 

190.3 

.28 

399.6 

2.52 

189.5 

.25 

398. 

2.45 

2J 

2.2 

193.1 

.26 

424.8 

2.53 

192. 

.24 

422.5 

2.47 

2.2 

2.3 

195.7 

.24 

450.1 

2.55 

194.4 

.22 

447.2 

2.48 

2.3 

2.4 

198.1 

.24 

475.6 

2.56 

196.6 

.22 

472. 

2.49 

2.4 

2.5 

200.5 

.22 

501.2 

2.57 

198.8 

.19 

496.9 

2.50 

2.5 

2.6 

202.7 

.20 

526.9 

2.59 

200.7 

.19 

521.9 

2.51 

2.6 

2.7 

204.7 

.20 

552.8 

2.60 

202.6 

.18 

547. 

2.52 

2.7 

2.8 

206.7 

.19 

578.8 

2.61 

204.4 

.16 

572.2 

2.53 

2.8 

2.9 

208.6 

.17 

604.9 

2.61 

206. 

.16 

597.5 

2.54 

2.9 

3. 

210.3 

631. 

207.6 

622.9 

3. 

OPEN    AND    CLOSED    CHANNELS. 


109 


TABLE   16. 

Based  on  Kutter's  formula,  with  ?i  — .01.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulas 

v  —  Cv/rs  =  c  X  \/-r   X  \A'   —  c\/r    X  \/s 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  10000^.528  ft.  per  mile 

1  in  7500  =  .704  ft.  per  mile 

Vr 

in  feet 

a  —  .0001 

*  ==  .000133333 

c 

diff. 
.01 

cVr 

diff.  I 
.01 

c 

diff. 
.01 

cv/r 

diff. 
.01 

.4 

91.4 

1.34 

36.6 

1:58 

94.9 

1.32 

38. 

1.61 

.4 

.5 

104.8 

1.12 

52.4 

1.72  ! 

108.1 

1.11 

54.1 

1.74 

.5 

.6 

116. 

.97 

69.6 

1.84 

119.2 

.94 

71.5 

1.85 

.6 

.7 

125.7 

.83 

88. 

1.92 

128.6 

.80 

90. 

1.93 

.7 

.8 

134. 

.73 

107.2 

2. 

136.6 

.70 

109.3 

2. 

.8 

.9     i  141.3 

.65 

127.2 

2.06  i 

143.6 

.02 

129.3 

2.05 

.9 

1. 

147.8 

.57 

147.8 

2.11  1 

149.8 

.54 

149.8 

2.10 

1. 

.1 

153.5 

.52 

168.9 

2.15 

155  .  2 

.49 

170.8 

2.13 

1.1 

.2 

158.7 

.46 

190.4 

2.18 

160.1 

.43 

192.1 

2.16 

1.2 

.3 

163.3 

.41 

212  2 

2  22 

164.4 

.39 

213.7 

2.19 

1.3 

.4 

167.4 

.38 

234!  4 

2^24 

168.3 

.36 

235.6 

2.22 

1.4 

.5 

171.2 

.35 

256.8 

2.27 

171.9 

.32 

257.8 

2.23 

1.5 

.6 

174.7 

.32 

279.5 

2.29 

175.1 

.29 

280.1 

2.26      1.6 

.7 

177.9 

.29 

302.4 

2.30 

178. 

.27 

302  .  7 

2.26 

1.7 

.8 

180.8 

.27 

325.4 

2.32  ; 

180.7 

.25 

325.3 

2.28      1  8 

.9 

183.5 

.25 

348.6 

2.34 

183.2 

.23 

348.1 

2.30      1.9   • 

2 

186. 

.23 

372. 

2.34 

185.5 

.22 

371.1 

2  .  30      2 

l'.\ 

188.3 

.22 

395.4 

2.36 

187.7 

.20 

394.1 

2.31      2.1 

2.2 

190.5 

.20 

419. 

2.37 

189.7 

.18 

417.2 

2.32      2  2 

2.3 

192.5 

.19 

442.7 

2.37 

191.5 

.17 

440.4 

2.33      2  3 

2.4 

194.4 

.17 

466.4 

2.39 

193.2 

.16 

463.7 

2.34      2.4 

2.5 

196.1 

.17 

490.3 

2.39 

194.8 

.15 

487.1      2.34     2  5 

2.6 

197.8 

.15 

514.2 

2.40 

196.3 

.15 

510.5  |  2.35      2.6 

2.7 

199.3 

.15 

538.2 

2.41 

197.8 

.13 

534. 

2.35  i  2.7 

2.8 

200.8 

.14 

562.3 

2.41 

199.1 

.13 

557.5 

3.36 

2.8 

2.9 

202.2 

.13 

586.4 

2.42 

200.4 

.12 

581.1 

2.36 

2.9 

3. 

203.5 

610.6 

201.6 

604.7 

3. 

110 


FLOW    OP    WATER    IN 


TABLE    16. 

Based  on  Kutter's  formula,  with  ??  =  .01.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c\/ra  =  c  X  \/r   X  \A'  ==  c\/r   X  %A' 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 

1  in  5000=1.056  ft.  per  mile 

1  in  3333.3=1.584  ft.  per  mile 

Vr 

8=  .0002 

s=.0003 

in  feet 

diff. 

diff. 

diff. 

diff. 

in  feet 

c 

.01 

cv/r 

.01 

c 

.01 

cx/r 

.01 

A          99. 

1.30  i     39.8 

1.64 

102. 

1.29 

40.8 

1.67 

.4 

.5     !   112. 

1.08 

56. 

1.77 

114.9 

1.06 

37.5 

1.78 

.5 

.6     !   122.8 

.91 

73.7 

1.86 

125.5 

.88 

75.3 

1.87 

.6 

.7     !   131.9 

.77 

92.3 

1.94 

134.3 

.75 

94. 

1.94        .7 

.8 

139.6 

.67 

111.7 

2. 

141.8 

.64 

113.4 

1.99 

.8 

.9 

146.3 

.58 

131.7 

2.04 

148.2 

.55 

133.3 

2.04 

.9 

1. 

152.1 

.51 

152.1 

2.08 

153.7 

.51 

153.7 

2.10 

1.1 

157.2 

.45 

172.9 

2.  12 

158.8 

.41 

174.7 

2.08        .1 

1.2 

161.7 

.41 

194.1 

2.'  14 

162.9 

.38 

195.5 

2.12        .2 

1.3 

165.8 

.36 

215.5 

2.17 

166.7 

.34 

216.7 

2.13        .3 

1.4 

169.4 

.33 

237.2 

2.18 

170.1 

.31 

238. 

2.18  [     .4 

1.5 

172.7 

.30 

259. 

2.20 

173.2 

.28 

259.8 

2.18 

.5 

1.6 

175.7 

.27 

281. 

2.22 

176. 

.25 

281.6 

2.19 

1.6 

1.7 

178.4 

.24 

303.2 

2~23 

178.5 

.24 

303.5 

2.20 

1.7 

1.8 

180.8 

.23 

325.5 

2.24 

180.9 

.21 

325.5 

2  22 

1.8 

1.9 

183.1 

.21 

347.9 

2.25 

183. 

.19 

347.7 

2.22 

1.9 

2. 

185.2 

.20 

370.4 

2.26 

184.9 

.18 

369.9 

2.23 

2. 

2.1 

187.2 

.18 

393. 

2.27 

186.7 

.17 

392.2 

2.23 

2.1 

2.2 

189. 

.16 

415.7 

2  27 

188.4 

.16 

414.5 

2.24 

2.2 

2.3 

190.6 

.16 

438.4 

2^28 

190. 

.14 

436.9 

2.25 

2.3 

2.4 

192.2 

.14 

461.2 

2.29 

191.4 

.14 

459.4 

2.25 

2.4 

2.5 

193.6 

.14 

484.1 

2.29 

192.8 

.12 

481.9 

2.26 

2.5 

2.6 

195. 

.13 

507. 

2.30 

194. 

.12 

504.5 

2.26 

2.6 

2.7 

196.3 

.12 

530. 

2.30 

195.2 

.11 

527.1 

2.26 

2.7 

2.8 

197.5 

.11 

553. 

2.30 

196.3 

.11 

549.7 

2.27 

2.8 

2.9 

198.6 

.11 

576. 

2.31 

197.4 

.10 

572.4 

2.27 

2.9 

3. 

199.7 

599.1 

198.4 

595.1 

3. 

OPEN    AND    CLOSED    CHANNELS. 


Ill 


TABLE  16. 

Based  on  Kutter's  formula,  with  n—  .01.     Values   of  the  factors  c  and 
c\/r  for  use  in  the  formulas 


v  =  c^/rs  =1  c  X  v/r    X  V*=  <*\/r    X 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  2500=2.114  ft.  per  mile. 

1  in  1000  =  5.  28  ft.  per  mile 

v/r 
in  feet 

0  =B  .0004 

*=.001 

c 

diff. 
.01 

<Vr 

diff. 
.01 

c 

diff. 
.01 

C\/r 

diff. 
.01 

.4 

103.7 

1.28 

41.5 

1.67 

106.9 

1.26 

42.7 

1.70 

.4 

.5 

116.5 

1.04 

58.2 

1.79 

119  5 

1.01 

59.7 

1.80 

.5 

.6 

126.9 

.87 

76.1 

1.88 

129.6 

.84 

77.7 

1.89 

.6 

.7 

135.6 

.73 

94.9 

1.94 

138. 

.70 

96.6 

1.94 

.7 

.8 

142.9 

.62 

114.3 

1.99 

145. 

.60 

116. 

1.99 

.8 

.9 

149.1 

.55 

134.2 

2.04 

151. 

.52 

135.9 

2.03 

.9 

1. 

154.6 

.47 

154.6 

2.06 

156.2 

.45, 

156.2 

2.06 

1. 

1.1 

159.3 

.42 

175.2 

2.10 

160.7 

.39 

176.8 

2.07 

1.1 

1.2 

163.5 

.37 

196.2 

2.11 

164.6 

.35 

197.5 

2.10 

1.2 

.3 

167.2 

.33 

217.3 

2.14 

168.1 

.31 

218.5 

2.11 

1.3 

.4 

170.5 

.28 

238.7 

2.15 

171.2 

.28 

239.6 

2.14 

1.4 

.5 

173.5 

.27 

260.2 

2.17 

174. 

.25 

261. 

2.14 

1.5 

.6 

176.2 

.24 

281.9 

2.18 

176.5 

.23 

282.4 

2.16 

1.6 

.7 

178.6 

.23 

303.7 

2.19 

178.8 

.21 

304. 

2.16 

1.7 

.8 

180.9 

.20 

325.6 

2.19 

180.9 

.19 

325.6 

2.17 

1.8 

.9 

182.9 

.19 

347.5 

2.21 

182.8 

.17 

347.3 

2.17 

1.9 

2.       j   184.8 

.17 

369.6 

2.21 

184.5 

.16 

369. 

2.18 

2 

2.1 

186.5 

.16 

391.7 

2.22 

186.1 

.15 

390.8 

2.19 

2!l 

2.2 

188.1 

.15 

413.9 

2.23 

187.6 

.14 

412.7 

2.20 

2.2 

2.3 

189.6 

.14 

436.2 

2.22 

189. 

.13 

434.7 

2.20 

2.3 

2.4 

191. 

.13 

458.4 

2.24 

190.3 

.12 

456.7 

2.20 

2.4 

2.5 

192.3 

.12 

480.8 

2.24 

191.5 

.11 

478.7 

2.21 

2.5 

2.6 

193.5 

.12 

503.2 

2.24 

192.6 

.11 

500.8 

2.22 

2.6 

2.7 

194.7 

.10 

525.6 

2^25 

193.7 

.10 

523. 

2^21 

2.7 

2.8 

195.7 

.10 

548.1 

2.24 

194.7 

.09 

545.1 

2.21 

2.8 

2.9  ' 

196.7 

.10 

570.5 

2.26 

195.6 

.08 

567.2 

2.20        2.9 

3. 

197.7 

593.1 

196.4 

589.2 

3. 

112 


FLOW    OF    WATER    IN 


TABLE    17. 

Based  on  Kutter's  formula,  with  n  ~  .011.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulas 


v  =  c^/rs  —  c  X  \/r   X  \A  =  c\/r   X  v7*1 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  20000=  .264  ft.  per  mile  |  1  in  15S40=.3333  ft.  per  mile 

Vr 
in  feet 

8  =  .00005 

a=.  0000631  31 

c 

diff. 
.01 

.  c\/r 

cL'ff. 
.01 

c 

diff. 
.01 

cx/r 

cliff. 
.01 

.4 

71.1 

1.22 

28.5 

1.31 

74.5 

1.21 

29.8 

1.35 

.4 

.5 

83.3 

1.07 

41.6 

1.48 

86.6 

1.06 

43.3 

1.50 

.5 

.6 

94. 

.95 

56.4 

.60 

97.2 

.94 

58.3 

1.63 

.6 

.7 

103.5 

.84 

72.4 

.71 

106.6 

.82 

74.6 

1.72 

.7 

.8 

111.9 

.76 

89.5 

.81 

114.8 

.74 

91.8 

1.81 

.8 

.9 

119.5 

.69 

107.6 

.88 

122  2 

.66 

109.9 

1.89 

.9 

126.4 

.63 

126.4 

.95 

128^8 

.59 

128.8 

1.94 

1. 

1 

132.7 

.57 

145.9 

2.02 

134.7 

.54 

148.2 

1.99 

1.1 

.2 

138.4 

.52 

.  166.1 

2.06 

140.1 

.50 

168.1 

2.05 

1.2 

.3 

143.6 

.48 

186.7 

2.11 

145.1 

.45 

188.6 

2.08 

1.3 

.4 

148.4 

.44 

207.8 

2.14 

149.6 

.41 

209.4 

2.11 

1.4 

.5        152.8 

.41 

229.2 

2.19 

153.7 

.38 

230.5 

2.15 

1.5 

.6 

156.9 

.38 

251.1 

2.21 

157.5 

.35 

252. 

2.17 

1.6 

.7 

160.7 

.36 

273.2 

2.26 

161. 

.33 

273.7 

2.20 

1.7 

.8 

164.3 

.33 

295.7 

2  27 

164.3 

.30 

295.7 

2.22 

1.8 

.9 

167.6 

.30 

.318.4      2.29 

167.3 

.29 

317.9 

2.24 

1.9 

2. 

170.6 

.29 

341.3 

2.31 

170.2 

.26 

340.3 

2.26 

2 

2.1 

173.5 

.28 

364.4 

2.34 

172.8 

.25 

362.9 

2.27 

2.1 

2.2 

176.3 

.25 

387.8 

2.34 

175.3 

.23 

385.6 

2.29 

2.2 

2.3 

178.8 

.24 

411.2 

2.37 

177.6 

.22 

408.5 

2.30 

2!3 

2.4 

181.2 

.23 

434.9 

2.39 

179.8 

•21 

431.5 

2.31 

2.4 

2.5 

183.5 

.21 

458.7 

2.38 

181.9 

.19 

454.6 

2.32 

2.5 

2.6 

185.6 

.20 

482.6 

2.41 

183.8 

.18 

477.8 

2.34 

2.6 

2.7 

187.6 

.20 

506.7 

2.41 

185.6 

.18 

501.2 

2.34 

2.7 

2  8 

189.6 

.18 

530.8 

2.43 

187.4 

.16 

524.6 

2.35 

2.8 

2.9 

191.4 

.18 

555.1 

2.45 

189. 

.16 

548.1 

2.36 

2.9 

3. 

193.2 

579.6 

190.6 

571.7 

3. 

OPEN    AND    CLOSED    CHANNELS . 


113 


TABLE    17. 

Based  on  Kutters  formula,  with  n  =  .011.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  fornrnlte 

X  \/!T  ~  c\/r~  X 


v  —  c-srs    -—  c  X 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


v/r 

1  in  10000=.52S  ft.  per  mile 

1  in  7500  ~  .704  ft.  per  mile 

Vr 

*=.0001 

s  ~  .000133333 

in  feet 

diff. 

diff. 

diff. 

diff. 

in  feet 

c 

.01 

c*Jr 

.01 

c 

.01 

cvr 

.01 

.4 

80.3 

1.22 

32.1 

.41 

83.5 

1.21 

33.4 

1.44 

.4 

.5 

92.5 

1.04 

46.2 

.55 

95.6 

1.02 

47.8 

1.57 

.5 

.6 

102.9 

.89 

61.7 

.65 

105.8 

.87 

63.5 

1.66 

.6 

.7 

111.8 

.78 

78.2 

.74 

114.5 

.77 

80.1 

1.76 

.7 

.8 

119.6 

.69 

95.6 

.82 

122.2 

.65 

97.7 

1.81 

.8 

.9 

126.5 

.61 

113.8 

.88 

128.7 

.59 

115.8 

1.88 

.9 

1. 

132.6 

.55 

132.6 

.93 

134.6 

.51 

134.6 

1.91 

1. 

1.1 

138.1 

.49 

151.9 

.97 

139.7 

.47 

153.7 

1.96 

1.1 

1  2 

143. 

.44 

171.6 

2. 

144.4 

.41 

173.3 

1.97 

1.2 

i!s 

147.4 

.40 

191.6 

2.03 

148.5 

.38 

193. 

2.02 

1.3 

1.4 

151.4 

.37 

211.9 

2.07 

152.3 

.34 

213.2 

2.03 

1.4 

1.5 

155.1 

.33 

232.6 

2.08 

155  .  7 

.32 

233.5 

2.07 

1.5 

1.6 

158.4 

.31 

253.4 

2.11 

158.9 

.28 

254.2 

2.07 

1.6 

1.7 

161.5 

.28 

274.5 

2.12 

161.7 

.27 

274.9 

2.10 

1.7 

1.8 

164.3 

.27 

295.7 

2.16 

164.4 

.24 

295.9 

2.10 

1.8 

1.9 

167. 

.24 

317.3 

2.15 

166.8 

.22 

316.9 

2.11 

1.9 

2. 

169.4 

.23 

338.8 

2.18 

169. 

.21 

338. 

2.13 

2. 

2.1 

171.7 

.21 

360.6 

2.18 

171.1 

.20 

359.3 

2.15 

2.1 

2.2 

173.8 

.19 

382.4      2.17 

173.1 

.18 

380.8 

2.15 

2.2 

2.3 

175.7 

.19 

404.1 

2.21 

174.9 

.17 

402.3 

2.15 

2.3 

2.4 

177.6 

.17 

426.2 

2.20 

176.6 

.16 

423.8 

2.17 

2.4 

2.5 

179.3 

.17 

448.2 

2.24 

178.2 

.15 

445.5 

2.17 

2.5 

2.6 

181. 

.15 

470.6 

2.21 

179.7 

.14 

467.2 

2.18 

2.6 

2.7 

182.5 

.15 

492.7 

2.25  It   181.1 

.13 

489. 

2.17 

2.7 

2.8 

i  184. 

.13 

515.2 

2.22    1   182.4 

.13 

510.7 

2.20 

2.8 

2.9 

185.3 

.13 

537  .  4 

2.24  |    183.7 

.11 

532.7 

2.17 

2.9 

3. 

186.6 

:  559.8 

184.8 

554.4 

3. 

114 


FLOW    OP    WATER    IN 


TABLE    17. 

Based  on  Kutter's  formula,  with  w  =  .011.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  cx/rs  =  c  X  \/'~  X  \A~—  CvA7  X  \/s~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1-  in  1000. 


Vr 

1  in  5000=1.056  ft.  per  mile 

1  in  3333.3=1.584  ft.  per  mile 

Vr 

a  =  .0002 

s  =  .0003 

in  feet 

d  iff. 

diff. 

diff. 

diff. 

in  feet 

c 

.01 

cVr 

.01 

c 

.01 

c^r 

.01 

.4 

87-1 

1.19 

34.8 

1.47 

89.8 

1.18 

35.9 

1.49 

.4 

.5 

99. 

1. 

49.5 

1.59 

101.6 

.99 

50.8 

.61 

.5 

.6 

109. 

.85 

65.4 

1.69 

111.5 

.82 

66.9 

.69 

.6 

.7 

117.5 

.73 

82.3 

1.75 

119.7 

.71 

83.8 

.76 

.7 

.8 

124.8 

.63 

99.8 

1.82 

126.8 

.61 

101.4 

.82 

.8 

.9 

131.1 

.55 

118. 

1.86 

132.9 

.53 

119.6 

.86 

.9 

1 

136.6 

.49 

136.6 

1.91 

138.2 

.46 

138.2 

.89 

1.1 

141.5 

.44 

155.7 

1.93 

142.8 

.41 

157.1 

.92 

.1 

1.2 

145.9 

.39 

175. 

1.97 

146.9 

.37 

176.3 

.95 

2 

1.3 

149.8 

.35 

194.7 

1.99 

150.6 

.34 

195.8 

.97 

.3 

1.4 

153.3 

.31 

214.6 

2.01 

154. 

.29 

215.5 

.99 

.4 

1.5 

156.4 

.29 

234.7 

2.02 

156.9 

.28 

235.4 

2.01 

.5 

1.6 

159.3 

.27 

254.9 

2.04 

159.7 

.24 

255.5 

2.01 

.6 

1.7 

162. 

.24 

275.3 

2.06 

162.1 

.23 

275.6 

2.03 

l^r 
.  / 

1.8 

164.4 

.22 

295.9 

2.07 

164.4 

.21 

295.9 

2.04 

.8 

1.9 

166.6 

.21 

316.6 

2.07 

166.5 

.19 

316.3 

2.05 

.9 

2. 

168.7 

.19 

337.3 

2.09 

168.4 

.18 

336.8 

2.06 

2. 

2.1 

170.6 

.17 

358.2 

2.09 

170.2 

.16 

357.4 

2.06 

2.1 

2.2 

172.3 

.17 

379.1 

2.11 

171.8 

.16 

378. 

2.06 

2.2 

2.3 

174. 

.15 

400.2 

2.11 

173.3 

.15 

398.7 

2.07 

2.3 

2.4 

175.5 

.15 

421.3 

2.11 

174.8 

.13 

419.5 

2.08 

2.4 

2.5 

177. 

.13 

442.4 

2.12 

176.1 

.13 

440.3 

2.08 

2.5 

2.6 

178.3 

.13 

463.6 

2.13 

177.4 

.11 

461.1 

2.09 

2.6 

2.7 

179.6 

.12 

484.9 

2.12 

178.5 

.11 

482. 

2.10 

2.7 

2.8 

180.8 

.11 

506.1 

2.14 

179.6 

.11 

503. 

2.10 

2.8 

2.9 

181.9 

.11 

527.5 

2.14 

180.7 

.09 

524. 

2.09 

2.9 

3. 

183. 

548.9 

181.6 

544.9 

3. 

OPEN    AND    CLOSED    CHANNELS. 


115 


TABLE  17. 

Based  on  Kutter's  formula,  with  n  =  .011.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c-v/rx  —  c  X  \/r~  X  \/*~  =  c-^/7~  X  \/$~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


N/r 

1  in  2500—2.114  ft.  per  mile 

1  in  1000=5.28  ft.  per  mile 

Vr 

s=.0004 

*  =  .001 

in  feet 

diff. 

diff. 

diff. 

diff. 

in  feet 

c 

.01 

c\/r 

.01 

c 

.01 

CN/F 

.01 

.4 

91.3 

1.18 

36.5 

1.50 

94.1 

1.16 

37.6 

1.52 

.4 

.5 

103.1 

.97 

51.5 

1.62 

105.7 

.95 

52.8 

1.63 

.5 

.6 

112.8 

.82 

67.7 

1.70 

115.2 

.79 

69.1 

1.71 

.6 

.7 

121. 

.69 

84.7 

1.76 

123.1 

.67 

86.2 

1.76 

.7 

.8 

127.9 

.59 

102.3 

1.81 

129.8 

.57 

103.8  - 

1.81 

.8 

.9 

133.8 

.52 

120.4 

1.86 

135.5 

.49 

121.9 

1.85 

.9 

1. 

139. 

.46 

139. 

1.89 

140.4 

.43 

140.4 

1.88 

1. 

1.1 

143.6 

.40 

157.9 

1.92 

144.7 

.39 

159.2 

1.91 

1.1 

1.2 

147.6 

.36 

177.1 

1.94 

148.6 

.34 

178.3 

1.93 

1.2 

1.3 

151.2 

.32 

196.5 

1.96 

152. 

.30 

197.6 

1.94 

.3 

1.4 

154.4 

.29 

216.1 

1.98 

155. 

.27 

217. 

1.95 

.4 

1.5 

157.3 

.26 

235.9 

2. 

157.7 

.25 

236.5 

1.98 

.5 

1.6 

159  .  9 

.24 

255.9 

2. 

160.2 

.22 

256.3 

1.98 

.6 

1.7 

162.3 

.22 

275.9 

2.02 

162.4 

.20 

276.1 

1.98 

.7 

1.8 

164.5 

.20 

296.1 

2.02 

164.4 

.19 

295.9 

2.01 

1.8 

1.9 

166.5 

.18 

316.3 

2.04 

166.3 

.17 

316. 

2. 

1.9 

2. 

168.3 

.18 

336.7 

2.04 

168. 

.16 

336. 

2.01 

2. 

2.1 

170.1 

.15 

357.1 

2.05 

169.6 

.15 

356.1 

2.03 

2.1 

2.2 

171.6 

.15 

377.6 

2.05 

171.1 

.13 

376.4 

2.01 

2.2 

2.3 

173.1 

.14 

398.1 

2.07 

172.4 

.13 

396.5 

2.04 

3.3 

2.4 

174.5 

.13 

418.8 

2.06 

173.7 

.12 

416.9 

2.03 

2.4 

2.5 

175.8 

.12 

439.4 

2.07 

174.9 

.11 

437.2 

2.04 

2.5 

2.6 

177. 

.11 

460.1 

2.07 

176. 

.10 

457.6 

2.04 

2.6 

2.7 

178.1 

.10 

480.8 

2.08 

177. 

.10 

478. 

2.04 

2.7 

2.8 

179.1 

.10 

501.6 

2.08 

178. 

.10 

498.4 

2.03 

2.8 

2.9 

180.1 

.10 

522.4 

2.08 

178.9 

.09 

518.7 

2.06 

2.9 

3. 

181.1 

543.2 

179.8 

539.3 

3. 

116 


FLOW    OF    WATER    IN 


TABLE    18. 

Based  on  Kutter's  formula,  with  w=.012.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formula 


•v  =  c^/rs  =  c  X  \/r   X  V*  =  c\/     X  \/ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr     i 
in  feet 

1  in  20000=.  264  ft.  per  mile 

1  in  15840=  .3333  ft.  per  mile 

Vr 
in  feet 

*  =  .00005 

s=.  000063131 

c 

diff. 
.01 

cVr 

diff. 
.01 

c 

diff. 
.01 

c\/r 

diff. 
.01 

.4 

63.2 

1.11 

25.3 

1.19 

66.1 

1.J2 

26.4 

1.22 

.4 

.5 

74.3 

.98 

37.2 

1.33 

77.3 

.98 

38.6 

1.36 

.5 

.6 

84.1 

.88 

50.5 

.45 

87.1 

.86 

52.2 

1.48 

.6 

.7 

92.9 

.79 

65. 

.57 

95.7 

.77 

67. 

1.57 

.7 

.8 

100.8 

.72 

80.7 

.65 

103.4 

.69 

82.7 

1.66 

,8 

.9 

108. 

.64 

97.2 

.72 

110.3 

.63 

99.3 

1.73 

.9 

114.4 

.59 

114.4 

.80 

116.6 

.56 

116.6 

1.78 

1. 

.1 

120.3 

.54 

132.4 

.85 

122.2        .52 

134.4 

1.85 

1.1 

.2 

125.7 

.50 

150.9 

.90 

127.4 

.47 

152.9 

1.88 

.2 

.3 

130.7 

.46 

169.9 

1.95 

132.1 

.43 

171.7 

1.92 

.3 

.4 

135.3 

.42 

189.4 

1.99 

136.4 

.39 

190.9 

1.95 

.4 

.5 

139.5 

.40 

209.3 

2.03 

140.3 

.37 

210.4 

2. 

.5 

.6 

143.5 

.36 

229.6 

2.05 

144. 

.34 

230.4 

2.02 

.6 

.7 

147.1 

.35 

250.1 

2.09 

147.4 

.32 

250.6 

2.05 

1.7 

1.8 

150.6 

.31 

271. 

2.11 

150.6 

.29 

271.1 

2.05 

1.8 

1.9 

153.7 

.30 

292.1 

2.14 

153.5 

.28 

291.6 

2.10 

1.9 

2. 

156.7 

.29 

313.5 

2.16 

156.3 

.27 

312.6 

2.13 

2 

2.1 

159.6 

.26 

335.1 

2.17 

159. 

.23 

333.9 

2.09 

2^1 

2.2 

162.2 

.25 

356.8 

2.20 

161.3 

.23 

354.8 

2.15 

2.2 

2.3 

164.7 

.23 

378.8 

2.21 

163.6 

22 

376.3 

2.16 

2.3 

2.4 

167. 

.23 

400.9 

2.22 

165.8 

.19 

397.9 

2.13 

2.4 

2.5 

169.3 

.21 

423.1 

2.25 

167.7 

.19 

419.2 

2.18 

2.5 

2.6 

171.4 

.20 

445.6 

2.25 

169.6 

.18 

441. 

2.18 

2.6 

2.7 

173.4 

.19 

468.1 

2.26 

171.4 

.17 

462.8 

2.19 

2.7 

2.8 

175.3 

.18 

490.7 

2.28 

173.1 

.17 

484.7 

2.22 

2.8 

2.9 

177.1 

.17 

513.5 

2.28 

174.8 

.15 

506.9 

2.20 

2.9 

3. 

178.8 

536.3 

176.3 

528.9 

3. 

OPEN    AND    CLOSED    CHANNELS. 


117 


TABLE  18. 

Based  on  Kutter's  formula,  with  n  =  .012.     Values  of  the  factors  c  and 
/T  for  use  in  the  formulae 


v  —  c^/rs    =  c  X  \/r~  X  \/s~  =  c\fr~  X 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  10000=.528  ft.  per  mile 

1  in  7500  =  .704  ft.  per  mile 

Vr 

in  feet 

s  =  .0001 

,9  =  .000133333 

c 

diff. 
.01 

cVr 

diff. 
.01 

c 

diff. 
.01 

cv/r 

diff. 
.01 

.4 

71.4 

1.11 

28.5 

1.27 

74.2 

1.11 

29.7 

.29 

.4 

.5 

82.5 

.96 

41.2 

1.40 

85  3 

.95 

42.6 

.43 

.5 

.6 

92.1 

.84 

55.2 

1.51 

94.8 

.82 

56.9 

.52 

.6 

.7 

100.5 

.74 

70.3 

1.60 

103. 

.71 

72.1 

.60 

.7 

.8 

107.9 

.65 

86.3 

1.66 

110.1 

.63 

88.1 

.66 

.8 

.9 

114.4 

.57 

102.9 

1.72 

116.4 

.55 

104.7 

.72 

.9 

1. 

120.1 

.52 

120.1 

1.77 

121.9 

50 

121.9 

.77 

1 

1.1 

125.3 

.47 

137.8 

1.82 

126.9 

.44 

139.6 

.79 

1.1 

1.2 

130. 

.42 

156. 

1.85 

131.3 

.40 

157.5 

.84 

1.2 

1.3 

134.2 

.39 

174.5 

1.88 

135.3 

.36 

175.9 

.86 

1.3 

1.4 

138.1 

.35 

193.3 

1.91 

138  9 

.33 

194  5 

.88 

1.4 

1.5 

141.6 

.33 

212.4 

1.94 

142.2 

.31 

213  3 

.92 

1.5 

1.6 

144.9 

.30 

231.8 

1.96 

145.3 

.28 

232.5 

1.93 

1.6 

1.7 

147.9 

.27 

251.4 

1.97 

148.1 

.25 

251.8 

1.93 

1.7 

1.8 

150.6 

.26 

271.1 

2. 

150.6 

.24 

271.1 

1.96 

1.8 

1.9 

153.2 

.24 

291.1 

2.01 

153. 

22 

290.7 

1.97 

1.9 

2. 

155.6 

.22 

311.2 

2.02 

155.2 

]21 

310.4 

1.99 

2. 

2.1 

157.8 

.21 

331.4 

2.04 

157.3 

.19 

330.3 

1.99 

2.1 

2.2 

159.9 

.19 

351.8 

2.03 

159  2 

.18 

350.2 

2.01 

2.2 

2.3 

161.8 

.18 

372.1 

2.05 

161. 

.16 

370.3 

1.99 

2.3 

2.4 

163.6 

.17 

392.6 

2.06 

162.6 

.16 

390  2 

2.03 

2.4 

2.5 

165.3 

.16 

413.2 

2.07 

164.2 

.15 

410  5 

2.03 

2.5 

2.6 

166.9 

.15 

433.9 

2.08 

165.7 

.14 

430.8 

2.04 

2.6 

2.7 

168.4 

.15 

454.7 

2.10 

167.1 

.13 

451.2 

2.03 

2.7 

2.8 

169.9 

.13 

475.7 

2.08 

168.4 

.12 

471.5 

2.03 

2.8 

2.9 

171.2 

.13 

496.5 

2.10 

169.6 

.12 

491.8 

2.06 

2.9 

3. 

172.5 

517.5 

170.8 

512.4 

3. 

118 


FLOW    OF    WATER    IN 


TABLE    18. 

Based  on  Kutter's  formula,  with  n  —  .012.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c-^/rs  =  c  X  V^  X  \/s~~-  c^/r'  X  \/T 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  5000=1.056  ft.  per  mile 

1  in  3333.3=1.584  ft.  per  mile 

Vr 
in  feet 

s  =  .0002 

s  =.0003 

c 

diff. 
.01 

cv'r 

diff. 
.01 

c 

diff. 
.01 

cVr 

diff. 
.01 

.4 

77.4 

1.10 

30.9 

1.33 

79.8 

1.10 

31.9 

1.35 

.4 

.5 

88.4 

.94 

44.2 

1.45 

90.8 

.92 

45.4 

1.46 

.5 

.6 

97.8 

.79 

58.7 

1.53 

100. 

.77 

60. 

1.54 

.6 

.7 

105.7 

.69 

74. 

1.61 

107.7 

.67 

75.4 

1.61 

.7 

.8 

112.6 

.60 

90.1 

1.66 

114.4 

.58 

91.5 

1.67 

.8 

.9 

118.6 

.53 

106.7 

1.72 

120.2 

.51 

108.2 

1.71 

.9 

1. 

123.9 

.46 

123.9 

1.74 

125.3 

.44 

125.3 

1.74 

1.1 

128.5 

.42 

141.3 

1.79 

129.7 

.40 

142.7 

1.77 

.1 

1.2 

132.7 

.38 

159.2 

.82 

133.7 

.36 

160.4 

.81 

.2 

1.3 

136.5 

.34 

177.4 

.84 

137.3 

.32 

178.5 

.82 

.3 

1.4 

139.9 

.30 

195.8 

.85 

140.5 

.29 

196.7 

.84 

.4 

1.5 

142.9 

.28 

214.3 

.88 

143.4 

.27 

215.1 

.86 

.5 

1.6 

145.7 

.26 

233.1 

.90 

146.1 

.24 

233.7 

.87 

.6 

1.7 

148.3 

.24 

252.1 

.92 

148.5 

.22 

252.4 

.88 

.7 

1.8 

150.7 

.21 

271.3 

.90 

150.7 

.20 

271.2 

.89 

.8 

1.9 

152.8 

.21 

290.3 

.95 

152.7 

.19 

290.1 

.91 

1.9 

2. 

154.9 

.18 

309.8 

.93 

154.6 

.18 

309.2 

.92 

2. 

2.1 

156.7 

.18 

329.1 

.96 

156.4 

.16 

328.4 

.92 

2.1 

2.2 

158.5 

.16 

348.7 

.95 

158. 

.16 

347.6 

.95 

2.2 

2.3 

160.1 

.15 

368.2 

.96 

159.6        .13 

367.1 

.90 

2.3 

2.4 

161.6 

.14 

387.8 

.97 

160.9 

.13 

386.1 

.94 

2.4 

2.5 

163. 

.14 

407.5 

.99 

162.2 

.12 

405.5 

.93 

2.5 

2.6 

164.4 

.12 

427.4 

.97 

163.4 

.12 

424.8 

.96 

2.6 

2.7 

165.6 

.12 

447.1 

.99 

164.6 

.11 

444.4 

1.96 

2.7 

2.8 

166.8 

.11 

467. 

.99 

165.7 

.10 

464. 

1.94 

2.8 

2.9 

167.9 

.11 

486.9 

2.01 

166.7 

.10 

483.4 

1.97 

2.9 

3. 

169. 

507. 

167.7 

503.1 

3. 

1 

1 

OPEN    AND    CLOSED    CHANNELS. 


119 


TABLE    IS. 

Based  on  Kutter's  formula,  with  n  =  .012.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  —  c\/rs  =  c  X  \/r~  X  \/s~=  c>Jr    X  \/s 
All  slopes  greater  than  1  iu  1000  have  the  same  co-efficient  as  1  in  1000. 


N/r 

1  in  2500=2.114  ft.  per  mile 

1  in  1000  =  5.28  ft.  per  mile 

V'r 

s  =  .0004 

s  =  .001 

in  feet 

diff. 

diff. 

diff. 

diff. 

in  feet 

c 

.01 

cVr 

.01 

c 

.01 

c\/r 

.01 

.4 

81.2 

1.09 

32.5 

1.25 

83.7 

1.09 

33.5 

1.38 

.4 

.5 

92.1 

.91 

46. 

1.47 

94.6 

.88 

47.3 

1.47 

.5 

.6 

101.2 

.76 

60.7 

1.54 

103.4 

.75 

62. 

1.56 

.6 

.7 

108.8 

.66 

76.1 

1.62 

110.9 

.63 

77.6 

1.61 

.7 

.8 

115.4 

.57 

92.3 

1.67 

117.2 

.55 

93.7 

1.67 

.8 

.9 

121.1 

.49 

109. 

1.70 

122.7 

.47 

110.4 

1.70 

.9 

1. 

126. 

.44 

126. 

1.74 

127.4 

.42 

127.4 

1.74 

1 

1.1 

130.4 

.39 

143.4 

1.77 

131.6 

.37 

144.8 

1.76 

1.1 

1.2 

134.3 

.34 

161.1 

.79 

135.3 

.32 

162.4 

.76 

1.2 

1.3 

137.7 

.31 

179. 

.81 

138.5 

.30 

180. 

.81 

1.3 

1.4 

140.8 

.29 

197.1 

.84 

141.5 

.26 

198.1 

.80 

1.4 

1.5 

143.7 

.25 

215.5 

.84 

144.1 

.24 

216.1 

.83 

1.5 

1.6 

146.2 

.23 

233.9 

.85 

146.5 

.22 

234.4 

.84 

1.6 

1.7 

148.5 

.22 

252.4 

1.89 

148.7 

.20 

252.8 

.84 

1.7 

1.8 

150.7 

.20 

271.3 

1.88 

150.7 

.18 

271.2 

.85 

1.8 

1.9 

152.7 

.18 

290.1 

1.89 

152.5 

.17 

289.7 

1.87 

1:9 

2. 

154.5 

.17 

309. 

1.90 

154.2 

.16 

308.4 

1.88 

2 

2.1 

156.2 

.15 

328. 

1.89 

155.8 

.14 

327.2 

1.86 

2.1 

2.2 

157.7 

.15 

346.9 

1.93 

157.2 

.14 

345.8 

.90 

2.2 

2.3 

159.2 

.13 

366.2 

1.90 

158.6 

.12 

364.8 

.87 

2.3 

2.4 

160.5 

.13 

385.2 

1.93 

159.8 

.12 

383.5 

.90 

2.4 

2.5 

161.8 

.12 

404.5 

1.93 

161. 

.11 

402.5 

.89 

2.5 

2.6 

163. 

.11 

423.8 

1.93 

162.1 

.10 

421.4 

.90 

2.6 

2.7 

164.1 

.10 

443.1 

1.92 

163.1 

.10 

440.4 

.91 

2.7 

2.8 

165.1 

.10 

462.3 

1.94 

164.1 

.09 

459.5 

.90 

2.8 

2.9 

166.1 

.09 

481.7 

1.93 

165. 

.09 

478.5 

.92 

2.9 

3. 

167. 

501. 

165.9 

497.7 

3. 

120 


FLOW    OF    WATER    IN 


TABLE    19. 

Based  on  Kutter's  formula,  with  n  =  .013.     Values  of  the  factors  c  and 
/F  for  use  in  the  formula? 

v  ==  c\/rs  =  c  X  \/r    X  \/~  =  c\/r    X  \/s 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  20000=.  264  ft.  per  mile 

1  in  15840=.  3333  ft.  per  mile 

8  =  .00005 

a  =  .000063131 

Vr 
in  feet 

c 

diff. 
.01 

c^r 

diff. 
.01 

c 

diff. 
.01 

cx/r 

diff. 
.01 

.4 

56.7 

1.02 

22.7 

1.08 

59.3 

1.03 

23.7 

1.11 

.4 

.5 

66.9 

.91 

33.5 

.21 

69.6 

.90 

34.8 

1.24 

.5 

.6 

76. 

.82 

45.6 

.33 

78.6 

.81 

47.2 

1.35 

.6 

.7 

84.2 

.74 

58.9 

.44 

86.7 

.73 

60.7 

1.45 

.7 

.8 

91.6 

.67 

73.3 

.51 

94. 

.65 

75.2 

1.52 

.8 

.9 

98.3 

.61 

88.4 

.60 

100.5 

.59 

90.4 

1.60 

.9 

104.4 

.56 

104.4 

.66 

106.4 

.53 

106.4 

1.65 

1. 

il 

110. 

.52 

121. 

.72 

111.7 

.49 

122.9 

1.70 

1.1 

.2 

115.2 

.47 

138.2 

.76 

116.6 

.45 

139.9 

1.76 

1.2 

.3 

119.9 

.44 

155.8 

.82 

121.1 

.41 

157.5 

1.78 

1.3 

.4 

124.3 

.40 

174. 

.85 

125.2 

.39 

175.3 

1.84 

1.4 

.5 

128.3 

.38 

192.5 

.89 

129.1 

.35 

193.7 

1.85 

1.5 

.6 

132.1 

.35 

211.4 

.92 

132.6 

.33 

212.2 

1.89 

1.6 

.7 

135.6 

.34 

230.6 

.96 

135.9 

.31 

231  .  1 

1.91 

1.7 

1.8 

139. 

.31 

250.2 

.97 

139. 

.29 

250.2 

1.93 

1.8 

1.9 

142.1 

.28 

269.9 

2. 

141.9 

.26 

269.5 

1.95 

1.9 

2. 

144.9 

.29 

289.9 

2.05 

144.5 

.25 

289. 

1.98 

2. 

2.1 

147.8 

.25 

310.4 

2.02 

147. 

.24 

308.8 

1.98 

2.1 

2.2 

150.3 

.24 

330.6 

2.06 

149.4 

.22 

328.6 

2.01 

2.2 

2.3 

152.7 

.23 

351.2 

2.07 

151.6 

.22 

348.7 

2.04 

2.3 

2.4 

155. 

.21 

371.9 

2.09 

153.8 

.19 

369.1 

2.01 

2.4 

2.5 

157.1 

.21 

392.8 

2.12 

155.7 

.18 

389.2 

2.03 

2.5 

2.6 

159.2 

.20 

414. 

2.12 

157.5 

.18 

409.5 

2.06 

2.6 

2.7 

161.2 

.19 

435  .  2 

2.14 

159.3 

.17 

430.1 

2  07 

2.7 

2  8 

163.1 

.18 

456.6 

2.16 

161. 

.16 

450.8 

2.07 

2.8 

2.9 

164.9 

.16 

478.2 

2.14 

162.6 

.16 

471.5 

2.10 

2.9 

3. 

166.5 

499.6 

164.2 

492.5 

3. 

OPEN    AND    CLOSED    CHANNELS. 


121 


TABLE   19. 

Based  on  Kutter's  formula,  with  n  =  .013.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c^/rs  =  c  X  \Sr~  X  V*~  =  c\/7~  X  v^s 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  10000=.528  ft.  per  mile 

1  in  7500=.  704  ft.  per  mile 

•v/V 
in  feet 

s  =  .0001 

s  =  .000133333 

c 

diff. 
.01 

c\/r 

diff. 
.01 

c 

diff. 
.01 

c\/r 

diff. 
.01 

.4 

64. 

1.03 

25.6 

.16 

66.5 

1.03 

26.6 

1.18 

.4 

.5 

74.3 

.90 

37.2 

.28 

76.8 

.89 

38.4 

.30 

.5 

.6 

83.3 

.78       50. 

.38 

85.7 

.76 

51.4 

.39 

.6 

.7 

91.1 

.69 

63.8 

.46 

93.3 

.67 

65.3 

.47 

.7 

.8 

98. 

.61 

78.4 

53 

100. 

.60 

80. 

.54 

.8 

.9 

104.1 

.56 

93.7 

.60 

106. 

.53 

95.4 

.59 

.9 

109.7 

.49 

109.7 

.63 

111.3 

.47 

111.3 

.63 

1 

.1 

114.6 

.45 

126. 

.69 

116. 

.43 

127.6 

.68 

11 

.2 

119.1 

.41 

142.9 

.72 

120.3 

.39 

144.4 

.70 

1  2 

.3 

123.2 

.37 

160.1 

.76 

124.2 

.35 

161.4 

.74 

1.3 

.4 

126.9 

.34 

177.7 

.78 

127.7 

.32 

178.8 

.76 

1.4 

.5 

130.3 

.31 

195  5 

1.80 

130.9 

.30 

196  4 

.78 

1.5 

1.6 

133.4 

.29 

213.5 

1  83 

133.9 

.27 

214.2 

.80 

1.6 

1.7 

136.3 

.27 

231.8 

1.84 

136.6 

.24 

232.2 

.80 

1.7 

1.8 

139. 

.25 

250.2 

.87 

139. 

.24 

250.2 

.84 

1.8 

1.9 

141.5 

.23 

268.9 

.88 

141.4 

.22 

268.6 

.85 

1.9 

2 

143.8 

.23 

287.7 

.90 

143.6 

.18 

287.1 

.85 

2 

2.1 

146.1 

.19 

306.7 

.90 

145  4 

.20 

305.6 

.88 

2.1 

2.2 

148. 

.19 

325.7 

.92 

147.4 

.18 

324.4 

.87 

2.2 

2.3 

149.9 

.18 

344.9 

.91 

149.2 

.15 

343.1 

.87 

2.3 

2.4 

151.7 

.17 

364 

.95 

150.7 

.16 

361.8 

.90 

2.4 

2.5 

153.4 

.15 

383  5 

.93 

152.3 

.15 

380.8 

.92 

2.5 

2.6 

154.9 

.15 

402.8 

.96 

153.8 

.13 

400. 

.89 

2.6 

2.7 

156.4 

.15 

422.4 

.96 

155  1 

.14 

418.9 

.92 

2.7 

2.8 

157.9 

.14 

442. 

2. 

156.5 

.12 

438.1 

.92 

2.8 

2.9 

159.3 

.13 

462. 

1.98 

157.7 

.11 

457.3 

.91 

2.9 

3. 

160.6 

481.8 

158.8 

476.4 

3. 

122 


FLOW    OF    WATER    IN 


TABLE    19. 

Based  on  Kutter's  formula,  with  n  —  .013.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c\/rs  =  c  X  Vr~  X  \/s~  =  c^/r~  X  \A~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


in  feet 

1  in  5000=1.056  ft.  per  mile  ; 

1  in  3333.3=1.584  ft.  per  mile 

in  feet 

s  =  .0002                     ! 

s  =  .0003 

c 

diff. 
.01 

cV'r 

diff. 
.01 

c 

diff. 
.01 

<v- 

diff. 
.01 

4          69.4 

1.03 

27.8 

1.20 

71.6 

1.02 

28.6 

.23 

.4 

.5 

79.7 

.87 

39.8 

1.32 

81.8 

.86 

40.9 

.34 

.5 

.6          88.4 

.75 

53. 

1.41 

90.4 

.73 

54  3 

.41 

.6 

7          95.9 

.65 

67.1 

1.48 

97.7 

.64 

68.4 

.49 

.7 

.8     !   102.4 

.57 

81.9 

1.54 

104.1 

.55 

83.3 

.45 

.8 

.9     i   108.1 

.51 

97.3 

1.59 

109.6 

.48 

97.8 

.66 

.9 

113.2 

.44 

113.2 

1.61 

114.4 

44 

114.4 

.63 

1. 

1 

117.6 

.40 

129.3 

1.66 

118.8 

.38 

130.7 

.64 

1.1 

2 

121.6 

.37 

145.9 

1.69 

122.6 

.35 

147.1 

.68 

1.2 

.3 

125.3 

.32 

162.8 

1.71 

126.1 

.31 

163.9 

1.70 

1.3 

.4 

128.5 

31 

179.9 

1.74 

129.2 

.28 

180.9 

1.71 

1.4 

.5 

131.6 

.27 

197.3 

1.75 

132. 

.26 

198. 

1.73 

1.5 

.6 

134.3 

.24 

214.8 

1.76 

134.6 

.23 

215.3 

1.74 

1.6 

.7 

136.7 

.24 

232.4 

1.79 

136.9 

.22 

232.7 

1.77 

1.7 

.8 

139.1 

.21 

250.3 

1.79 

139.1 

.20 

250.4 

1.76 

1.8 

.9 

141.2 

.19 

268.2 

1.81 

141.1 

.19 

268. 

1.80 

1.9 

2. 

143.1 

.20 

286.3 

1  83 

143. 

.16 

286. 

1.77 

2. 

2.1 

145.1 

.16 

304.6 

1  81 

144.6 

.17 

303.7 

1.81 

2.1 

2.2 

146.7 

.16 

322.7 

1.83 

146.3 

.14 

321.8 

1.80 

2.2 

2.3 

148.3 

.16 

341. 

1.86 

147.7 

.14 

339.8 

1.81 

2.3 

24 

149.9 

.13 

359.6 

1.85 

149.1 

.13 

357.9 

1.82 

2.4 

2.5 

151.2 

.14 

378.1 

1.85 

150.4 

.12 

376.1 

1.83 

2.5 

26 

152.6 

.12 

396.6 

1.85 

151.7 

.13 

394.4 

1.83 

2.6 

2.7 

153.8 

.12 

415.1 

1.88 

152.9 

.12 

412.7 

1.82 

2.7 

2.8 

155. 

.11 

433  9 

1.88 

153.9 

.10 

430.9 

1.85 

2.8 

2.9 

156.1 

.10 

452.7 

1.86 

155. 

.11 

449.4 

1.82 

2.9 

3.       i  157.1 

I 

471.3 

155.9 

.09 

467.6 

3. 

OPEN    AND    CLOSED    CHANNELS 


123 


TABLE   19. 

Based  on  Kutter's  formula,  with  n  —  .013.     Values  of  the  factors  c  and 
c\/r  for  Tise  in  the  formulae 

v  -—  c\/rs  -—cX  x//7  X  V~  =  Cx/r   X  \/s~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


in  feet 

I  in  2500  =  2.114  ft.  per  mile 

1  in  1000  =  5.28  ft.  per  mile 

in  feet 

s  =  .0004 

8  =  .001 

c 

diff. 

.01 

«VF 

diff. 
.01 

c 

diff. 
.01 

cvr 

diff. 
.01 

.4 

72.8 

1.02 

29.1 

.24 

75.2 

1.01 

30.1 

.25 

.4 

.5 

83. 

.85 

41.5 

.34 

85.3 

.83 

42.6 

.46 

.5 

.6 

91.5 

.73 

54.9 

.42 

93.6 

.71 

56.2 

.43 

.6 

.7 

98.8 

.62 

69.1 

.49 

100.7 

.60 

70.5 

.49 

.7 

.8 

105. 

.54 

84. 

.54 

106.7 

.52 

85.4 

.53 

.8 

.9 

110.4 

.48 

99.4 

.58 

111.9 

.46 

100.7 

.57 

.9 

1. 

115.2 

.41 

115.2 

.61 

116.5 

.40 

116.5 

.60 

1. 

.1 

119.3 

.38 

131.3 

.64 

120.5 

.35 

132.5 

.63 

1.1 

.2 

123.1 

.34 

147.7 

.67 

124. 

.32 

148.8 

.66 

1.2 

.3 

126.5 

.29 

164.4 

.68 

127.2 

.29 

165.4 

.67 

1.3 

.4 

129.4 

.29 

181.2 

.72 

130.1 

.26 

182.1 

.69 

1.4 

.5 

132.3 

.24 

198.4 

.72 

132.7 

.23 

199. 

.70 

1.5 

.6 

134.7 

.23 

215.6 

.73 

135. 

.21 

216. 

.71 

1.6 

.  7 

137. 

.21 

232.9 

1.75 

137.1 

.20 

233  .  1 

.73 

1.7 

.8 

139.1 

.19 

250.4 

1.73 

139.1 

,18 

250.4 

.73 

1.8 

1.9 

141. 

.18 

267.7 

1.79 

140.9 

.17 

267.7 

1.75 

1.9  • 

2. 

142.8 

.18 

285.6 

1  80 

142.6 

.15 

285.2 

1.74 

2. 

2.1 

144.6 

.14 

303.6 

1.77 

144.1 

.14 

302.6 

1.75 

2.1 

2  2 

146. 

.14 

321.3 

1.77 

145.5 

.14 

320.1 

.78 

2.2 

2.3 

147.4 

.14 

339. 

.81 

146.9 

.12 

337.9 

.75 

2.3 

2.4 

148.8 

.12 

357.1 

.79 

148.1 

.11 

355.4 

77 

2.4 

2.5 

150. 

.12 

375. 

1.81 

149.2 

.11 

373.1 

78 

2.5 

2.6 

151.2 

.11 

393.1 

.81 

150.3 

.10 

390.9 

.77 

2.6 

2.7 

152.3 

.10 

411  2 

.80 

151.3 

.10 

408.6 

.79 

2.7 

2.8 

153.3 

.10 

429.2 

1.83 

152.3 

.09 

426.5 

1.79 

2.8 

2.9 

154.3 

.09 

447.5 

1.81 

153.2 

.09 

444.4 

1.80 

2.9 

3.           155.2 

465.6 

154.1 

462.4 

3. 

124 


FLOW    OF    WATER    IN 


TABLE  20. 

Based  011  Kutter's  formula,  with  n  =  .015.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  CV/TS  =  c  X xA7  X  \/«~  =  c\/r~  X  \A 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  20000  =  .264  ft.  per  mile 

1  in  15840=.  3333  ft.  per  mile 

Vr 
in  feet 

8  =  .00005 

s  =  .000063131 

c 

diff. 
.01 

cx/r 

diff. 
.01 

c 

diff. 
.01 

cV~ 

diff. 
.01 

.4 

46.8 

.87 

18.7 

.91 

48.9 

.88 

19.6 

.93 

.4 

.  5 

55.5 

.79 

27.8 

1.02 

57.7 

.79 

28.9 

1  05 

.5 

.6 

63.4 

.70 

38. 

1.13 

65.6 

.69 

39.4 

1.14 

.6 

.7 

70.4 

.67 

49.3 

1.24 

72.5 

.66 

50.8 

.25 

M 

.    / 

.8 

77.1 

.60 

61.7 

1.31 

79.1 

58 

63.3 

.31 

.8 

.9 

83.1 

.55 

74.8 

1.38 

84.9 

53 

76.4 

.38 

.9 

88.6 

.50 

88.6 

1.44 

90.2 

49 

90.2 

.45 

:  !i 

93.6 

.47 

103. 

1.50 

95.1 

.45 

104.7 

.49 

J 

.2 

98.3 

.44 

118. 

.55 

99.6 

.42 

119.6 

.53 

.2 

.3 

102.7 

.40 

133.5 

.59 

103.8 

.38 

134.9 

.57 

.3 

.4 

106.7 

.38 

149.4 

.63 

107.6 

.36 

150.6 

.61 

.4 

.5 

110.5 

.35 

165.7 

.67 

111.2 

.33 

166.7 

.64 

.5 

.6 

114. 

.33 

182.4 

.70 

114.5 

.31 

183  1 

.68 

.6 

rr 

.  / 

117.3 

.31 

199.4 

.73 

117.6 

28 

199.9 

.68 

.7 

1.8 

120.4 

.29 

216.7 

1,76 

120.4 

.27 

216.7 

.72 

.8 

1.9 

123.3 

.28 

234.3 

1.78 

123.1 

.26 

233.9 

.74 

.9 

2. 

126.1 

.25 

252  1 

1.80 

125.7 

.24 

251.3 

-77 

2. 

2.1 

128.6 

.25 

270.1 

1.83 

128.1 

.22 

269. 

.77 

2  1 

2.2 

131.1 

.23 

288.4 

1.84 

130.3 

.21 

286.7 

.79 

2.2 

2.3 

133.4 

.22 

306.8 

1.87 

132.4 

.21 

304.6 

.82 

2.3 

2.4 

135.6 

.21 

325.5 

1.87 

134.5 

.18 

322.8 

.81 

2.4 

2.5 

137.7 

.20 

344.2 

1.91 

136.3 

.19 

340.9 

.83 

2.5 

2.6 

139.7 

.19 

363.3 

1.91 

138.2 

.17 

359.2 

.87 

2.6 

2.7 

141.6 

.18 

382.4 

1.91 

139.9 

.17 

377.9 

1.85 

2.7 

2.8 

143.4 

.17 

401.5 

1.93 

141.6 

.15 

396.4 

1.87 

2.8 

2.9 

145.1 

.16 

420.8 

1.94 

143.1 

.14 

415  1 

1.85 

2.9 

3. 

146.7 

440.2 

144.5 

433.6 

3. 

1 

OPEN    AND    CLOSED    CHANNELS. 


125 


TABLE  20. 

Based  on  Kutter's  formula,  with  n  =  .015,     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c\/rs  =  c  X  \/r    X  N/.S    =  c\/r    X  \/s 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  10000=.528  ft.  per  mile 

1  in  7500  =  .704  ft.  per  mile 

Vr 
in  feet 

s  —  .0001 

s  =  .000133333 

c 

diff. 
.01 

c^/r 

diff. 
.01 

c 

diff. 
.01 

cv/r 

diff. 
.01 

.4 

52.7 

.89 

21.1 

.97 

54.7 

.90 

21.9 

.99 

.4 

.5 

61.6 

.78 

30.8 

.09 

63.7 

.78 

31.8 

1.11 

.5 

.6 

69  4 

.68 

41.7 

.17 

71.5 

.67 

42.9 

1.18 

.6 

.7 

76.2 

.63 

53.4 

.26 

78.2 

.61 

54.7 

1.28 

.7 

.8 

82.5 

.56 

66. 

.33 

84.3 

.54 

67.5 

1.32 

.8 

.9 

88.1 

.50 

79.3 

.38 

89.7 

.48 

80.7 

1.38 

.9 

1. 

93.1 

.46 

93.1 

.43 

94.5 

.44 

94.5 

1.43 

1. 

1.1 

97.7 

.41 

107.4 

.47 

98.9 

.39 

108.8 

1.46 

1.1 

1.2 

103.8 

.38 

122.1 

.51 

102.8 

.37 

123.4 

1.50 

1.2 

1.3 

105.6 

.34 

137,2 

.54 

106.5 

.32 

138.4 

1.52 

1.3 

1.4 

109. 

.32 

152,6 

.57 

109.7 

.30 

153.  G 

1.55 

1.4 

1.5 

112.2 

.30 

168.3 

.60 

112.7 

.28 

169.1 

1.58 

1.5 

1.6 

115.2 

.27 

184.3 

.62 

115.5 

.26 

184.9 

1.59 

1.6 

1.7 

117.9 

.25 

200.5 

.63 

118.1 

.24 

200.8 

1.61 

1.7 

1.8 

120.4 

.25 

216,8 

.66 

120.5 

.22 

216.9 

1.62 

1.8 

1.9 

122.9 

.21 

233.4 

.67 

122.7 

.21 

233.  1 

1.65 

1.9 

2. 

125. 

.21 

250.1 

.69 

124.8 

.19 

249.6 

1.65 

2. 

21 

127.1 

.20 

267. 

.70 

126.7 

.18 

266.1 

1.66 

2.1 

2.2 

129.1 

.18 

284. 

.70 

128.5 

.17 

282.7 

1.68 

2.2 

2.3 

130.9 

.17 

301. 

.73 

130.2 

.16 

299.5 

1.68 

2.3 

2.4 

132.6 

.17 

318.3 

.74 

131.8 

.15 

316.3 

1.69 

2.4 

2.5 

134.3 

.15 

335.7 

.75 

133.3 

.14 

333.2 

1.70 

2.5 

26 

135.8 

.15 

353  2 

.75 

134.7 

.13 

350.2 

1.71 

2.6 

2.7 

137.3 

.14 

370.7 

.76 

136. 

.13 

367.3 

1.72 

2.7 

2.8 

138.7 

.13 

388.3 

.78 

137.3 

.12 

384.5 

1.72       2.8 

2.9 

140. 

.12 

406.1 

.75 

138.5 

.12 

401.7 

1.69       2.9 

3 

141.2 

423.6 

139.7 

558.6 

3. 

126 


FLOW    OF    WATER    IN 


TABLE  20. 

Based  on  Kutter's  formula,  with  n  =  .015.     Values  of  the  factors  c  and 
c\/V  for  use  in  the  formulae 

v  =  cvVs  =  c  X  \/r~  X  \/s~  =  c\/r~  X  %A~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


v~ 

in  feet 

1  in  5000=1.056  ft.  per  mile  j  1  in  3333.3=1.584  ft.  per  mile 

-v/r 

in  feet 

s  =  .0002 

s  =  .0003 

c 

diff. 
.01 

c\/r 

diff. 
.01 

c 

diff. 
.01 

c^r 

diff. 
.01 

.4 

57.1 

.90 

22.9 

1.01 

59. 

.89 

23.6 

1.03 

.4 

.5 

66.1 

.77 

33. 

1.13 

67.9 

.76 

33.9 

.14 

.5 

.6 

73.8 

.65 

44.3 

1.19 

75.5 

.65 

45.3 

.21 

.6 

.7 

80.3 

.60 

56  2 

1.29 

82. 

.58 

57.4 

.28 

.7 

.8 

86.3 

.52 

69.1 

1.33 

87.8 

.50 

70.2 

.33 

.8 

.9 

91.5 

.46 

82.4 

1.37 

92.8 

.45 

83.5 

.38 

.9 

1. 

96.1 

.42 

96.1 

1.42 

97.3 

.40 

97.3 

.41 

1. 

1.1 

100.3 

.37 

110.3 

1.45 

101.3 

.36 

111.4 

.45 

1.1 

1.2 

104. 

.34 

124.8 

1.48 

104.9 

.32 

125.9 

.47 

1.2 

1.3 

107.4 

.31 

139.6 

1.51 

108.1 

.30 

140.6 

.49 

1.3 

1.4 

110.5 

.28 

154.7 

1.53 

111.1 

.26 

155.5 

.51 

1.4 

1.5 

113.3 

.26 

170. 

1.54 

113.7 

.25 

170.6 

1.53 

1.5 

1.6 

115.9 

.24 

185.4 

1.57 

116.2 

.22 

185.9 

1.54 

1.6 

1.7 

118.3 

22 

201.1 

1.58 

118.4 

.21 

201.3 

1.56 

1.7 

1.8 

120.5 

/21 

216.9 

1.60 

120.5 

.20 

216.9 

1.58 

1.8 

1.9 

122.6 

.19 

232.9 

1.60 

122.5 

.17 

232.7 

1.58 

1.9 

2. 

124.5 

.17 

248.9 

1.60 

124.2 

.17 

248.5 

1.58 

2. 

2.1 

126.2 

.17 

264.9 

1.65 

125.9 

.15 

264.3 

1.59 

2.1 

2.2 

127.9 

.15 

281.4 

1.62 

127.4 

.15 

280.2 

1.63 

2.2 

2.3 

129.4 

.14 

297.6 

1.64 

128.9 

.13 

296.5 

1  59 

2.3 

2.4 

130.8 

.14 

314. 

1.65 

130.2 

.13 

312.4 

1  63 

2.4 

2.5 

132.2 

.13 

330.5 

1.67 

131.5 

.12 

328.7 

1.63 

2.5 

2.6 

133.5 

.12 

347.2 

1.66 

132.7 

.11 

345. 

1.63 

2.6 

2.7 

134.7 

.12 

363.8 

1.67 

133.8 

.11 

361.3 

1.64 

2.7 

2.8 

135.9 

.10 

380.5 

1.66 

134.9 

.09 

377.7 

1.62 

2.8 

2.9 

136.9 

.11 

397.1 

1.69 

135.8 

.07 

393  .  9 

1.65 

2.9 

3. 

138. 

414. 

136.8 

410.4 

3. 

| 

OPEN    AND    CLOSED    CHANNELS. 


127 


TABLE  20. 

Based  on  Kutter's  formula,  with  n  =  .015.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  --=  c\/rs  —  c  X  \/r   X  ^/&  =  c\/r   X  \/s~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


^ 

in  feet 

1  in  2500=2.114  ft.  per  mile 

1  in  1000=5.28  ft.  per  mile 

Vr 
in  feet 

a  —  .0004 

s=.001 

c 

diff. 
.01 

evT 

diff. 
.01 

c 

diff. 
.01 

c\/r 

diff. 
.01 

.4 

60. 

.89 

24. 

1.04 

62. 

.88 

24.8 

1.06 

.4 

'.5 

68.9 

.75 

34.4 

1.15 

70.8 

.75 

35.4 

1.16 

.5 

.6 

76.4 

.64 

45.9 

1.21 

78.3 

.63 

47. 

.22 

.6 

.7 

82.8 

.58 

58. 

1.29 

84.6 

.55 

59.2 

.29 

.7 

.8 

88.6 

.50 

70.9 

1.33 

90.1 

.48 

72.1 

.33 

.8 

.9 

93.6 

.43 

84.2 

1.37 

94  9 

.42 

85.4 

.37 

.9 

1. 

97.9 

.39 

97.9 

1.41 

99.1 

.38 

99.1 

.41 

1. 

1.1 

101.8 

.35 

112. 

1.44 

102.9 

.33 

113.2 

.42 

1.1 

1.2 

105.3 

.32 

126.4 

1.46 

106.2 

.30 

127.4 

.46 

1.2 

1.3 

108.5 

.28 

141. 

1.49 

109.2 

.27 

142. 

.47 

1.3 

.4 

111.3 

.27 

155.9 

1.50 

111.9 

.25 

156.7 

.49 

1.4 

.5 

114. 

.23 

170.9 

1.52 

114.4 

.22 

171.6 

.50 

1.5 

.6 

116.3 

22 

186.1 

1.54 

116.6 

.20 

186.6 

.50 

1.6 

.7 

118.5 

.20 

201.5 

1.55 

118.6 

.19 

201.6 

.53 

1.7 

.8 

120.5 

.19 

217. 

1.55 

120.5 

.18 

216.9 

.55 

1.8 

.9 

122.4 

.17 

232.5 

1.56 

122.3 

.16 

232.4 

.54 

1.9    ' 

2. 

124.1 

.16 

248.1 

1.59 

123.9 

.15 

247.8 

.55 

2 

2.1 

125.7 

.15 

264. 

1.59 

125.4 

.14 

263  3 

1.57 

2^1 

2.2 

127.2 

.14 

279.9 

1.59 

126.8 

.12 

279. 

1.54 

2.2 

2.3 

128.6 

.13 

295.8 

1.59 

128. 

.13 

294.4 

1.59 

2.3 

2.4 

129.9 

.12 

311.7 

1.60 

129.3 

.11 

310.3 

1.57 

2.4 

2.5 

131.1 

.12 

327.7 

1.43 

130.4 

.10 

326. 

1.56 

2.5 

2.6 

132.3 

.10 

342. 

1.80 

131.4 

.11 

341.6 

1.62 

2.6 

2.7 

133.3 

.11 

360. 

1.63 

132.5 

.09 

357.8 

1.57 

2.7 

2.8 

134.4 

.10 

376.3 

1.63 

133.4 

.09 

373.5 

1.60 

2.8 

2.9 

135.4 

.08 

392.6 

1.61 

134.3 

.08 

389.5 

1.58 

2.9 

3. 

136.2 

408.7 

135.1 

405.3 

3. 

128 


FLOW    OF    WATER    IN 


TABLE  21. 

Based  on  Kutter's  formula,  with  n  —  .017.     Values  of  the  factors  c  and 
for  use  in  the  fornmlee 

v  =  c\/rs  =  c  X  \/r   X  \/s  =  c\/r~  X  \/s~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 

1  in  20000=.264  ft.  per  mile 

1  in  15840=.  3333  ft.  per  mile 

Vr 

«=.  00005 

«=.  0000631  31 

in  feel 

diff. 

diff.  ! 

diff. 

diff. 

in  feet 

c 

.01 

.01 

c 

.01 

c\/r 

.01 

.4 

39.6 

.76 

15.9 

.77 

41.3 

.77 

16.5 

.80 

.4 

.5 

47.2 

.70 

23.6 

.89 

49. 

.70 

24.5 

.91 

.5 

.6 

54.2 

.63 

32.5 

.99 

56. 

.63 

33.6 

.6 

.7 

60.5 

.59 

42.4 

.07 

62.3 

.58 

43.6 

.09 

.7 

.8 

66.4 

.54 

53.1 

.15 

68.1 

.52 

54.5 

.15 

.8 

.9 

71.8 

.49 

64.6 

.21 

73.3 

.49 

66. 

.22 

.9 

1. 

76.7 

.47 

76.7 

.28 

78.2 

.45 

78.2 

.27 

1. 

1.1 

81.4 

.43 

89.5 

.33 

82.7 

.41 

90.9 

.32 

1.1 

1.2 

85.7 

.40 

102.8 

.38 

86.8 

.38 

104.1 

.37 

1.2 

.3 

89.7 

.37 

116.6 

.42 

90.6 

.36 

117.8 

.40 

1.3 

.4 

93.4 

.35 

130.8 

.46 

94.2 

.33 

131  .  8 

.44 

1.4 

.5 

96.9 

.33 

145.4 

.49 

97.5 

.31 

146.2 

.47 

1.5 

.6 

100.2 

.31 

160.3 

1.53 

100.6 

.29 

160.9 

.51 

1.6 

.7 

103.3 

.29 

175.6 

1.56 

103.5 

.27 

176. 

.52 

1.7 

.8 

106.2 

.28 

191.2 

1.59 

106.2 

.26 

191.2 

.55 

1.8 

.9 

109. 

.26 

207.1 

1.61 

108.8 

.24 

206.7 

.58 

1.9 

2. 

Ill  6 

.24 

223.2 

1.63 

111.2 

.23 

222  5 

.59 

2 

2.1 

114. 

.24 

239.5 

1.65 

113.5 

.22 

238.4 

.61 

2  1 

2.2 

116.4 

.22 

256. 

1.68 

115.7 

.20 

254.5 

.62 

2.'2 

2.3 

118.6 

.21 

272.8 

1.69 

117.7 

.20 

270.7 

.65 

2.3 

2.4 

120.7 

.20 

289.7 

1.71 

119.7 

.18 

287.2 

.66 

2.4 

2.5 

122.7 

.19 

306.8 

1.73 

121.5 

.17 

303.8 

.66 

2.5 

2.6 

124.6 

.19 

324.1 

1.73 

123.2 

.17 

320.4 

.69 

2.6 

2.7 

126.5 

.17 

341.4 

1.76 

124.9 

.16 

337  .  3 

.69 

2.7 

2.8 

128.2 

.17 

359. 

1.76 

126.5 

.15- 

354.2 

.70 

2.8 

2.9 

129  9 

.16 

376.6 

1.78 

128. 

.15 

371.2 

.72 

2.9 

3. 

131.5 

.15 

394.4 

1.79 

129.5 

.14 

388.4 

.73 

3. 

3.1 

133. 

.15 

412.3 

.80 

130.9 

.13 

405  .  7 

.73 

3.1 

3.2 

134.5 

.14 

430.3 

.81 

132.2 

.12 

423. 

1.74 

3.2 

3.3 

135.9 

.13 

448.4 

.82 

133.4 

.13 

440.4 

1.75 

3.3 

3.4 

137.2 

.13 

466.6 

.83 

134.7 

.11 

457.9 

1.75 

3.4 

35 

138.5 

.13 

484.9 

.83 

135.8 

.12 

475.4 

1.76 

3  5 

3.6 

139.8 

.12 

503.2 

.84 

137. 

.10 

493. 

1.77 

3.6 

3.7 

141. 

.11 

521.6 

.85 

138. 

.11 

510.7 

1.77 

3.7 

3.8 

142.1 

.12 

540.1 

1.86 

139.1 

.10 

528.4 

1.79 

3.8 

3.9 

143.3 

.10 

558.7 

1.87 

140.1 

.9 

546.3 

1.78 

3.9 

4. 

144.3 

577.4 

141. 

564.1 

4. 

OPEN    AND    CLOSED    CHANNELS. 


129 


TABLE  21. 

Based  on  Kutter's  formula,  with  n  =  .017.     Values  of  the  factors  c  and 
/V  for  use  in  the  formulae 


v  =  cVrs  —  c  X  V~  X  V~=  c\/~  X  ->/? 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 

1  in  10000=.  528  ft.  per  mile 

1  in  7500=704  ft.  per  mile 

Vr 

a  =  .0001 

s  =  .000133333 

in  feet 

c 

diff. 
.01 

cVF 

diff. 
.01 

c 

diff. 
.01 

c\A* 

diff. 
.01 

in  feet 

.4 

44.5 

.78 

17.8 

.83 

46.2 

.78 

18.5 

.85 

.4 

.5 

52.3 

.69 

26.1 

.94 

54. 

.70 

27.0 

.96 

.5 

.6 

59.2 

.62 

35.5 

1.03 

61. 

.61 

36.6 

.04 

.6 

.7 

65.4 

.57 

45.8 

1.11 

67.1 

.55 

47.0 

.11 

.7 

.8 

71.1 

.50 

56.9 

1.16 

72.6 

.49 

58.1 

.16 

.8 

.9 

76.1 

.46 

68.5 

1.22 

77.5 

.44 

69.7 

.22 

.9 

80.7 

.41 

80.7 

1.26 

81.9 

.41 

81.9 

.27 

.1 

84.8 

.39 

93.3 

1.31 

86. 

.36 

94.6 

.29 

]l 

.2 

88.7 

.35 

106.4 

1.35 

89.6 

.34 

107.5 

.34 

.2 

.3 

92.2 

.32 

119.9 

1.37 

93. 

.31 

120.9 

.36 

.3 

.4 

95.4 

.31 

133.6 

1.42 

96.1 

.28 

134.5 

.38 

.4 

.5 

98.5 

.27 

147.8 

1.41 

98.9 

.27 

148.3 

.42 

.5 

.6 

101.2 

.26 

161.9 

1.46 

101  .  6 

.24 

162.5 

.43 

.6 

K 
.  / 

103.8 

.25 

176.5 

1.48 

104. 

.23 

176.8 

.45 

1.7 

1.8 

106.3 

.22 

191.3 

1.48 

106.3 

.21 

191.3 

1.47 

1.8- 

1.9 

108.5 

.21 

206.1 

1.51 

108.4 

.20 

206. 

1.48 

1.9 

2. 

110.6 

.21 

221.2 

1,54 

110.4 

.18 

220.8 

1.48 

2. 

2.1 

112.7 

.18 

236.6 

.53 

112.2 

.18 

235.6 

1.52 

2.1 

2.2 

114.5 

.18 

251.9 

.56 

114. 

.16 

250.8 

1.51 

2.2 

2.3 

116.3 

.17 

267.5 

.57 

115.6 

.16 

265.9 

.54 

2.3 

2.4 

118. 

.16 

283.2 

.58 

117.2 

.14 

281.3 

.52 

2.4 

2.5 

119.6 

.15 

299. 

.58 

118.6 

.14 

296.5 

.55 

2.5 

2.6 

121.1 

.14 

314.8 

.59 

120. 

.13 

312. 

.55 

2.6 

2.7 

122.5 

.13 

330.7 

.59 

121.3 

.13 

327.5 

.58 

2.7 

2.8 

123.8 

.13 

346.6 

1.62 

122.6 

.11 

343.3 

.54 

2.8 

2.9 

125.1 

.12 

362.8 

1.61 

123.7 

.12 

358.7 

1.60 

2.9 

3. 

126.3 

.12 

378.9 

1.66 

124.9 

.10 

374.7 

1.56 

3. 

3.1 

127.5 

.11 

395.3 

1.62 

125.9 

.10 

390.3 

1.58 

3.1 

3.2 

128.6 

.11 

411.5 

1.65 

126.9 

.10 

406.1 

1.60 

3.2 

3.3 

129.7 

.10 

428. 

1.64 

127.9 

.09 

422.1 

.58 

3.3 

3.4 

130.7 

.10 

444.4 

1.65 

128.8 

.09 

437.9 

.61 

3.4 

3.5 

131.7 

.09 

460.9 

1.65 

129.7 

.09 

454. 

.62 

3.5 

3.6 

132.6 

.09 

477.4 

1.65 

130.6 

.08 

470.2 

.60 

3.6 

3.7 

133.5 

.08 

493.9 

1.64 

131.4 

.07 

486.2 

.58 

3.7 

3.8 

134.3 

.09 

510.3 

1.70 

132.1 

.08 

502. 

.63 

3.8 

3.9 

135.2 

.08 

527.3 

1.65 

132.9 

.07 

518.3 

.61 

3.9 

4. 

136. 

543.8 

133.6 

534.4  ! 

4. 

130 


FLOW    OF    WATER    IN 


TABLE  21. 

Based  on  Kutter's  formula,  with  n==  .017.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  Cv/Vs  =  c  X  \/r  X  \/s  =  c\/r  X  \/~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  5000=1.056  ft.  per  mile 

1  in  3333.3=1.584  ft.  per  mile 

Vr 
in  feet 

8=  .0002 

a  =  .0003 

c 

diff. 
.01 

<VT 

diff. 
.01 

c 

diff. 
.01 

Cv/r 

diff. 
.01 

.4 

48.2 

.79 

19.3 

.87 

49.8 

.78 

19.9 

.89 

.4 

.5 

56  1 

.68 

28. 

.98 

57.6 

.68 

28.8 

.98 

.5 

.6 

62.9 

.61 

37.8 

1.05 

64.4 

.60 

38.6 

1.07 

.6 

.7 

69. 

.53 

48.3 

l.U 

70.4 

.52 

49.3 

1.12 

.7 

.8 

74.3 

.48 

59.4 

1.18 

75.6 

.46 

60.5 

1.17 

.8 

.9 

79.1 

42 

71.2 

1.21 

80.2 

.42 

72.2 

1.22 

.9 

1. 

83.3 

.39 

83.3 

1  22 

84.4 

.37 

84.4 

1.25 

1. 

1.1 

87.2 

.35 

95.9 

1.29 

88.1 

.34 

96.9 

1.29 

1.1 

1.2 

90.7 

.32 

108  8 

1.32 

91.5 

.30 

109.8 

1.30 

1.2 

1.3 

93.9 

.29 

122. 

1.35 

94.5 

.28 

122.8 

1.34 

1.3 

1.4 

96.8 

.26 

135.5 

1.37 

97.3 

.25 

136.2 

1.35 

1.4 

1.5 

99.4 

.25 

149.2 

1.38 

99.8 

.24 

149.7 

1.38 

1.5 

1.6 

101.9 

.23 

163. 

1.41 

102.2 

.21 

163.5 

.38 

1.6 

1.7 

104.2 

.21 

177.1 

1.43 

104.3 

.20 

177.3 

.40 

1.7 

1.8 

106.3 

.20 

191  4 

1.43 

106  3 

.19 

191.3 

.43 

1.8 

1.9 

108.3 

.18 

205.7 

1.45 

108.2 

.17 

205.6 

.42 

1.9 

2. 

110.1 

.17 

220.2 

1.46 

109.9 

.16 

219.8 

.43 

2. 

2.1 

111.7 

.16 

234.8 

1.47 

111.5 

.15 

234.1 

.45 

2.1 

2.2 

113.4 

.15 

249.5 

1.48 

113. 

.14 

248.6 

.45 

2.2 

2.3 

114.9 

.14 

264.3 

1.49 

114.4 

.13 

263.1 

.46 

2.3 

2.4 

116.3 

.14 

279.2 

1.50 

115  7 

.13 

277.7 

.48 

2.4 

2.5 

117.7 

.12 

294.2 

.50 

117. 

.11 

292.5 

.46 

2.5 

2.6 

118.9 

.12 

309.2 

.51 

118.1 

.12 

307.1 

.50 

2.6 

2.7 

120.1 

.11 

324.3 

.51 

119.3 

.10 

322.1 

.47 

2.7 

2.8 

121.2 

.11 

339.4 

.52 

120.3 

.10 

336.8 

.50 

2.8 

2.9 

122.3 

.10 

354.6 

.53 

121.3 

.09 

351.8 

.48 

2.9 

3. 

123.3 

.10 

369.9 

.53 

122.2 

.09 

366.6 

.50 

3. 

3.1 

124.3 

.09 

385.2 

54 

123.1 

.08 

381.6 

.49 

3.1 

3.2 

125.2 

.09 

400.6 

1.54 

123.9 

.08 

396.5 

•50 

3.2 

3.3 

126.1 

.08 

416. 

1.54 

124.7 

.08 

411.5 

.52 

3.3 

3.4 

126.9 

.08 

431.4 

1.54 

125.5 

.07 

426.7 

.50 

3.4 

3.5 

127.7 

.08 

446.8 

1.58 

126.2 

.07 

441.7 

.51 

3.5 

3.6 

128.5 

.07 

462.6 

1.53 

126.9 

.07 

456.8 

.53 

3.6 

3.7 

129.2 

.06 

477.9 

1.55 

127.6 

.06 

472.1 

.51 

3.7 

3.8  . 

129.8 

.07 

493.4 

1.57 

128.2 

.07 

487.2 

.55 

3.8 

3.9 

130.5 

.07 

509.1 

1.55 

128.9 

.06 

502.7 

.55 

3.9 

4. 

131.2 

524.6 

129.5 

518.2 

4. 

OPEN    AND    CLOSED    CHANNELS. 


131 


TABLE  21. 

Based  on  Kutter's  formula,  with  n  =  .017.     Values  of  the  factors  c  and 
/r  for  use  in  the  formulae 


v  =  c^/rs  =  c  X  \/r   X  V      — 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feel 

1  in  2500  =  2.114  ft.  per  mile 

1  in  1666.7=3.168  ft.  per  mile 

Vr 
in  feet 

s  =  .0004 

s  =  .0006 

c 

diff. 
.01 

Cv/F 

diff. 
.01 

c 

diff. 
.01 

cVr 

diff. 
.01 

.4 

50.5 

.78 

20.2 

.90 

51.5 

.79 

20.6 

.91 

.4 

.5 

58.3 

.68 

29.2 

.99 

59.4 

.67 

29.7 

1.00 

.5 

.6 

65.1 

.59 

39.1 

1.06 

66.1 

.58 

39.7 

1.07 

.6 

.7 

71. 

.52 

49.7 

1.12 

71.9 

.51 

50.4 

1.12 

.7 

.8 

76.2 

.45 

60.9 

.18 

77. 

.45 

61.6 

1.18 

.8 

.9 

80.7 

.41 

72.7 

.21 

81  5 

.40 

73.4 

1.21 

.9 

1. 

84.8 

.37 

84.8 

.25 

85.5 

.36 

85.5 

1.25 

1. 

1.1 

88.5 

.32 

97.3 

.28 

89.1 

.31 

98. 

1.27 

1.1 

1.2 

91.7 

.30 

110.1 

.30 

92.2 

.30 

110.7 

1.31 

1.2 

.3 

94.7 

.27 

123.1 

.33 

95.2 

.26 

123.8 

1.32 

1.3 

.4 

97.4 

.25 

136.4 

.35 

97.8 

.24 

137. 

1.33 

1.4 

.5 

99.9 

.23 

149.9 

.36 

100.2 

.22 

150.3 

1.36 

1.5 

.6 

102.2 

21 

163.5 

.38 

102.4 

.21 

163.9 

1.37 

1.6 

..  .7 

104.3 

.19 

177.3 

.39 

104.5 

.21 

177.6 

1.38 

1.7 

1.8 

106.2 

.18 

191.2 

.40 

106.3 

.18 

191.4 

1.39 

1.8. 

1.9 

108. 

.17 

205.2 

.42 

108.1 

.16 

205.3 

1.40 

1.9 

o 

109.7 

.15 

219.4 

.42 

109.7 

.15 

219.3 

1.42 

2. 

2.1 

111.2 

.15 

233.6 

.43 

111.2 

.14 

233.5 

1.41 

2!l 

2.2 

112.7 

.14 

247.9 

.44 

112  6 

.13 

247.6 

1.44 

2.2 

2.3 

114.1 

.12 

262.3 

.45 

113.9 

.12 

262. 

1.42 

2.3 

2.4 

115.3 

.12 

276.8 

.45 

115.1 

.11 

276.2 

1.44 

2.4 

2.5 

116.5 

.11 

291.3 

.46 

116.2 

.11 

290.6 

1.44 

2.5 

2.6 

117.6 

11 

305.9 

.46 

117.3 

.10 

305. 

1.45 

2.6 

2.7 

118.7 

.10 

320.5 

.47 

118.3 

.10 

319.5 

1.45 

2.7 

2.8 

119.7 

.10 

335.2 

.47 

119.3 

.09 

334. 

1.46 

2.8 

2.9 

120.7 

.09 

349.9 

.48 

120.2 

.09 

348.6 

1.46 

2.9 

3. 

121.6 

.08 

364.7 

.48 

121.1 

.08 

363.2 

1.46 

3. 

3.1 

122.4 

.08 

379.5 

.49 

121.9 

.08 

377.8 

.47 

3.1 

3  2 

123.2 

.08 

394.4 

.48 

122.7 

.07 

392.5 

.47 

3.2 

3  3 

124. 

.08 

409.2 

.51 

123.4 

.07 

407.2 

.47 

3.3 

3.4 

124.8 

.07 

424.3 

.48 

124.1 

.07 

421.9 

.48 

3.4 

3.5 

125.5 

.06 

439.1 

.50 

124.8 

.06 

436.7 

.48 

3.5 

3.6 

126.1 

.07 

454.1 

.51 

125.4 

.06 

451.5 

.47 

3.6 

3.7 

126.8 

.06 

469.2 

.52 

126. 

.06 

466.2 

.48 

3.7 

3.8 

127.4 

.06 

484.4 

.47 

126.6 

.06 

481. 

1.49 

.   3.8 

3.9 

128. 

.05 

499.1 

.50 

127.2 

.05 

495.9 

1.49 

3.9 

4. 

128.5 

514.1 

127.7 

510.8 

4. 

132 


FLOW    OF    WATER    IN 


TABLE   21. 

Based  on  Kutter's  formula,  with  n  —  .017.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulas 


v  =  c^/rs  =  cX  Vr   X  Vs    SB  c^r   X  V 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 

1  in  1250  =4.224  ft.  per  mile 

1  in  1000=5.28  ft.  per  mile 

Vr 

s  =  .0008 

s  =  .001 

in  feet 

diff. 

diff. 

diff. 

diff. 

in  feet 

c 

.01 

cVr 

.01 

c 

.01 

cVr 

.01 

.4 

52. 

.78 

20.8 

.91 

52.3 

.78 

20.9 

.91 

.4 

.5 

59.8 

.68 

29.9 

1. 

60.1 

.67 

30. 

1.01 

.5 

.6 

66.6 

.58 

39.9 

1.08 

66.8 

.58 

40.1 

1.07 

.6 

.  7 

72.4 

.50 

50.7 

1.12 

72.6 

.51 

50.8 

1.14 

.7 

.8 

77.4 

.45 

61.9 

1.18 

77.7 

.44 

62.2 

.17 

.8 

.9 

81.9 

.39 

73.7 

1.21 

82.1 

.39 

73.9 

.21 

.9 

1. 

85.8 

.34 

85.8 

1.23 

86. 

.35 

86. 

.24 

1. 

1.1 

89.2 

.33 

98.1 

1.29 

89.5 

.31 

98.4 

.27 

1.1 

1.2 

92.5 

.29 

111. 

1.30 

92.6 

.29 

111.1 

.30 

1.2 

1.3 

95.4 

.26 

124. 

1.32 

95.5 

.26 

124.1 

.32 

1.3 

1.4 

98. 

.23 

137.2 

1.33 

98.1 

.23 

137.3 

.33 

1.4 

1.5 

100.3 

.22 

150.5 

1.35 

100.4 

.21 

150.6 

.34 

1.5 

1.6 

102.5 

.20 

164. 

1.37 

102.5 

.20 

104. 

.36 

1.6 

1.7 

104.5 

.18 

177.7 

1.37 

104.5 

.18 

177.6 

.37 

1.7 

1.8 

106.3 

.17 

191.4 

1.39 

106.3 

.17 

191.3 

.39 

1.8 

1.9 

108. 

.16 

205.3 

1.39 

108. 

.16 

205.2 

.40 

1.9 

2. 

109.6 

.15 

219.2 

1.41 

109.6 

.14 

219.2 

.39 

2 

2.1 

111.1 

.13 

233.3 

1.41 

111. 

.14 

233.1 

.42 

2.1 

2.2 

112.4 

.13 

247.4 

1.42 

112.4 

.12 

247.3 

.40 

2.2 

2.3 

113.7 

.12 

2G1.6 

1.42 

113.6 

.12 

261.3 

.42 

2.3 

2.4 

114.9 

.11 

275.8 

1.43 

114.8 

.12 

275.5 

.48 

2.4 

2.5 

116. 

.11 

290.1 

1.44 

116.1 

.13 

290.3 

.40 

2.5 

2.6 

117.1 

.10 

304.5 

1.44 

117.1 

.10 

304.3 

1.46 

2.6 

2.7 

118.1 

.09 

318.9 

1.44 

118.1 

.10 

318.9 

1.43* 

2.7 

2.8 

119. 

.09 

333.3 

1.45 

119. 

.09 

333.2 

1.45 

2.8 

2.9 

119.9 

09 

347.8 

1.45 

119.9 

.09 

347.7 

1.44 

2.0 

3. 

120.8 

.08 

362.3 

1.46 

120.7 

.08 

362.1 

1.46 

3. 

3.1 

121.6 

.07 

376.9 

1.44 

121  .  5 

.08 

376.7 

1.43 

3.1 

3.2 

122.3 

.07 

391  .  3 

1.47 

122.2 

.07 

391. 

1.46 

3.2 

3.3 

123. 

.07 

406. 

1.47 

122.9 

.07 

405.6 

1.46 

3.3 

3.4 

123.7 

.07 

420.7 

1.47 

123.6 

.07 

420.2 

1.49 

3.4 

3.5 

124.4 

.06 

435.4 

1.46 

124.3 

.07 

435.1 

1  45 

3.5 

3  6 

125. 

.07 

450. 

1.51 

124.9 

.06 

449.6 

1.47 

3.6 

3.7 

125.7 

.05 

465.1 

1.44 

125.5 

.06 

464.3 

1.48 

3.7 

3.8 

126.2 

.05 

479.5 

1.47 

126.1 

.06 

479.1 

1.46 

3.8 

3.9 

126.7 

.05 

494.2 

1.48 

126.6 

.05 

493.7 

1.47 

3.9 

4. 

127.2 

509. 

127.1 

.05 

508.4 

4. 

OPEN    AND    CLOSED    CHANNELS. 


133 


TABLE   22. 

Based  on  Kutter's  formula,  with  n  —  .02.     Values  of  the  factors  c  and 
/r  for  use  in  the  formulas 

v  •=  c\/rs    =  c  X  \/r    X  \A    =  c-v/r    X  -s/s 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


x/r 

in  feet 

1  in  20000=.  264  ft.  per  mile 

1  in  15840  =  .3333  ft.  per  mile 

Vr 

in  feet 

s  —  .00005 

s  :-_=  .000063131 

c 

diff. 
.01 

c^/r 

diff. 
.01 

c 

diff. 
.01 

cVT 

diff. 
.01 

.4 

32. 

.63 

12.8 

.64 

33.3 

.65 

13.3 

.66 

.4 

.5 

38.3 

.59 

19.2 

.73 

39.8 

.58 

19.9 

.75 

.5 

.6 

44.2 

.54 

26.5 

.82 

45.6 

.55 

27.4 

.83 

.6 

.7 

49.6 

.51 

34.7 

.91 

51.1 

.49 

35.7 

.91 

.7 

.8 

54.7 

.47 

43.8 

.96 

56. 

.46 

44.8 

.98 

.8 

.9 

59.4 

.43 

53.4 

.03 

60.6 

.43 

54.6 

1.03 

.9 

63.7 

.41 

63.7 

.09 

64.9 

.39 

64.9 

1.08 

1. 

.1 

67.8 

.38 

74.6 

.13 

68.8 

.38 

75.7 

1.14 

1.1 

.2 

71.6 

.36 

85.9 

.18 

72.6 

.34 

87.1 

1.17 

1.2 

.3 

75.2 

.34 

97.7 

.23 

76. 

.32 

98.8 

1.21 

1.3 

.4 

78.6 

.31 

110. 

.26 

79.2 

.30 

110.9 

1.25 

1.4 

.5 

81.7 

.31 

122.6 

.30 

82.2 

.29 

123.4 

1.28 

1.5 

.6 

84.8 

.28 

135.6 

.33 

85.1 

.27 

136.2 

1.30 

1.6 

.7 

87.6 

.26 

148.9 

.35 

87.8 

.25 

149.2 

1.33 

1.7 

.8 

90.2 

.26 

162.4 

.40 

90.3 

.24 

162.5 

1.36 

1.8 

.9 

92.8 

.24 

176.4 

.40 

92.7 

.22 

176.1 

1.38 

1.9 

2. 

95.2 

.23 

190.4 

.44 

94.9 

.22 

189.9 

1.39 

2 

2.1 

97.5 

.22 

204.8 

.44 

97.1 

.20 

203.8 

1.42 

2^1 

2.2 

99.7 

.21 

219.4 

.46 

99.1 

.19 

218. 

1.43 

2.2 

2.3 

101  8 

.20 

234.2 

.49 

101. 

.18 

232.3 

1.45 

.  2.3 

2.4 

103.8 

.19 

249  1 

.51 

102.8 

.18 

246.8 

1.47 

2.4 

2.5 

105.7 

.18 

264.2 

.53 

104.6 

.17 

261.5 

1.49 

2.5 

2.6 

107.5 

.18 

279.5 

.55 

106.3 

.16 

276.4 

1.48 

2.6 

2.7 

109.3 

.16 

295. 

.54 

107.9 

.15 

291.2 

1.51 

2.7 

2.8 

110.9 

.15 

310.4 

.57 

109.4 

.14 

306.3 

1.51 

2.8 

2.9 

112.4 

.16 

326.1 

.59 

110.8 

.14 

321.4 

1.53 

2.9 

3. 

114. 

.15 

342. 

.61 

112.2 

.14 

336.7 

1.55 

3. 

3.1 

115  5 

.14 

358.1 

.60 

113.6 

.13 

352.2 

1.55 

3.1 

3.2 

116.9 

.14 

374.1 

.59 

114.9 

.12 

367.7 

1.54 

3  2 

3.3 

118.3 

.13 

390. 

.66 

116.1 

.12 

383.1 

1.57 

3.3 

3.4 

119.6 

.12 

406.6 

.62 

117.3 

.11 

398.8 

1.56 

3.4 

3.5 

120.8 

.12 

422.8 

.64 

118.4 

.11 

414.4 

1.58 

3.5 

3.6 

122. 

.12 

439.2 

.66 

119.5 

.11 

430.2 

1.60 

3.6 

3.7 

123.2 

.11 

455.8 

.65 

120.  G 

.10 

446.2 

1.59 

3.7 

3.8 

124.3 

.11 

472.3 

.68 

121.  G 

.09 

462.1 

1.56 

3.8 

3.9 

125.4 

.11 

489.1 

1.69 

122.5 

.10 

477.7 

1.63 

3.9 

4. 

126.5 

5G6. 

123.5 

494. 

4. 

1 

134 


FLOW    OF    WATER    IN 


TABLE  22. 

Based  on  Kntter's  formula,  with  n  --  .02.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c^/rs~  —  c  X  \/r~  X  V~  =  c\/r~ X  V*~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  10000^.528  ft.  per  mile. 

1  in  7500  =  .704  ft  .  per  mile 

Vr 

in  feet 

a  =  .0001 

s=.  000133333 

c 

diflf. 
.01 

cVT 

diff. 
.01 

c 

diff. 
.01 

CN/r 

diff. 
.01 

.4 

35.7 

.66 

14.3 

.69 

37.1 

.66 

14.8 

.70 

.4 

.5 

42.3 

.59 

21.2 

.77 

43.7 

.59 

21.8 

.80 

.5 

.6 

48.2 

.54 

28.9 

.86 

49.6 

.53 

29.8 

.86 

.6 

.7 

53.6 

.48 

37.5 

.92 

54.9 

.48 

38.4 

.94 

.7 

.8 

58.4 

.45 

46.7 

.99 

59.7 

.43 

47.8 

.98 

.8 

.9 

62.9 

.40 

56.6 

1.03 

64. 

.40 

57.6 

1.04 

.9 

1. 

66.9 

.38 

66.9 

1.08 

68. 

.36 

68. 

1.08 

1.1 

70.7 

34 

77.7 

1.13 

71.6 

.33 

78.8 

1.11 

:  .1 

.2 

74.1 

.32 

89. 

1.15 

74.9 

.31 

89.9 

1.15 

.2 

.3 

77.3 

.30 

100.5 

1.19 

78. 

.28 

101  4 

1.18 

.3 

.4 

80.3 

.28 

112.4 

1.22 

80.8 

.27 

113.2 

1.20 

.4 

.5 

83.1 

.25 

124.6 

1.24 

83.5 

.24 

125.2 

1.23 

1.5 

.6 

85.6 

.24 

137. 

1.27 

85.9 

.23 

137.5 

1.24 

1.6 

.7 

88. 

.23 

149.7 

1.29 

88.2 

.21 

149.9 

1.27 

1.7 

.8 

90.3 

.21 

162.6 

.30 

90.3 

.20 

162.6 

1  28 

1.8 

1.9 

92.4 

.20 

175.6 

.33 

92  3 

.19 

175.4 

1.30 

1.9 

2. 

94.4 

.19 

188.9 

.33 

94.2 

.17 

188.4 

1.31 

2 

2.1 

96.3 

.18 

202.2 

.36 

95.9 

.17 

201.5 

1.32 

2.1 

2.2 

98.1 

.17 

215  8 

.37 

97.6 

.16 

214.7 

1.34 

2.2 

2.3 

99.8 

.16 

229.5 

.38 

99.2 

.15 

228.1 

1.25 

2.3 

2.4 

101.4 

.15 

243.3 

.39 

100.7 

.14 

241.6 

1.35 

2.4 

2.5 

102.9 

.14 

257.2 

.40 

102.1 

.13 

255.1 

1.37 

2.5 

2.6 

104.3 

.14 

271.2 

.41 

103.4 

.12 

268.8 

1.37 

2.6 

2.7 

105.7 

.13 

285.3 

.43 

104.6 

.12 

282.5 

1.39 

2.7 

2.8 

107. 

.12 

299.6 

.43 

105.8 

.12 

296.4 

1.38 

2.8 

2.9 

108.2 

.12 

313.9 

.43 

107. 

.11 

310.2 

1.40 

2.9 

3. 

109.4 

.11 

328.2 

.45 

108.1 

.10 

324.2 

1.40 

3. 

3.1 

110.5 

.11 

342.7 

.45 

109.1 

.10 

338.2 

1.41 

3.1 

3.2 

111.6 

.11 

357.2 

.46 

110.1 

.09 

352.3 

1.41 

3.2 

3.3 

112.7 

.10 

371.8 

.46 

111. 

.09 

366.4 

1.42 

3.3 

3.4 

113.7 

.09 

386.4 

.47 

111.9 

.09 

380.6 

1.43 

3.4 

3.5 

114.6 

.09 

401.1 

.47 

112.8 

.09 

394.9 

1.42 

3.5 

3.6 

115.5 

.09 

415.8 

.49 

113.7 

.08 

409.1 

1.46 

3.6 

3.7 

116.4 

.08 

430.7 

.47 

114.5 

.07 

423.7 

1.41 

3.7 

3.8 

117.2 

.08 

445.4 

1.48 

115.2 

.07 

437.8 

1.44 

3.8 

3.9 

118. 

.08 

460.2 

1.51 

115.9 

.08 

452.2 

1.45 

3.9 

4. 

118.8 

475.3 

116.7 

466.7 

4. 

OPEN   AND    CLOSED    CHANNELS. 


135 


TABLE  22. 

Based  on  Kutter's  formula,  with  n  =  .02.     Values  of  the  factors   c  and 
/r  for  use  in  the  formulae 


v  =  c-v/r*  •=  c  X  Vr~  X  \/T  —  c  *Jr~  X  \A~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 

1  in  5000=1.056  ft.  per  mile 

1  in  3333.3—1.584  ft.  per  mile 

Vr 

s  =  .0002 

s  ==  .0003 

in  feet 

diff. 

diff. 

diff. 

/  — 

diff. 

in  feet 

c 

.01 

Cv/r 

.01 

c 

.01 

c\/r 

.01 

.4 

38.7 

.66 

15.5 

.72 

39.9 

.67 

16. 

.73 

.4 

.5 

45.3 

.59 

22.7 

.80 

46.6 

.58 

23  3 

.82 

.5 

.6 

51.2 

.52 

30.7 

.88 

52.4 

.52 

31  5 

.88 

.6 

.7 

56.4 

.47 

39.5 

.94 

57.6 

.46 

40.3 

.95 

.7 

.8 

61.1 

.43 

48.9 

.99 

62.2 

.42 

49.8 

.99 

.8 

.9 

65.4 

.38 

58.8 

1.04 

66.4 

.37 

59.7 

1.04 

.9 

1. 

69.2 

.35 

69.2 

1.07 

70.1 

.33 

70.1 

1.07 

1. 

1.1 

72.7 

.31 

79.9 

1.11 

73.4 

.31 

80.8 

1.10 

1.1 

1.2 

75.8 

.30 

91. 

1.14 

76.5 

.28 

91.8 

1.13 

1.2 

1.3 

78.8 

.26 

102.4 

1.16 

79.3 

.26 

103.1 

1.16 

1.3 

1.4 

81.4 

.25 

114. 

1.19 

81.9 

.23 

114.7 

1.17 

1.4 

1.5 

83.9 

.23 

125.9 

1.21 

84.2 

.22 

126.4 

1.19 

».« 

1.6 

86.2 

.22 

138. 

1.22 

86.4 

.20 

138.3 

1.21 

1.6 

1.7 

88.4 

.19 

150.2 

.24 

88.4 

.20 

150.4 

1.23 

1.7 

1.8 

90.3 

.19 

162.6 

.26 

90.4 

.17 

162.7 

1.24 

1.8. 

1.9 

92.2 

.17 

175.2 

.27 

92.1 

.16 

175.1 

1.24 

1.9 

2. 

93.9 

.17 

187.9 

.    .28 

93.7 

.16 

187.5 

.26 

2. 

2.1 

95.6 

.15 

200.7 

.29 

95.3 

.14 

200.1 

.27 

2.1 

2.2 

97.1 

.14 

213.6 

.30 

96.7 

.14 

212.8 

.28 

2.2 

2.3 

98.5 

.14 

226.6 

.31 

98.1 

.12 

225.6 

.27 

2.3 

2.4 

99.9 

.13 

239.7 

.32 

99.3 

.12 

238.3 

.30 

2.4 

2.0 

101.2 

.12 

252.9 

.33 

100.5 

.12 

251.3 

.30 

2.5 

2.6 

102.4 

.11 

266.2 

.33 

101.7 

.10 

264.3 

.30 

2.6 

2.7 

103.5 

.11 

279.5 

.34 

102.7 

.10 

277.3 

.32  !  2.7 

2.8 

104.6 

.10 

292.9 

.35 

103.7 

.10 

290.5 

.31 

2.8 

2.9 

105.6 

.10 

306.4 

.35 

104.7 

.09 

303.6 

.32 

2.9 

3. 

106.6 

.10 

319.9 

.36 

105.6 

.09 

316.8 

.33 

3. 

3.1 

107.6 

.09 

333.5 

.36 

106.5 

.08 

330.1 

.33 

3.1 

3.2 

108.5 

.08 

347.1 

.37 

107.3 

.08 

343.4 

.34 

3.2 

3.3 

109.3 

.08 

360.8 

.37 

108.1 

.68 

356.8 

.34 

3.3 

3.4 

110.1 

.08 

374.5 

.37 

108.9 

.07 

370.2 

.34 

3.4 

3.5 

110.9 

.08 

388.2 

.38 

109.6 

.07 

383.6 

.34 

3.5 

3.6 

111.7 

.07 

402. 

.39 

110.3 

.07 

397. 

1.35 

3.6 

3.7 

112.4 

.07 

415.9 

.39 

111. 

.06 

410.5 

1.35 

3.7 

3.8 

113.1 

.06 

429.8 

.43 

111.6 

.06 

424. 

1.35 

3.8 

3.9 

113.7 

.07 

443.6 

.39 

112.2 

.06 

437.5 

1.36 

3.9 

4. 

114.4 

457.5 

112.8 

451.1 

4. 

136 


FLOW    OP    WATER    IN 


TABLE   22. 

Based  on.  KutterV;  formula,  with  n  -~  .02.     Values  of  the  factors   c  and 
c\/r  for  use  in  the  formulae 

v  —  c\/rs  =  c  X  x/r"  X  v/JT  =  CX/T    X  \A" 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  2500=2.  112  ft.  per  mile    il  in  1666.7=3.168  ft.  per  mile] 

a  -•=  .0004 

*  =  .0006 

Vr 
in  feet 

c 

diff. 
.01 

cx/r 

diff. 
.01 

c 

diff. 
.01 

<Vr~ 

diff. 
.01 

.4 

40.6 

.67 

16.2 

.74 

41.3 

.67 

16.5 

.75 

.4 

.5 

47.3 

.58 

23.6 

.83 

48. 

.58 

24. 

.83 

.5 

.6 

53.1 

.51 

31.9 

.89 

53.8 

.51 

32.3 

.90 

.6 

.7 

58.2 

.46 

40.8 

.95 

58.9 

.45 

41.3 

.94 

.7 

.8 

62.8 

.41 

50.3 

.99 

63.4 

.41 

50.7 

1. 

.8 

.9 

66.9 

.37 

60.2 

.04 

67.5 

.35 

60.7 

1.03 

.9 

1. 

70.6 

.32 

70.6 

.06 

71. 

.33 

71. 

1.07 

1. 

1.1 

73.8 

.31 

81.2 

.10 

74.3 

.30 

81.7 

1.10 

1.1 

1.2 

76.9 

.27 

92.2 

.13 

77.3 

.26 

92.7 

1.12 

1.2 

1.3 

79.6 

.25 

103.5 

.15 

79.9 

.25 

103.9 

1.14 

1.3 

.4 

82.1 

.23 

115. 

.17 

82.4 

.22 

115.3 

1.16 

1.4 

.5 

84.4 

.22 

126.7 

.18 

84.6 

.21 

126.9 

1.21 

1.5 

.6 

86.6 

.19 

138.5 

.20 

86.7 

.19 

138.7 

1.19 

1.6 

.7 

88.5 

.18 

150.5 

1.21 

88.6 

.18 

150.6 

1.21 

1.7 

.8 

90.3 

.17 

162.6 

1.23 

90.4 

.16 

162.7 

.21 

1.8 

.9 

92. 

.16 

174.9 

1.24 

92. 

.15 

174  8 

.23 

1.9 

2. 

93.6 

.15 

187.3 

1.25 

93.5 

.15 

187.1 

.23 

'2. 

2.1 

95.1 

.15 

199.8 

1.25 

95. 

.13 

199.4 

.24 

2.1 

2.2 

96.6 

.12 

212.3 

1.27 

96.3 

.13 

211.8 

.27 

2.2 

2.3 

97.8 

.12 

225. 

1.27 

97.6 

.11 

224.5 

.24 

2.3 

2.4 

99. 

.12 

237.7 

1.28 

98  7 

.12 

236.9 

.28 

2.4 

2.5 

100.2 

.11 

250.5 

1.29 

99.9 

.10 

249.7 

.27 

2.5 

2.6 

101.3 

.10 

263.4 

1.29 

100.9 

.10 

262.4 

1.27 

2.6 

2.7 

102.3 

.10 

276.3 

1.29 

101.9 

.09 

275.1 

1.28 

2.7 

2.8 

103.3 

.09 

289.2 

1.30 

102.8 

.09 

287.9 

1.29 

2.8 

2.9 

104.2 

.09 

302.2 

.31 

103.7 

.08 

300.8 

1.28 

2.9 

3. 

105.1 

.08 

315.3 

.31 

104.5 

.09 

313.6 

1.30 

3. 

8.1 

105.9 

.08 

328.4 

.31 

105.4 

.07 

326.6 

1.30 

3.1 

3.2 

106.7 

.08 

341.5 

.32 

106.1 

.08 

339.6 

1.30 

3.2 

3.3 

107.5 

.07 

354.7 

.32 

106.9 

.07 

352  .  6 

1.31 

3.3 

3.4 

108.2 

.07 

367  .  9 

.33 

107.6 

.06 

365.7 

1.30 

3.4 

3.5 

108.9 

.07 

381.2 

.32 

108.2 

.06 

378.7 

1.31 

3.5 

3.6 

109.6 

.06 

394.4 

.34 

108.8 

.07 

391.8 

1.32 

3.6 

3.7 

110.2 

.06 

407.8 

1.32 

109.5 

.05 

405. 

1.31 

3.7 

3.8 

110.8 

.06 

421. 

1.35 

110. 

.06 

418.1 

1.32 

3.8 

3.9 

111.4 

.06 

434.5 

1.33 

110.6 

.05 

431.3 

1.32 

3.9 

4. 

112. 

447.8 

111.1 

444.5 

4. 

OPEN    AND    CLOSED    CHANNELS. 


137 


TABLE  22. 

Based  on   Kutter's  formula,  with  ?i  — .02.     Values  of  the  factors  c  arid 
c\/r  for  use  in  the  formulae 

v  =  c\/rs    =  c  X  \/r~  X  %A    —  c\Jf    X  \A~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


1 

Vr 
in  feet 

1  in  1250r=4.224  ft.  per  mile 

1  in  1000  =  5.28  ft.  per  mile 

Vr 
in  feet 

s  =  .0008 

»  =  .001 

c 

diff. 
.01 

CX/F 

diff. 
.01 

c 

diff. 
.01 

cvT 

diff. 
.01 

.4 

41.7 

.67 

16.7 

.75 

41.9 

.67 

16.8 

.75 

.4 

.5 

48.4 

.58 

24.2 

.83 

48.6 

.58 

24  3 

.83 

.5 

.6 

54.2 

.51 

32.5 

.90 

54.4 

.51 

32.6 

.90 

.6 

.7 

59.3 

.45 

41.5 

.95 

59.5 

.45 

41.6 

.96 

.7 

.8 

63.8 

.40 

51. 

1. 

64. 

.40 

51.2 

1.00 

.8 

.9 

67.8 

.35 

61. 

1.03 

68. 

.35 

61.2 

.03 

.9 

1. 

71.3 

.32 

71.3 

1.07 

71.5 

.32 

71.5 

.08 

1 

1.1 

74.5 

.29 

82. 

1.09 

74.7 

.29 

82.3 

.08 

1   1 

.2 

77.4 

.27 

92.9 

1.12 

77.6 

.26 

93.1 

.12 

1.2 

.3 

80.1 

.24 

104.1 

1.14 

80.2 

.24 

104.3 

.13 

1.3 

.4 

82.5 

.22 

115.5 

1.16 

82.6 

22 

115.6 

.16 

1.4 

.5 

84.7 

.20 

127.1 

1.17 

84.8 

/20 

127.2 

.17 

1.5 

.6 

86.7 

.19 

138.8 

1.18 

86.8 

.18 

138.9 

1.17 

1.6 

.7 

88.6 

.18 

150.6 

.21 

88.6 

.18 

150.6 

1.21 

1.7 

.8 

90.4 

.16 

162.7 

.21 

90.4 

.16 

162.7 

1.21 

1.8 

.9 

92. 

.15 

174.8 

.22 

92. 

.15 

174.8 

1.22 

1.9 

2. 

93.5 

.14 

187. 

.22 

93.5 

.13 

187. 

1.21 

2. 

2.1 

94.9 

.13 

199.2 

.25 

94.8 

.13 

199.1 

1.23 

2.1 

2.2 

96.2 

.13 

211.7 

.25 

96.1 

.13 

211.4 

1.26 

2.2 

2.3 

97.5 

.11 

224.2 

.24 

97.4 

.11 

224. 

1.24 

2.3 

2.4 

98.6 

.11 

236.6 

.26 

98.5 

.11 

236.4 

1.26 

2.4 

2.5 

99.7 

.10 

249.2 

.27 

99.6 

.10 

249. 

1.25 

2.5 

2.6 

100.7 

.10 

261.9 

.27 

100.6 

.09 

261.5 

1.26 

2.6 

2.7 

101.7 

.09 

274.6 

.27 

101.5 

.09 

274.1 

1.26 

2.7 

2.8 

102.6 

•09 

287.3 

.28 

102.4 

.09 

286.7 

1.29 

2.8 

2.9 

103.5 

.08 

300.1 

.27 

103.3 

.08 

299.6 

.27 

2.9 

3. 

104.3 

.08 

312.8 

.30 

104.1 

.08 

312.3 

.29 

3. 

3.1 

105.1 

.07 

325.8 

.28 

104.9 

.07 

325.2 

.27 

3.1 

3.2 

105.8 

.07 

338.6 

.28 

105.6 

.07 

337.9 

.29 

3.2 

3.3 

106.5 

.07 

351.4 

.31 

106.3 

.07 

350.8 

.30 

3.3 

3.4 

107.2 

.07 

364.5 

.31 

107. 

.06 

363.8 

.28 

3.4 

3.5 

107.9 

.06 

377.6 

.30 

107.6 

.06 

376.6 

.29 

3.5 

3.6 

108.5 

.06 

390.6 

.31 

108.2 

.06 

389.5 

.31 

3.6 

3.7 

109.1 

.05 

403.7 

.28 

108.8 

.06 

402.6 

.31 

3.7 

3.8 

109.6 

.06 

416.5 

.33 

109.4 

.05 

415.7 

.29 

3.8 

3.9 

110.2 

.05 

429.8 

.30 

109.9 

.05 

428.6 

1.30 

3.9 

4. 

110.7 

442.8 

110.4 

441.6 

4. 

138 


PLOW    OF    WATER    IN 


TABLE   23. 

Based  on  Kutter's  formula,  with  n=  .0225.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c\/rs  =  c  X  \/~  X  \/s~=  c\/'r  X  \A' 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 

1  in  20000=:.  264  ft.  per  mile 

1  in  15840^.3333  ft.  per  mile 

Vr 

s  ==  .00005 

*  ==  .000063131 

in  feet 

diff. 

diff. 

diff. 

c^—      diff. 

in  feet 

c 

.01 

(V> 

.01 

c 

.01 

.01 

.4 

27.4 

.78 

11. 

.50 

28.5 

.57 

11.4 

.57 

.4 

.5 

33. 

.52 

16.5 

.64 

34.2 

.52 

17.1 

.65 

.5 

.6 

38.2 

.48 

22.9 

.72 

39.4 

.48 

23.6 

.74 

.6 

.7 

43. 

.45 

30.1 

.79 

44.2 

.45 

31. 

.79 

.7 

.8 

47.5 

.42 

38. 

.85 

48.7 

.41 

38.9 

.87 

.8 

.9 

51.7 

.40 

46.5 

.92 

52.8 

.39 

47.6 

.91 

.9 

1. 

55.7 

.37 

55.7 

.96 

56.7 

.36 

56.7 

.96 

I. 

I.I 

59.4 

.36 

65.3 

1.03 

60.3 

.34 

66.3 

.02 

1.1 

1.2 

63. 

.32 

75.6 

1.05 

63.7 

.32 

76.5 

.05 

1.2 

1.3 

66.2 

.31 

86.1 

1.09 

66.9 

.30 

87. 

.08 

1.3 

1.4 

69.3 

.30 

97. 

1.15 

69.9 

.28 

97.8 

.13 

.4 

1.5 

72.3 

.28 

108.5 

1.17 

72.7 

.27 

109.1 

.15 

.5 

1.6 

75.1 

.26 

120.2 

1.19 

75.4 

.25 

120.6 

.18 

.6 

1.7 

77.7 

.25 

132.1 

1.23 

77.9 

.23 

132.4 

.20 

.7 

1.8 

80.2 

.24 

144.4 

1.25 

80.2 

.23 

144.4 

.23 

.8 

1.9 

82.6 

.23 

156.9 

1.29 

82.5 

.21 

156.7 

.25 

1.9 

2 

84.9 

.22 

169.8 

.31 

84.6 

.21 

169.2 

.25 

2. 

2.1 

87.1 

.20 

182.9 

.31 

86.7 

.19 

182. 

.28 

2.1 

2.2 

89.1 

.20 

196. 

.35 

88.6 

.18 

194.9 

.31 

2  "2 

2.3 

91.1 

.19 

209.5 

.37 

90.4 

.18 

208. 

.32 

2.3 

2.4 

93. 

.18 

223.2 

.38 

92.2 

.17 

221.2 

.35 

2.4 

2.5 

94.8 

.18 

237. 

.42 

93.9 

.16 

234.7 

.35 

2.5 

2.6 

96.6 

.16 

251.2 

.39 

95.5 

.15 

248.2        .37 

2.6 

2.7 

98.2  |    .16 

265.1 

.43 

97. 

.15 

261.9  !     .38 

2.7 

2.8 

99.8 

.16 

279.4 

.47 

98.5 

.14 

275.7 

.39 

2.8 

2.9 

101.4 

.14 

294.1 

.43 

99.9 

.13 

289.6 

.41 

2.9 

3. 

102.8 

.15 

308.4 

.49 

101.2 

.13 

303.7 

.41 

3. 

3.1 

104.3 

.13 

323.3 

.46 

102.5 

.13 

317.8 

.42 

3.1 

3.2 

105.6 

.13 

337.9 

.52 

103.8 

.12 

332. 

.44 

3.2 

3.3 

106.9 

.13 

353.1 

.49 

105. 

.11 

346.4 

.44 

3.3 

3.4 

108.2 

.13 

368. 

.51 

106.1 

.11 

360.8 

.45 

3.4 

3.5 

109.5 

.12 

383.1 

.53 

107.2 

.11 

375.3 

.46 

3.5 

3.6 

110.7 

.11 

398.4 

.53 

108.3 

.10 

389.9 

.47 

3.6 

3.7 

111.8 

.11 

413.7 

.53 

109.3 

.10 

404.6 

.47 

3.7 

3.8 

112.9 

.11 

429. 

.55 

110.3 

10 

419.3 

1.48 

3.8 

3.9 

114. 

.10 

444.5 

.56 

111.3 

.09 

434.1 

1.48 

3.9 

4. 

115. 

460.1 

112.2 

448.9 

4. 

OPEN    AND    CLOSED    CHANNELS. 


139 


TABLE  23. 

Based  on  Kntter's  formula,  with  n  =  .0225.     Values  of  the  factors  c  and 
^/r  for  use  in  the  formulas 

v  =  c\/rs  =  c  X  \/r~  X  \A'  =  c^/r   X  \A 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr_ 

1  in  10000=.528  ft.  per  mile 

1  in  7500—  .704  ft.  per  mile 

Vr 

s=.0001 

s  =  .000133333 

in  feet 

diff. 

_ 

diff. 

diff. 

__ 

diff.  ihl  feet 

c 

.01 

c\/r 

.01 

c 

.01 

C^/T 

.01 

.4 

30.5 

.58 

12.2 

.00 

31.6 

.59 

12.6 

.61 

.4 

.5 

30.  3 

.53 

18.2 

.08 

37.5 

.52 

18.7 

.69 

.5 

.6 

41.6 

.48 

25 

.75 

42.7 

.48 

25.6 

.77 

.6 

py 
.  t 

46.4 

.43 

32.5 

.81 

47.5 

.43 

33.3 

.81 

.7 

.8 

50.7 

.41 

40.6 

.87 

51.8 

.40 

41.4 

.88 

.8 

.9 

54.8 

.37 

49.3 

.92 

55.8 

.36 

50.2 

.92 

.9 

1. 

58.5 

.34 

58.5 

.96 

59.4 

.33 

59.4 

.96 

1. 

1.1 

61.9 

.32 

68.1 

1. 

62.7 

.31 

69. 

1. 

1.1 

1.2 

65.1 

.30 

78.1 

1.04 

65.8 

.29 

79. 

1.03 

1.2 

1.3 

68.1 

.27 

88.5 

1.06 

68.7 

.26 

89.3 

1.05 

1.3 

1.4 

70.8 

.26 

99.1 

1.10 

71.3 

.25 

99.8 

1.09 

1.4 

1.5 

73.4 

.25 

110.1 

1.13 

73.8 

.23 

110.7 

1.11 

1.5 

1.6 

75.9 

.22 

121.4 

1.14 

76.1 

.22 

121.8 

1.13 

1.6 

1.7 

78.1 

.22 

132.8 

1.17 

78.3 

.20 

133.1 

1.14 

1.7 

1.8 

80.3 

.20 

144.5 

1.19 

80.3 

.18 

144.5 

1.17 

1.8 

1.9 

82.3 

.19 

156.4 

1.20 

82.1 

.16 

156.2 

1.18 

1.9 

2 

84.2 

.18 

168.4 

1.22 

83.7 

.16 

168. 

1.18 

2. 

2*1 

86. 

.17 

180.6 

1.23 

85.3 

.15 

179.8 

1.20 

2  1 

2.2 

87.7 

.16 

192.9 

1.25 

86.8 

.13 

191.8 

1.24 

2^2 

2^3 

89.3 

.15 

205.4 

1.25 

88.1 

.14 

204.2 

1.23 

3.3 

2.4 

90.8 

.15 

217.9 

1.29 

89.5 

.12 

216.5 

1.23 

2.4 

2.5 

92.3 

.14 

230.8 

1  28 

90.7 

.12 

228.8 

1.25 

2.5 

2.6 

93.7 

.13 

243.6 

1.29 

91.9 

.11 

241.3 

1.25 

2.6 

2.7 

95. 

.13 

256.5 

1.31 

93. 

.11 

253.8 

1.28 

2.7 

2.8 

96.3 

.12 

269.6 

1.32 

94.1 

.10 

266.6 

1.27 

2.8 

2.9 

97.5 

.11 

282  8 

1.30 

95.1 

.10 

279.3 

1.29 

2.9 

3. 

98.6 

.11 

295.8 

1.33 

96.1 

.09 

292.2 

1.28 

3. 

3.1 

99.7 

.11 

309.1 

1.35 

97. 

.09 

305. 

1.31 

3.1 

3.2 

100.8 

.10 

322.6 

1.33 

97.9 

.08 

318.1 

1.29 

3.2 

3.3 

101.8 

.10 

335.9 

1.36 

98.7 

.08 

331. 

1.31 

3.3 

3.4 

102.8 

.09 

349.5 

1.35 

99.5 

.08 

344.1 

1.29 

3.4 

3.5 

103.7 

.09 

363. 

1.36 

100.3 

.07 

357. 

1.31 

3.5 

3.6 

104.6 

.09 

376.6 

.38 

101. 

.07 

370.1 

1.32 

3.6 

3.7 

105.5 

.08 

390.4 

.35 

101.7 

.07 

383.3 

1.34 

3.7 

3.8 

106.3 

.08 

403.9 

.38 

102.4 

.07 

396.7 

1.36 

3.8 

3.9 

107.1 

.08 

417.7 

.39 

103.1 

.06 

410.3 

1.37 

3.9 

4. 

107.9 

431.6 

103.7 

424. 

4. 

140 


FLOW    OF    WATER    IN 


TABLE  23 

Based  on  Kutter's  formula,  with,  n  =  .0225.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formula} 

v  =  cx/ni  =  c  X  V^~  X  V~~  c^/r~X  V~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  5000=1.056  ft.  per  mile  | 

1  in  3333.3=1.584  ft.  per  mile 

Vr 
in  feet 

s  =  .0002 

*  =  .0003 

c 

diff. 
.01 

,—      diff. 
c^r        .01 

c 

diff. 
.01 

.—      diff. 
c^r    \     .01 

i 

.4 

33. 

.59 

13.2 

.62 

34. 

.59 

13.6 

.64 

.4 

.5 

38.8 

.52 

19.4 

.71 

39.9 

.53 

20. 

.71 

.5 

.6 

44.1 

.48 

26.5 

.77 

45.2 

.46 

27.1 

.78 

.6 

.7 

48.9 

.42 

34.2 

.83 

49.8 

.44 

34.9 

.85 

.7 

.8 

53.1 

.38 

42.5 

.87 

54.2 

.30 

43.4 

.86 

.8 

.9 

56.9 

.36 

51.2 

.93 

57.8 

.34 

52. 

.92 

.9 

60.5 

.32 

60.5 

.96 

61.2 

.32 

61.2 

.96 

'.1 

63.7 

.29 

70.1 

.98 

64.4 

.23 

70.8 

.98 

.1 

.2 

66.6 

.27 

79.9 

1.02 

67.2 

.20 

80.6 

1.01 

.2 

.3 

69.3 

.26 

90.1 

1.06 

69.8 

.25 

90.7 

1.05 

.3 

!4 

71.9 

.23 

100.7 

1.06 

72.3 

.22 

101.2 

1.06 

.4 

.5 

74.2 

.22 

111.3 

1.09 

74.5 

.21 

111.8 

1.08 

.5 

.6 

76.4 

.20 

122.2 

1.11 

76.6 

.19 

122.6 

1.09 

.6 

1.7 

78.4 

.19 

133.3 

1.12 

78.5 

.17 

133.5 

1.09 

1.7 

1.8 

80.3 

.18 

144.5 

1.15 

80.2 

.17 

144.4 

1.12 

1.8 

1.9 

82.1 

.16 

156. 

1114 

81.9 

.16 

155.6 

1.14 

1.9 

o 

83.7 

.16 

167.4 

.17 

83.5 

.15 

167. 

1.15 

2 

2.1 

85.3 

.15 

179.1 

.19 

85. 

.14 

178.5 

1.16. 

2'.1 

2.2 

86.8 

.13 

191. 

.16 

86.4 

.13 

190.1 

1.16 

2.2 

2.3 

88.1 

.14 

202.6 

.22 

87.7 

.13 

201.7 

1.19 

2.3 

2.4 

89.5 

.12 

214.8 

.20 

89. 

.11 

213.6 

1.17 

2.4 

2.5 

90.7 

.12 

226.8 

.21 

90.1 

.11 

225.3 

1.18 

2.5 

2.6 

91.9 

.11 

238.9 

1.22 

91.2 

.11 

237.1 

1.21 

2.6 

2.7 

93. 

.11 

251.1 

1.24 

92.3 

.10 

249.2 

1.20 

2.7 

2.8 

94.1 

.10 

263.5 

1.23 

93.3 

.09 

261.2 

1.20 

2.8 

2.9 

95.1 

.10 

275.8 

1.25 

94.2 

.09 

273.2 

1.21 

2.9 

3. 

96.1 

.09 

288.3 

1.24 

95.1 

.09 

285.3 

1.23 

3. 

3.1 

97. 

.09 

300.7 

1.26 

96. 

.08 

297.6 

1.22 

3.1 

3.2 

97.9 

.08 

313.3 

1.24 

96.8 

.07 

309.8 

1.19 

3.2 

3.3 

98.7 

.08     j  325.7 

1.26 

97.5 

.07 

321.7 

1.22 

3.3 

3.4 

99.5 

.08     i  338.3 

1.27 

98.2 

.08 

333.9 

1.26 

3.4 

3.5 

100.3 

.07 

351. 

1.26 

99. 

.07 

346.5 

1.24 

3.5 

3.6 

101. 

.07 

363.6 

1.27 

99.7 

.07 

358.9 

1.26 

3.6 

3.7 

101.7 

.07 

376.3 

1.28 

100.4 

.06 

371.5 

1.23 

3.7 

3.8 

102.4 

.07 

389.1 

1.30 

101. 

.06 

383.  8 

1.24 

3.8 

3.9 

103.1 

.06 

402.1 

1.27 

101.6 

.06 

396.2 

1.26 

3.9 

3. 

103.7 

414.8 

102.2 

408.8 

4. 

OPEN    AND    CLOSED    CHANNELS. 


141 


TABLE  23. 

Based  on  Kutter's  formula,  with  n  =  .0225.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c\/rs  =  c  X  \/~r~  X  \/#~  =  c\/r~  X  \/!T 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 

1  in  2500=2.112  ft.  per  mile 

1  in  1666.6=3.168  ft.  per  mile 

Vr 

s  —  .0004 

s  =  .0006 

in  feet 

diff. 

diff. 

diff. 

diff. 

in  feet 

c 

.01 

cW 

.01 

c 

.01 

c^r 

.01 

.4 

34.6 

.59 

13.8 

.65 

35.2 

.59 

14.1 

.65 

.4 

.5 

40.5 

.52 

20.3 

.71 

41.1 

.52 

20.6 

.75 

.5 

.6 

45.7 

.47 

27.4 

.79 

46.3 

.47 

28.1 

.76 

.6 

fj 
.  I 

50.4 

.41 

35.3 

.83 

51. 

.41 

35.7 

.84 

.7 

.8 

54.5 

.38 

43.6 

.89 

55.1 

.37 

44.1 

.88 

.8 

.9 

58.3 

.34 

52.5 

.92 

58.8 

.33 

52.9 

.92 

.9 

1. 

61.7 

.30 

61.7 

.95 

62.1 

.30 

62.1 

.95 

1. 

1.1 

64.7 

.28 

71.2 

.98 

65.1 

.28 

71.6 

.99 

1.1 

1.2 

67.5 

.26 

81. 

1.01 

67.9 

.25 

81.5 

1. 

1.2 

1.3 

70.1 

.24 

91.1 

.04 

70.4 

.23 

91.5 

1.03 

1.3 

1.4 

72.5 

.22 

101.5 

.04 

72.7 

.21 

101.8 

1.07 

14 

1.5 

74.7 

.20 

111.9 

.08 

74.8 

.20 

112.5 

1.05 

1.5 

16 

76.7 

.19 

122.7 

.09 

76.8 

.18 

123. 

1.08 

1.6 

1.7 

78.6 

.17 

133.6 

.09 

78.6 

.17 

133.8 

1.07 

1.7 

1.8 

80.3 

.16 

144.5 

.11 

80.3 

.16 

144.5 

1.11 

1.8 

1.9 

81.9 

.16 

155.6 

.14 

81.9 

.15 

155.6 

1.12 

1.9 

2 

83.5 

.14 

167. 

1.13 

83.4 

.13 

166.8 

1.09 

2. 

2  1 

84.9 

.13 

178.3 

1.13 

84.7 

.13 

177.7 

1.11 

2.1 

2.2 

86.2 

.13 

189.6 

1.17 

86. 

.13 

188.8 

1.15 

2.2 

2.3 

87.5 

.12 

201.3 

1.16 

87.3 

.11 

200.3 

1.14 

2.3 

2.4 

88.7 

.11 

212.9 

1.16 

88.4 

.11 

211.7 

1.13 

2.4 

2.5 

89.8 

.11 

224.5 

1.18 

89.5 

.10 

223. 

1.15 

2.5 

2.6 

90.9 

.10 

236.3 

1.18 

90.5 

.10 

234.5 

1.17 

2.6 

2.7 

91.9 

.09 

248.1 

.17 

91.5 

.09 

246.2 

1.14 

2.7 

2.8 

92.8 

.09 

259.8 

.19 

92.4 

.09 

257.6 

1.18 

2.8 

2.9 

93.7 

.09 

271.7 

.21 

93.3 

.08 

269.4 

1.29 

2.9 

3 

94.6 

.08 

283.8 

.19 

94.1 

.08 

282.3 

1.19 

3. 

3.1 

95.4 

.08 

295.7 

.21 

94.9 

.07 

294.2 

1.04 

3.1 

3.2 

96.2 

.08 

307.8 

.23 

95.6 

.08 

304.6 

1.19 

3.2 

3.3 

97. 

.07 

320.1 

1.21 

96.4 

.06 

316.5 

1.16 

3.3 

3.4 

97.7 

.07 

332.2 

1.22 

97. 

.07 

328.1 

1.20 

3.4 

3.5 

98.4 

.06 

344.4 

1.20 

97.7 

.06 

340.1 

1.18 

3.5 

3.6 

99. 

.06 

356.4 

1.23 

98.3 

.06 

351.9 

1.20 

3.6 

3.7 

99.6 

.06 

368.7 

1.23 

98.9 

.06 

363.9 

1.19 

3.7 

3.8 

100.2 

.06 

381. 

1.22 

99.5 

.06 

375.8 

1.19 

3.8 

3.9 

100.8 

.06 

393.2 

1.23 

100.1 

.05 

387.7 

1.20 

3.9 

4. 

101.4 

405.5 

100.6 

399.7 

4. 

142 


FLOW    OF    WATER    IN 


TABLE  23. 

Based  on  Kutter's  formula,  with  n  =  .0225.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulas 

v  =  c\/rs  =  c  X\/r    X  \A    =  c\/r    X  \A 
All  slopes  greater  than  1  in  lOOO'have  the  same  co-efficient  as  1  in  1000. 


iii  feet 

1  in  1250=4.224  ft.  per  mile 

1  in  1000—5.28  ft.  per  mile 

in  feet 

g  ==  .0008 

s  =  .001 

c 

diff. 
.01 

^ 

diff. 
.01 

c 

diff. 
.01 

diff. 
.01 

.4 

35.5 

.60 

14.2 

.65 

35.7 

.60 

14.3 

.65 

.4 

.5 

41.5 

.52 

20.7 

.73 

41.7 

.52 

20.8 

.73 

.5 

.6 

46.7 

.46 

28. 

.79 

46.9 

.46 

28.1 

.80 

.6 

.7 

51.3 

.41 

35.9 

.84 

51.5 

.40 

36.1 

.83 

.7 

.8 

55.4 

.36 

44.3 

.88 

55.5 

.37 

44.4 

.89 

.8 

.9 

59. 

.33 

53.1 

.92 

59.2 

.33 

53.3 

.92 

.9 

1. 

62.3 

.30 

62.3 

.95 

62.5 

.29 

62.5 

.94 

1 

1.1 

65.3 

.27 

71.8 

.98 

65.4 

.27 

71.9 

.98 

1.1 

1.2 

68. 

.25 

81.6 

1.01 

68.1 

.25 

81.7 

1.01 

1.2 

1.3 

70.5 

.23 

91.7 

1  02 

70.6 

.23 

91.8 

1.03 

1.3 

1.4 

72.8 

.21 

101.9 

1.05 

72.9 

.21 

102.1 

1.04 

1.4 

1.5 

74.9 

.19 

112.4 

1.05 

75. 

.19 

112.5 

1.05 

1.5 

1.6 

76.8 

.18 

122.9 

1.07 

76.9 

.18 

123. 

1.08 

1.6 

1.7 

78.6 

.17 

133.6 

1.09 

78.7 

.16 

133.8 

1.07 

1.7 

1.8 

80.3 

.16 

144.5 

1.11 

80.3 

.16 

144.5 

1.11 

1.8 

1.9 

81.9 

.14 

155.6 

1.10 

81.9 

.14 

155.6 

1.10 

1.9 

2, 

83.3 

.14 

166.6 

1.13 

83.3 

.13 

166.6 

1.11 

2. 

2.1 

84.7 

.12 

177.9 

1.11 

84.6 

.12 

177.7 

1.11 

2.1 

2.2 

85.9 

.12 

189. 

1.13 

85.8 

.13 

188.8 

1.15 

2.2 

2.3 

87.1 

.12 

200.3 

1.16 

87.1 

.11 

200.3 

1.14 

2.3 

2.4 

88.3 

.10 

211.9 

1.14 

88.2 

.10 

211.7 

1.13 

2.4 

2.5 

89.3 

.10 

223.3 

1.15 

89.2 

.10 

223. 

1.15 

2.5 

2.6 

90.3 

.10 

234.8 

1.17 

90.2 

.10 

234.5 

1.17 

2.6 

2.7 

91.3 

.09 

246.5 

1.17 

91.2 

.08 

246.2 

1.14 

2.7 

2.8 

92.2 

.08 

258.2 

1.15 

92. 

.09 

257.6 

1.18 

2.8 

2.9 

93. 

.08 

269.7 

1.17 

92.9 

.08 

269.4 

1.17 

2.9 

3. 

93.8 

.08 

281.4 

1.19 

93.7 

.08 

281.1 

1.19 

3. 

3.1 

94.6 

.08 

293.3 

1.20 

94.5 

.07 

293. 

1.16 

3.1 

3.2 

95.4 

.07 

305.3 

1.18 

95.2 

.07 

304.6 

1.19 

3.2 

3.3 

96.1 

.06 

317.1 

1.17 

95.9 

.06 

316.5 

1.16 

3.3 

3.4 

96.7 

.07 

328.8 

1.20 

96.5 

.07 

328.1 

1.20 

3.4 

3.5 

97.4 

.06 

340.8 

1.19 

97.2 

.06 

340.1 

1.18 

3.5 

3.6 

98. 

.06 

352.7 

1.20 

97.8 

.05 

351.9 

1.20 

3.6 

3.7 

98.6 

.05 

364.7 

1.20 

98.3 

.06 

363.9 

1.19 

3.7 

3.8 

99.1 

.06 

376.7 

1.20 

98.9 

.05 

375.8 

1.19 

3.8 

3.9 

99.7 

.05 

388.7 

1.20 

99.4 

.05 

387.7 

1.20 

3.9 

4. 

100.2 

400.7 

99.9 

399.7 

4. 

OPEN    AND    CLOSED    CHANNELS. 


143 


TABLE   24. 

Based  on  Kutter's  formula,  with  n  =  .025.       Values  of  the  factors  c  and 
/V  for  use  in  the  formulae 

v  =  c^/rs  =  c  X  \Xr~X  %/*""=  c^/r~  X  \A~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 

1  in  20000  =  .264  ft.  per  mile 

1  in  15840  =  .3333  ft.  per  mile 

s  =  .00005 

8  =  .000063131 

in  feet 

diff. 

diff. 

diff. 

_ 

diff. 

in  feet 

c 

.01 

cVr 

.01 

c 

.01 

cVr 

.01 

.4 

23.9 

.56 

9.6 

.48 

24.8 

.51 

9.94 

.50 

.4 

.5 

28.9 

.46 

14.4 

.57 

29.9 

.47 

14.9 

.57 

.5 

.6 

.44 

20.1 

.64 

34.6 

.43 

20.6 

.66 

.6 

.7 

37.9 

.41 

26.5 

.71 

38.9 

.41 

27.2 

.72 

.7 

.8 

42. 

.38 

33.6 

.76 

43. 

.37 

34.4 

.77 

.8 

.9 

45.8 

.36 

41.2 

.82 

46.7 

.36 

42.1 

.82 

.9 

1. 

49.4 

.34 

49.4 

.87 

50.3 

.33 

50.3 

.87 

1. 

1.1 

52.8 

.32 

58.1 

.92 

53.6 

.32 

59. 

.91 

1.1 

1.2 

56. 

.31 

67.3 

.95 

56.8 

.29 

68.1 

.95 

1.2 

1.3 

59.1 

.29 

76.8 

• 

59.7 

.28 

77.6 

.99 

1.3 

1.4 

62. 

.27 

86.8 

.03 

62.5 

.26 

87.5 

1.02 

1.4 

1.5 

64.7 

.26 

97.1 

!06 

65.1 

.25 

97.7 

1.05 

1.5 

1.6 

67.3 

.25 

107.7 

.10 

67.6 

.24 

108.2 

1.07 

1.6 

1.7 

69.8 

.24 

118.7 

.12 

70. 

.22 

118.9 

.11 

1.7 

1.8 

72.2 

.22 

129.9 

.15 

72.2 

.21 

130. 

.12 

1.8 

1.9 

74.4 

.22 

141.4 

.18 

74.3 

.21 

141.2 

.15 

1.0 

2. 

76.6 

.21 

153.2 

.20 

76.4 

.19 

152.7 

.17 

2. 

2.1 

78.7 

.19 

165.2 

.22 

78.3 

.18 

164.4 

.19 

2.1 

2.2 

80.6 

.19 

177.4 

.24 

80.1 

.18 

176.3 

.21 

2.2 

2.3 

82.5 

.18 

189.8 

.26 

81.9 

.17 

188.4 

.22 

2.3 

2.4 

84.3 

.18 

202.4 

.28 

83.6 

.16 

200.6 

.24 

2.4 

2.5 

86.1 

.16 

215.2 

1.29 

85.2 

.15 

213. 

.25 

2.5 

2.6 

87.7 

.16 

228  .  1 

1.31 

86.7 

.15 

225.5 

.27 

2.6 

2.7 

89.3 

.16 

241.2 

1.33 

88.2 

.14 

238.2 

.28 

2.7 

2.8 

90.9 

.15 

254.5 

1.34 

89.6 

.14 

251. 

.29 

2.8 

2.9 

92.4 

.14 

267.9 

1.35 

91. 

.13 

263.9 

.30 

2.9 

3. 

93.8 

.14 

281.4 

.36 

92.3 

.13 

276.9 

.32 

3. 

3.1 

95.2 

.13 

295. 

.38 

93.6 

.12 

290.1 

.32 

3.1 

3.2 

96.5 

.13 

308.8 

.39 

94.8 

.12 

303.3 

.33 

3.2 

3.3 

97.8 

.12 

322.7 

.40 

96. 

.11 

316.6 

.35 

3.3 

3.4 

99. 

.12 

336.7 

.41 

97.1 

.11 

330.1 

1.35 

3.4 

3.5 

100.2 

.12 

350.8 

.42 

98.2 

.10 

343.6 

1.36 

3.5 

3.6 

101.4 

.11 

365. 

.43 

99.2 

.10 

357.2 

1.37 

3.6 

3.7 

102.5 

.11 

379.3 

.43 

100.2 

.10 

370.9 

1.37 

3.7 

3.8 

103.6 

.10 

393.6 

.45 

101.2 

.10 

384.6 

1.38 

3.8 

3.9 

104.6 

.11 

408.1 

.47 

102.2 

.09 

398.4 

1.39 

3.9 

4. 

105.7 

422.8 

103.1 

412.3 

4. 

144 


FLOW    OF    WATEIl    IN 


TABLE  24. 

Based  on  Kutter's  formula,  with  n  —  .025.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c\/rs  =1  c  X  \/r   X  \/s~  =  cv/F  X  \/» 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 

in  feet 

1  in  10000=  .528  ft.  per  mile 

1  in  7500=.  704  ft.  per  mile 

Vr 

in  feet 

s  =  .0001 

s  =  .000133333 

c 

diff. 
.01 

c\/r 

diff. 
.01 

c 

diff. 
.01 

cVr 

diff. 
.01 

.4 

26.5 

.52 

10.6 

.53 

27.4 

.52 

11. 

.53 

.4 

.5 

31.7 

.47 

15.9 

.59 

32.6 

.47 

16.3 

.61 

.5 

.6 

36.4 

.43 

21.8 

.67 

37.3 

.43 

22.4 

.67 

.6 

.7 

40.7 

.40 

28.5 

.73 

41.6 

.40 

29.1 

.'74 

,  .7 

.8 

44.7 

.37 

35.8 

.78 

45.6 

.36 

36.5 

.78 

.8 

.9 

48.4 

.34 

43.6 

.82 

49.2 

.34 

44.3 

.83 

.9 

51.8 

.32 

51.8 

.87 

52.6 

.31 

52.6 

.87 

1. 

!i 

55. 

.30 

60.5 

.91 

55.7 

.28 

61.3 

.89 

1.1 

.2 

58. 

.27 

69.6 

.93 

58.5 

.27 

70.2 

.94 

1.2 

.3 

60.7 

.26 

78.9 

.97 

61.2 

.25 

79.6 

.96 

1.3 

.4 

63.3 

.25 

88.6 

1.01 

63.7 

.24 

89.2 

1.4 

.5 

65.8 

.22 

98.7 

1.01 

66.1 

.21 

99.2 

.99 

1.5 

.6 

68. 

.22 

108.8 

1.05 

68.2 

.21 

109.1 

.04 

1.6 

.7 

70.2 

.22 

119.3 

1.07 

70.3 

.19 

119.5 

.05 

1.7 

.8 

72.2 

.19 

130. 

1.08 

72.2 

.19 

130. 

.08 

1.8 

1.9 

74.1 

.19 

U0.8 

1.12 

74.1 

.17 

140.8 

.08 

1.9 

2. 

76. 

.17 

152. 

1.12 

75.8 

.16 

151.6 

.09 

2. 

2.1 

77.7 

.16 

163.2 

1.13 

77.4 

.16 

162.5 

.13 

2.1 

2.2 

79.3 

.16 

174.5 

1.16 

79. 

.14 

173.8 

.11 

2.2 

2.3 

80.9 

.15 

186.1 

1.17 

80.4 

.14 

184.9 

.14 

2.3 

2.4 

82.4 

.14 

197.8 

1.17        81.8 

.13 

196.3 

.15 

2.4 

2.5 

83.8 

.13 

209.5 

1.18 

83.1 

.13 

207.8 

.16 

2.5 

2.6 

85.1 

.13 

221.3 

1.20 

84.4 

.12 

219.4        .17 

2.6 

2.7 

86.4 

.12 

233.3 

1.20 

85.6 

.11 

231.1  i     .17 

2.7 

2.8 

87.6 

.12 

245.3 

1.22 

86.7 

.11 

242.8 

.18 

2.8 

2.9 

88.8 

.11 

257.5 

.22 

87.8 

.11 

254.6 

.21 

2.9 

3. 

89.9 

.11 

269.7 

.24 

88.9 

.10 

266.7 

.20 

3. 

3.1 

91. 

.10 

282.1 

.23 

89  9 

.09 

278.7  !     .19 

3.1 

3.2 

92. 

.10 

294.4 

.25 

90.8 

.09 

290.6 

.20 

3.2 

3.3 

83. 

.10 

306.9 

.27 

91.7 

.09 

302.6 

.19 

3.3 

3.4 

94. 

.09 

319.6 

1.25 

92.5 

.09 

314.5 

.22 

3.4 

3.5 

94.9 

.09 

332.1 

1.27 

93.3 

.09 

326.7 

.23 

3.5 

3.6 

95.8 

.08 

344.8 

1.27 

94.2 

.07 

339. 

22 

3.6 

3.7 

96.6 

.09 

357.5 

1.28 

94.9 

.08 

351.2 

.'24 

3.7 

3.8 

97.5 

.07 

370.3 

1.29 

95.7 

.07 

363.6 

.24 

3.8 

3.9 

98.2 

.08 

383.2 

1.28 

96.4 

.07 

376. 

.24 

3.9 

4. 

99. 

396. 

97.1 

388.4 

4. 

OPEN    AND    CLOSED    CHANNELS. 


145 


TABLE  24. 

Based  on  Kutter's  formula,  with  n  =  .025.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulas 


v  =  c\/rs  =  c  X 


X 


—  c^/r   X 


All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 

iii  feet 

1  in  5000=1.056  ft.  per  mile  ||l  in  3333.3=1.584  ft.  per  mile 

Vr 

in  feet 

s  =  .0002                                         s  =  .0003 

c 

diff. 
01 

c-v/F 

diff. 
.01 

c 

diff. 
.01 

<vT 

diff. 
.01 

.4 

28.6 

.53 

11.4 

.56 

29.5 

.53 

11.8 

.56 

.4 

.5 

33.9 

.47 

17. 

.62 

34.8 

.47 

17.4 

.63 

.5 

.6 

38.6 

.43 

23.2 

.68 

39.5 

.43 

23.7 

.70 

.6 

.7 

42.9 

.39 

30. 

.74 

43.8 

.38 

30.7 

.74 

.7 

.8 

46.8 

.35 

37.4 

.79 

47.6 

.35 

38.1 

.79 

.8 

.9 

50.3 

.33 

45.3 

.83 

51.1 

.32 

46. 

.83 

.9 

1. 

53.6 

.30 

53.6 

.87 

54.3 

.29 

54.3 

.86 

1. 

i.l 

56.6 

.29 

62.3 

.89 

57.2 

.27 

62.9 

.90 

1.1 

1.2 

59.3 

.26 

71.2 

.93 

59.9 

.24 

71.9 

.91 

1.2 

1.3 

61.9 

.24 

80.5 

.95 

62.3 

.23 

81. 

.94 

1.3 

1.4 

64.3 

.22 

90. 

.98 

64.6 

.21 

90.4 

.97 

1.4 

1.5 

66.5 

.20 

99.8 

.98 

66.7 

.20 

100.1 

.98 

1.5 

1.6 

68.5 

.19 

109.6 

.01 

68.7 

.18 

109.9 

1. 

1.6 

1.7 

70.4 

.19 

119.7 

.04 

70.5 

.18 

119.9 

.02 

1.7 

1.8 

72.3 

.16 

130.1 

.03 

72.3 

.17 

130.1 

.03 

1.8 

1.9 

73.9 

.17 

140.4 

.08 

73.9 

.15 

140.4 

.04 

1.9' 

2. 

75.6 

.15 

151.2 

.07 

75.4 

.14 

150.8 

.05 

2. 

2.1 

77.1 

.14 

161.9 

.08 

76.8 

.13 

161.3 

.05 

2  1 

2.2 

78.5 

.13 

172.7 

.08 

78.1 

.13 

171.8 

.08 

2  2 

2.3 

79.8 

.13 

183.5 

.11 

79.4 

.12 

182.6 

.08 

2.'3 

2.4 

81.1 

.12 

194.6 

.12 

83.6 

.11 

193.4 

.09 

2.4 

2.5 

82.3 

.12 

205.8 

.13 

81.7 

.11 

204.3 

.10 

2.5 

2.G 

83.5 

.10 

217.1 

.11 

82.8 

.10 

215.3 

.10 

2.6 

2.7 

84.5 

.11 

228.2 

.15 

83.8 

.10 

226.3 

.11 

2.7 

2.8 

85.6 

.10 

239.7 

.14 

84.8 

.09 

237.4 

.11 

2.8 

2.9 

86.6 

.09 

251.1 

.14 

85.7 

.09 

248.5 

.13 

2.9 

3. 

87.5 

.09 

262.5 

.15 

86.6 

.09 

559.8 

.15 

3. 

3.1 

88.4 

.09 

274. 

1.18 

87.5 

.08 

271.3 

.13 

3.1 

3.2 

89.3 

.08 

285.8 

1.15 

88.3 

.07 

282.6 

.11 

3.2 

3.3 

90.1 

.08 

297.3 

1.18 

89. 

.08 

293.7 

.16 

3.3 

3.4 

90.9 

.08 

309.1 

1.17 

89.8 

.07 

305.3 

.13 

3.4 

3.5 

91.7 

.07 

320.8 

1.18 

90.5 

.06 

316.6 

.15 

3.5 

3.6 

92.4 

.07 

332.6 

1.18 

91.1 

.07 

328.1 

.15 

3.6 

3.7 

93.1 

.07 

344.4 

1.19 

91.8 

.06 

339.6 

.16 

3.7 

3.8 

93.8 

.06 

356.3 

1.19 

92.4 

.06 

351.2 

.16 

3.8 

3.9 

94.4 

.06 

368.2 

1.19 

93. 

.06 

362.8 

1.1G 

3.9 

4. 

95. 

380.1 

93.6 

374.4 

4. 

10 


146 


FLOW    OP    WATER    IN 


TABLE  24. 

Baaed  on  Kutter's  formula,  with  n  =  .025.     Values  of  the  factors  c  and 
c\/r  for  use  iii  the  formula) 

v  —  c\/rs  =  c  X  N/V   X  \A'    =  CX/F  X  \/~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


•v/r 

in  feet 

1  in  2500=2.112  ft.  per  mile 

1  in  1666.7=3.168  ft.  per  mile 

Vr 

in  feet 

s  =  .0004 

s  =  .0006 

c 

cliff. 
.01 

cVr 

diflf. 
.01 

c 

diff. 
.01 

CV/F 

diff. 
.01 

.4 

30. 

.53 

12. 

.57 

30.5 

.53 

12.2 

.57 

.4 

.5 

35,3 

.47 

17.7 

.63 

35.8 

.47 

17.9 

.64 

.5 

.6 

40. 

.42 

24. 

.69 

40.5 

.42 

24.3 

.70 

.6 

.7 

44.2 

.38 

30.9 

.75 

44.7 

.38 

31.3 

.75 

.  / 

.8 

48. 

.35 

38.4 

.80 

48.5 

.34 

38.8 

.79 

.9 

51.5 

.31 

46.4 

.82 

51.9 

.31 

46.7 

.83 

'.9 

1. 

54.6 

.29 

54.6 

.87 

55. 

.29 

55. 

.87 

1. 

1.1 

57.5 

.26 

63.3 

.88 

57.9 

.25 

63.7 

.88 

1.1 

1  2 

60.1 

.25 

72.1 

.93 

60.4 

.24 

72.5 

.91 

1.2 

1.3 

62.6 

.22 

81.4 

.93 

62.8 

.22 

81.6 

.94 

1.3 

1.4 

64.8 

.21 

90.7 

.97 

65. 

.20 

91. 

.95 

1.4 

1.5 

66.9 

.19 

100.4 

.97 

67. 

.19 

100.5 

.97 

1.5 

1.6 

68.8 

.18 

110.1 

.99 

68.9 

.17 

110.2 

.98 

l.G 

1.7 

70.6 

.17 

120. 

1.01 

70.6 

.17 

120. 

1.01 

1.7 

1.8 

72.3 

.15 

130.1 

1.01 

72.3 

.15 

130.1 

1.01 

1.8 

1.9 

73.8 

.15 

140.2 

1.04 

73.8 

.14 

140.2 

1.C2 

1.9 

2 

75.3 

.14 

150.6 

1.05 

75.2 

.13 

150.4 

1.03 

o 

2^1 

76.7 

.13 

161  1 

1.05 

76.5 

.13 

160.7 

1.05 

2.1 

2.2 

78. 

.12 

171.6 

1.06 

77.8 

.12 

171.2 

1.05 

2.2 

2.3 

79.2 

.12 

182.2 

1.08 

79. 

.11 

181.7 

1.05 

2.3 

2.4 

80.4 

.11 

193. 

1.08 

80.1 

.11 

192.2 

1.08 

2.4 

2.5 

81.5 

.10 

203.8 

1.07 

81.2 

.10 

203. 

1.07 

2.5 

2.6 

82.5 

.10 

214.5 

1.10 

82.2 

.09 

213.7 

1.07 

2.6 

2.7 

83.5 

.09 

225.5 

1.08 

83.1 

.09 

224.4 

1.08 

2.7 

2.8 

84.4 

.09 

236.3 

1.11 

84. 

.09 

235.2 

1.10 

2.8 

2.9 

85.3 

.09 

247.4 

.12 

84.9 

.08 

246.2 

1.09 

2.9 

3. 

86.2 

.08 

258.6 

.11 

85.7 

.08 

257.1 

1.10 

3. 

3.1 

87. 

.07 

269.7 

.09 

86.5 

.07 

268.  1 

1.09 

3.1 

3.2 

87.7 

.08 

280.6 

.14 

87.2 

.07 

279. 

1.11 

3.2 

3.3 

88.5 

.07 

292. 

.13 

87.9 

.07 

290.1 

1.11 

3.3 

3.4 

89.2 

.07 

303.3 

.12 

88.6 

.06 

301.3 

1.11 

3.4 

3.5 

89.9 

.06 

314.5 

.13 

89.2 

.06 

312.3 

1.11 

3.5 

3.6 

90.5 

.06 

325.8 

.14 

89.8 

.06 

323.4 

1.12 

3.6 

3.7 

91.1 

.06 

337.2 

.13 

90.4 

.06 

334.6 

1.12 

3.7 

3.8 

91.7 

.06 

348.5 

.15 

91. 

.06 

345.8 

1.13 

3.8 

3.9 

92.3 

.05 

360. 

1.14 

91.6 

.05 

357.1 

1.12 

3.9 

4. 

92.8 

371.4 

92.1 

368.3 

4.. 

OPEN    AND    CLOSED    CHANNELS. 


147 


TABLE  24. 

Based  on  Kutter's  formula,  with  n=  .025.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formula 


=  c  X  xA    X  \A     =  c^r  X 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  1250=4.224  ft.  per  mile 

1  in  1000=5.28  ft.  per  mile 

Vr 

in  feet 

s  =  .0008 

*=.001 

c 

diff. 
.01 

cVr~ 

diff. 
.01 

c 

diff. 
.01 

cx/F 

diff. 
.01 

.4 

30.8 

.53 

12.3 

.58 

30.9 

.54 

12.4 

.58 

.4 

.5 

36.1 

.47 

18.1 

.64 

36.3 

.47 

18.2 

.64 

.5 

.6 

40.8 

.42 

24.5 

.70 

41 

.42 

24.6 

.70 

.6 

.7 

45. 

.38 

31.5 

.75 

45.2 

.37 

31.6 

.75 

.7 

.8 

48.8 

.34 

39. 

.80 

48.9 

.34 

39.1 

.80 

.8 

.9 

52  2 

.30 

47. 

.82 

52.3 

.31 

47.1 

.83 

.9 

55.2 

.28 

55.2 

.86 

55.4 

.28 

55.4 

.86 

1. 

.1 

58. 

.26 

63.8 

.89 

58.2 

.25 

64. 

.88 

1.1 

.2 

60.6 

.23 

72.7 

.91 

60.7 

.23 

72.8 

.91 

1.2 

.3 

62.9 

22 

81.8 

.93 

63. 

.22 

81.9 

.94 

.3 

.4 

65.1 

.20 

91.1 

.96 

65.2 

.20 

91.3 

.95 

.4 

.5 

67.1 

.18 

100.7 

.95 

67.2 

.18 

100.8 

.96 

.5 

.6 

68.9 

.18 

110.2 

1. 

69. 

.17 

110.4 

.98 

.6 

.7 

70.7 

.16 

120.2 

.99 

70.7 

.16 

120.2 

.99 

.7 

.8 

72.3 

.15 

130.1 

1.01 

72.3 

.15 

130.1 

1.01 

.8 

.9 

73.8 

.14 

140  2 

.02 

73.8 

.13 

140.2 

1. 

.9 

2. 

75.2 

.13 

150.4 

.03 

75.1 

.13 

150.2 

1.02 

2. 

2.1 

76.5 

12 

160.7 

.02 

76.4 

.13 

160.4 

1.05 

2.1 

2.2 

77.7 

.12 

170.9 

.06  ! 

77.7 

.11 

170.9 

.1.03 

2.2 

2.3 

78.9 

.11 

181.5 

.05 

78.8 

.11 

181.2 

1.06 

2.3 

2.4 

80. 

.10 

192. 

.05 

79.9 

.10 

191.8 

1.05 

2.4 

2.5 

81. 

10 

202  5 

.07 

80.9 

.10 

202.3 

1.06 

2.5 

2.6 

82. 

.09 

213.2 

.06 

81.9 

.09 

212.9 

1.07 

2.6 

2.7 

82.9 

.09 

223.8 

.08 

82.8 

.09 

223.6 

1.08 

2.7 

2.8 

83.8 

.08 

234.6 

.07 

83.7 

.08 

234  .4 

1.07 

2.8 

2.9 

84.6 

.08 

245.3 

.09 

84.5 

.08 

245.1 

1.08 

2.9 

3. 

85.4 

.08 

256.2 

.10 

85.3 

.07 

255.9 

1.07 

3. 

3.1 

86.2 

.07 

267.2 

.09 

86. 

.07 

266.6 

1.08 

3.1 

3.2 

86.9 

.07 

278.1 

.10 

86.7 

.07 

277.4 

1.07 

3.2 

3.3 

87.6 

.07 

289.1 

.11 

87.4 

.07 

288.4 

1.11 

3.3 

3.4 

88.3 

.06 

300.2 

.10 

88.1 

.06 

299.5 

1.10 

3.4 

3.5 

88.9 

.06 

311.2 

.10 

88.7 

.06 

310.5 

1.10 

3.5 

3.6 

89.5 

.06 

322  2 

.11 

89.3 

.06 

321.5 

1.10 

3.6 

3.7 

90.1 

.05 

333.3 

.12 

89.9 

.05 

332.5 

1.11 

3.7 

3.8 

90.6 

.06 

344.5 

.11 

90.4 

.06 

343.6 

1.11 

3.8 

3.9 

91.2 

.05 

355.6 

.12 

91. 

.05 

354.7 

1.11 

3.9 

4. 

91.7 

366.8 

91.5 

365.8 

4. 

148 


FLOW    OF    WATER    IN 


TABLE   25. 

Based  on  Emitter's  formula,  with  n  =  .0275.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c^/rs  =  c  X  x/r"  X  \A~  =  c\/r~  X  \A~ 
All  slopes  greater  thaii  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


x/r 
in  feet 

1  in  20000^.264  ft.  per  mile 

1  in  15840=.3333  ft.  per  mile 

Vr 
in  feet 

8  =  .00005 

'a  —  .  000063  131 

c 

diflf. 
.01 

cVr 

diff. 
.01 

C 

^    *r 

diff. 
.01 

4 

21.2 

.44 

8.5 

.43 

22. 

.45 

8.8 

.44 

.4 

.5 

25.6 

.42 

12.8 

.51 

26.5 

.42 

13.2 

.52 

5 

.6 

29.8 

.40 

17.9 

.58 

30.7 

40 

18.4 

.59 

.6 

.7 

33.8 

.37 

23.7 

.63 

34.7 

.37 

24.3 

.64 

.7 

8 

37.5 

.35 

30. 

.69 

38.4 

.35 

30.7 

.70 

.8 

.9 

41 

.34 

36.9 

.75 

41.9 

.32 

37.7 

.74 

.9 

44.4 

.31 

44.4 

.78 

45.1 

.31 

45.1 

.79 

•1 

47.5 

.30 

52.2 

.84 

48.2 

.29 

53. 

.83 

.1 

2 

50.5 

.28 

60.6 

.87 

51.1 

.28 

61.3 

.87 

2 

.3 

53.3 

.27 

69.3 

.91 

53.9 

.26 

70. 

.90 

.3 

4 

56. 

.26 

78.4 

.95 

56.5 

.24 

79. 

.94 

.4 

.5 

58.6 

.24 

87.9 

.98 

58.9 

.24 

88.4 

.96 

.5 

.6 

61. 

.24 

97.7 

.01 

61.3 

.22 

98. 

.00 

.6 

.7 

63.4 

.22 

107.8 

.05 

63.5 

.21 

108. 

.01 

.7 

.8 

65.6 

.22 

118.3 

.04 

65.6 

.20 

118.1 

.03 

.8 

.9 

67.8 

.20 

128.7 

.09 

67.6  i    .20 

128.4 

.06 

1.9 

2. 

69.8 

.19 

139.6 

.11 

69.5 

.19 

139. 

.10 

2 

2.1 

71.7 

.19 

150.7 

.13 

71.4 

.18 

150. 

.10 

2.1 

22 

73.6 

.18 

162. 

.15 

73.2 

.17 

161. 

.12 

2.2 

2.3 

75.4 

.18 

173.5 

.17 

74.9 

.16 

172.2 

.14 

2.3 

2.4 

77.2 

.16 

185.2 

.19 

76.5 

.15 

183.6 

.15 

2.4 

2  5 

78.8 

.16 

197.1 

.20 

78. 

.15 

195.1 

.17 

2.5 

2.6 

80.4 

.16 

209.1 

.22 

79.5  j    .15 

206.8 

.18 

2.6 

2.7 

82          .15 

221  3 

.24 

81.         .13 

218.6 

.19 

2.7 

2.8 

83.5      .14 

233.7 

.25 

82.3      .14 

230.5 

.21 

2.8 

2.9 

84.9  i    .14 

246.2 

.27 

83.7      .12     i  242.6 

.22 

2.9 

3. 

86.3 

.13 

258.9 

.28 

84.9      .12        254.8 

.23 

3. 

3.1 

87.6 

.13 

271.7 

.28 

86.1  1   .12        267.1 

24 

3.1 

3.2 

88.9 

.13 

284.5 

.31 

87.3      .12     i  279.5 

.25 

3.2 

3.3 

90.2 

.12 

297.6 

.31 

88.5  |    .11     !  292. 

.25 

3.3 

3.4 

91.4 

.11 

310.7 

.32 

89.6  j   .10     !  304.5 

.27 

3.4 

3.5 

92.5 

.12 

323.9 

.33 

90.6 

.10     |  317.2 

.28 

3.5 

3.6 

93.7 

11 

337.2 

.34 

91.6 

.11        330. 

.28 

3.6 

3.7 

94.8 

.10 

350.6 

.35 

92.7 

.09        342.8 

.29 

3.7 

3.8 

95.8 

.11 

364.1 

.37 

93.6 

.09     !  355.7 

.30 

3.8 

3.9 

96.9 

.10 

377.8 

.38 

94.5 

.09 

368.7 

.31 

3.9 

4. 

97.9 

391.6 

.38         95.4 

- 

381.8 

4. 

OPEN    AND    CLOSED    CHANNELS. 


149 


TABLE  25. 

Based  on  Kutter's  formula,  with  n  =  .0275.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulas 

v  —  c\/fi*  =  c  X  \/r    X  \A    =  c>/r    X  \/s 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  10000=:.  528  ft.  per  mile 

1  in  7500=.  704  ft.  per  mile 

Vr 

in  feet 

s  —  .0001 

s  =  .000133333 

c 

diff. 
.01 

cV~ 

diff. 
.01 

c 

diff. 
.01 

/-      diff. 
cVr         .01 

.4 

23.4 

.46 

9.4        .46 

24.2 

.47 

9.7  I     .47 

.4 

.5 

28. 

.4$ 

14.           .54 

28  9 

.43 

14.4 

.55 

.5 

.6 

32.3 

.40 

19.4 

.60 

33.2 

.39 

19.9 

.61 

.6 

.7 

36.3 

.36     I     25.4 

.65 

37.1 

.36 

28. 

.66 

.7 

.8 

39.9 

34 

31.9 

.71 

40.7 

.34 

32.6 

.71 

.8 

.9 

43.2 

.32 

39. 

.75 

44.1 

.31 

39.7 

.75 

.9 

46.5      .29          46.5 

.79 

47.2 

.29 

47.2 

.79 

1. 

.1 

49.4 

.28     i     54.4 

.82 

50.1 

.26 

55.1 

.82 

1.1 

.2 

52.2 

.26 

62.6 

.86 

52.7 

.25 

63.3 

.85 

1.2 

.3 

54.8 

.24 

71.2 

.89 

55.2 

.24 

71.8 

.88 

1.3 

.4 

57.2 

.23 

80.1 

.92 

57.6 

.22 

80.6 

.91 

1.4 

.5 

59.5 

.22 

89.3 

.94 

59.8 

.21 

89.7 

.93 

1.5 

.6 

61.7 

.20 

98.7 

.96 

61.9 

.19 

99. 

.94 

1.6 

.7 

63.7 

.19 

108.3 

.99 

63.8 

.19 

108.4 

.98 

1.7 

.8 

65.6 

.19 

118.2 

1. 

65.7 

.17 

118.2 

.98 

1..8 

.9 

67.5 

.17 

128.2 

1  02 

67.4 

.16 

128. 

.01 

1.9 

2. 

69.2 

.17 

138.4 

.04 

69. 

.16 

138.1 

.01 

2. 

2.1 

70.9 

.15 

148.8 

.04 

70.6 

.15 

148.2 

.03 

2.1 

2.2 

72.4 

.15 

159.4 

.07 

72.1 

.14 

158.5 

.05 

2.2 

2.3 

73.9 

.15 

170.1 

,08 

73.5 

.13 

169. 

.05 

2.3 

2.4 

75.4 

.13 

180.9 

.09 

74.8 

.13 

179.5 

.07 

2.4 

2.5 

76.7 

.13 

191.8 

.10 

76.1 

.12 

190.2 

.08 

2.5 

2.6 

78. 

.13 

202.8 

.12 

77.3 

.12 

201. 

.10 

2.6 

2.7 

79.3 

.12 

214. 

.13 

78.5 

.11 

212. 

1.08 

2.7 

2.8 

80.5 

.11 

225.3 

.14 

79.6 

.10 

222.8 

1.09 

2.8 

2.9 

81.6 

.11 

236.7 

.14 

80.6 

.10 

233.7 

1.12 

2.9 

3. 

82.7 

.11 

248.1 

.15 

81  6 

.10 

244.9 

1.12 

3. 

3.1 

83.8 

.10 

259.6 

.  17 

82.6 

.09 

256.1 

1.12 

3.1 

3.2 

84.8 

.10 

271.3 

.17 

83.5 

.09 

267.3 

1.14 

3.2 

3.3 

85.8 

.09 

283. 

.17 

84.4 

.09 

278.7 

1.13 

3.3 

3.4 

86.7 

.09 

294.7 

.19 

85.3 

.08 

290. 

4.15 

3.4 

3.5 

87.6 

.09 

306.6 

.19 

86.1 

.08 

301.5 

1.14 

3.5 

3.6 

88.5 

.08 

318.5 

.19 

86.9 

.08 

312.9 

1.16 

3.6 

3.7 

89.3 

.08 

330.4 

.20 

87.7 

.07 

224.5 

1.16 

3.7 

3.8 

90.1 

.08 

342.4 

.21 

88.4 

.07 

336.1 

1.16 

3.8 

3.9 

90.9 

.07 

354  5 

.21 

89.1 

.07 

347.7 

1.17 

3.9 

4. 

91.6 

366.6 

89.8 

359.4 

4. 

150 


FLOW    OF    WATER    IN 


TABLE   25. 

Based  on  Kutter's  formula,  with  n  =  .0275.     Values  of  the  factors  c  and 
/r  for  use  in  the  formulae 

v  =  c\/rs  =  c  X  \/r~  X  \f~s~  =  c\/r    X  \A 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  5000=1.056  ft.  per  mile 

1  in  3333.3—1.584  ft.  per  mile 

-v/r 
in  feet 

s  =  .0002 

s  =  .0003 

c 

diff. 
.01 

c\/r 

diff. 
.01 

c 

diff. 
.01 

c\A* 

diff. 
.01 

.4 

25.2 

.47 

10.1 

.    .49 

25.9 

.48 

10.4 

.50 

.4 

.5 

29.9 

.43 

15. 

.55 

30.7 

.43 

15.4 

.56 

5 

.6 

34.2 

.39 

20.5 

.62 

35. 

.39 

21. 

.62 

.6 

.7 

38.1 

.36 

26.7 

.67 

38.9 

.35 

27.2 

.67 

.7 

.8 

41.7 

.33 

33.4 

.71 

42.4 

.33 

33.9 

.72 

.8 

.9 

45. 

.30 

40.5 

.75 

45.7 

.29 

41.1 

.75 

.9 

1. 

48. 

.28 

48. 

.79 

48.6 

.28 

48.6 

.79 

1.1 

50.8 

.26 

55.9 

.82 

51.4 

.25 

56.5 

.82 

:  i 

1.2 

53.4 

.24 

64.1 

.84 

53.9 

.23 

64.7 

.84 

.2 

1.3 

55.8 

.22 

72.5 

.87 

56.2 

.22 

73.1 

.86 

.3 

1.4 

58. 

.21 

81.2 

.90 

58.4 

.20 

81.7 

.89 

.4 

1.5 

60.1 

.20 

90.2 

.92 

60.4 

.19 

90.6 

.90 

5 

1.6 

62.1 

.18 

99.4 

.93 

62.3 

.17 

99.6 

.92 

.6 

1.7 

63.9 

.18 

108.7 

.95 

64. 

.17 

108.8 

.94 

7 

1.8 

65.7 

.16 

118.2 

.97 

65.7 

.15 

118.2 

.95 

.8 

1.9 

67.3 

.15 

127.9 

.98 

67.2 

15 

127.7 

.97 

.9 

2 

68.8 

.15 

137.7 

.99 

68.7 

.14 

137.4 

.97 

2 

2.1 

70.3 

.13 

147.6 

1.00 

70.1      .13 

147.1 

.99 

2.1 

2.2 

71.6 

.13 

157.6 

1.02 

71.4 

.12 

157. 

.99 

2.2 

2.3 

72.9 

.13 

167.8 

1.03 

72.6 

.11 

166.9 

1.01 

2.3 

2.4 

74.2 

.12 

178.1 

1.03 

73.7 

.11 

177. 

.01 

2.4 

2.5 

75.4 

.11 

188.4 

1.05 

74.8 

.11 

187.1 

.02 

2.5 

2.6 

76.5 

.10 

198.9 

1.05 

75.9 

.10 

197.3 

.03 

2.6 

2.7 

77.5 

.11 

209.4 

1.06 

76.9 

.10 

207.6 

.04 

2.7 

2.8 

78.6 

.09 

220. 

1.06 

77.9 

.09 

218. 

.04 

2.8 

2.9 

79.5 

.09 

230.6 

1.08 

78.8 

.08 

228.4 

.05 

2.9 

3. 

80.4 

.09 

241.4 

1.08 

79.6 

.08 

238.9 

.05 

3. 

3.1 

81.3 

.09 

252.2 

1.08 

80.4 

.08 

249.4 

.06 

3.1 

3.2 

82.2 

.08 

263. 

1.09 

81.2 

.08 

260. 

.06 

3.2 

3.3 

83. 

.08 

273.9 

1.10 

82. 

.07 

270.6 

.07 

3.3 

3.4 

83.8 

.07 

284.9 

1.10 

82.7 

.07 

281.3 

.07 

3.4 

3.5 

84.5 

.08 

295.9 

1.10 

83.4 

.07 

292. 

.07 

3.5 

3.6 

85.3 

.06 

306.9 

1.11 

84.1 

.06 

302.7 

.08 

3.6 

3.7 

85.9 

.07 

318. 

1.11 

84.7 

.06 

313.5 

.08 

3.7 

3.8 

86.6 

.07 

329.1 

1.12 

85.3 

.06 

324.3 

.09 

3.8 

3.9 

87.3 

.06 

340.3 

1.12 

85.9 

.06 

335.2 

1.08 

3.9 

4. 

87.9 

351.5 

86.5 

346. 

4. 

OPEN    AND    CLOSED    CHANNELS. 


151 


TABLE   25. 

Based  on  Kutter's  formula,  with  n  — -  .0275.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c\/rs  =  c  X  \/r    X  \A    =  c\/r    X  \A' 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  2500=2.114  ft.  per  mile 

1  in  1666.7=3.168  ft.  per  mile 

Vr 

in  feet 

8=  .0004 

s  =  .0006 

c 

diff. 
.01 

j-VC-     diff- 
c^r        .01 

c 

diff. 
.01 

cVr 

diff. 
.01 

,4 

26.4 

.48 

10.5 

.51 

26.8 

.48 

10.7 

.51 

.4 

.5 

31.2 

.43 

15.6 

.57 

31.6 

.43 

15.8 

.57 

.5 

.6 

35.5 

.38 

21.3 

.62 

35.9 

.39 

21.5 

.63 

.6 

.7 

39.3 

.35 

27.5 

.68 

39.8 

.35 

27.8 

.68 

.7 

.8 

42.8 

.32 

34.3 

.71 

43.3 

.31 

34.6 

.72 

.8 

.9 

46. 

.30 

41.4 

.76 

46.4 

.29 

41.8 

.75 

.9 

1. 

49. 

.27 

49. 

.78 

49.3 

.27 

49.3 

.79 

1. 

1.1 

51.7 

.24 

56.8 

.81 

52. 

.24 

57.2 

.81 

1.1 

1.2 

54.1 

.23 

64.9 

.85 

54.4 

.23 

65.3 

.84 

1.2 

1.3 

56.4 

.21 

73.4 

.86 

56.7 

.20 

73.7 

.85 

1.3 

1.4 

58.5 

.20 

82. 

.88 

58.7 

.20 

82.2 

.88 

1.4 

1.5 

60.5 

.19 

90.8 

.90 

60.7 

.18 

91. 

.89 

1.5 

1.6 

62.4 

.17 

99.  8 

.91 

62.5 

.16 

99.9 

.91 

1.6 

1.7 

64.1 

.16 

108.9 

.93 

64.1 

.16 

109. 

.92 

1.7 

1.8 

65.7 

.15 

118.2 

.95 

65.7 

.15 

118.2 

.94 

1.8 

1.9 

67.2 

.14 

127.7 

.95 

67.2 

.13 

127.6 

.94 

1.9 

2. 

68.6 

.13 

137.2 

.97 

68.5 

.13 

137. 

.96 

2. 

2.1 

69.9 

.12 

146.9 

.96 

69.8 

.12 

146.6 

.97 

2.1 

2.2 

71.1 

.13 

156.5 

1. 

71. 

.12 

156.3 

.97 

2.2 

2.3 

72.4 

.12 

166.5 

1. 

72.2 

.11 

166. 

.99 

2.3 

2.4 

73.6 

.10 

176.5 

1. 

73.3 

.10 

175.9 

.99 

2.4 

2.5 

74.6 

.10 

186.5 

1. 

74.3 

.10 

185.8 

.99 

2.5 

2.6 

75.6 

.10 

196.5 

1.02 

75.3 

.09 

195.7 

1.01 

2.6 

2.7 

76.6 

.10 

206.7 

1.04 

76.2 

.09 

205.8 

1.01 

2.7 

2.8 

77.6 

.08 

217.1 

1.03 

77.1 

.08 

215.9 

1.01 

2.8 

2.9 

78.4 

.08 

227.4 

1.02 

77.9 

.08 

226. 

1.02 

2.9 

3. 

79.2 

.08 

237.6 

1.03 

78.7 

.08 

236.2 

.02 

3. 

3.1 

80. 

.07 

247.9 

1.05 

79.5 

.07 

246.4 

.03 

3.1 

3.2 

80.7 

08 

258.4 

1.04 

80.2 

.07 

256.7 

.03 

3.2 

3.3 

31.5 

.07 

268.8 

1.06 

80.9 

.07 

267. 

.04 

3.3 

3.4 

82.2 

.06 

279.4 

1.05 

81.6 

.06 

277.4 

.04 

3.4 

3.5 

82.8 

.07 

289.9 

1.06 

82.2 

.06 

287.8 

.04 

3.5 

3.6 

83.5 

.06 

300.5 

1.06 

82.8 

.06 

298.2 

1.05 

3.6 

3.7 

84.1 

.06 

311.1 

1.07 

83.4 

.06 

308.7 

1.05 

3.7 

3.8 

84.7 

.05 

321.8 

1.07 

84. 

.05 

319.2 

1.05 

3.8 

3.9 

85.2 

.06 

332.5 

1.07 

84.5 

.06 

329.7 

1.06 

3.9 

4. 

85.8 

343.2 

85.1 

340.3 

4. 

152 


FLOW    OF    WATER    IN 


TABLE  25. 

Based  on  Kutter's  formula,  with  n  =  .0275      Values  of  the  factors  c  and 
r.\/r  for  use  in  the  formulas 

v  —  c\/rs  =  c  X  \fr  X  -N/S"  =  c\/r  X  \/s 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  1250=4.224  ft.  per  mile  j 

1  in  1000=5.28  ft.  per  mile 

Vr 
in.  feet 

*  ==  .0008 

s  =  .001 

c 

diff. 
.01 

CV/F 

diff. 
.01 

c 

i 

diff. 
.01 

c\/r 

diff. 
.01 

.4 

27.1 

48 

10.8 

.51 

27.2 

.48 

10.9 

.51 

.4 

.5 

31.9 

.43 

15.9 

.58 

32. 

.43 

16. 

.58 

.5 

.6 

36.2 

.38 

21.7 

.63 

36.3 

.39 

21.8 

.63 

.6 

.7 

40. 

.35 

28. 

.68 

40.2 

.34 

28.1 

.68 

.7 

.8 

43.5 

.32 

34.8 

.72 

43  6 

.32 

34.9 

.72 

.8 

.9 

46.7 

.28 

42. 

.75 

46.8 

.28 

42.1 

.75 

.9 

1 

49.5 

.27 

49.5 

.78 

49.6 

.27 

49.6 

.79 

1. 

1.1 

52.2 

.24 

57.3 

.82 

52.3 

.23 

57.5 

.81 

1.1 

1.2 

54.6 

.22 

65.5 

.83 

54.6 

.23 

65.6 

.83 

1.2 

1.3 

56.8 

20 

73.8 

.86 

56.9 

.20 

73.9 

.85 

1.3 

.4 

58.8 

.19 

82.4 

.87 

58.9 

.19 

82.4 

.88 

1.4 

.5 

60.7 

18 

91.1 

.89 

60.8 

.17 

91.2 

.89 

1.5 

.6 

62.5 

.17 

100. 

.91 

62.5 

.17 

100.1 

.90 

1.6 

m 
.  1 

64  2 

.15 

109.1 

.91 

64.2 

.15 

109.1 

.91 

1.7 

8 

65  7 

14 

118.2 

.94 

65.7 

.14 

118.2 

.93 

1.8 

.9 

67.1 

.14 

127.6 

.94 

67.1 

.14 

127.5 

.94 

1.9 

2 

68.5 

.13 

137. 

.95 

68.5 

.12 

136.9 

.95 

2. 

21 

69.8 

.11 

146.5 

.96 

69.7 

.12 

146.4 

.96 

2.1 

2.2 

70.9 

.12 

156.1 

.97 

70.9 

.11 

156. 

.96 

2.2 

2.3 

72.1 

.11 

165.8 

.98 

72. 

.11 

165.6 

.98 

2.3 

2.4 

73.2 

.10 

175.6 

.98 

73.1 

.10 

175.4 

.98 

2.4 

25 

74.2 

.09 

185.4 

.99 

74.1 

.09 

185.2 

.99 

2.5 

2.6 

75.1 

.09 

195.3 

1. 

75. 

.09 

195.1 

.99 

2.6 

2.7 

76. 

09 

205.3 

1. 

75.9 

.09 

205. 

1. 

2.7 

2.8 

76.9 

.08 

215.3 

1.01 

76.8 

.08 

215. 

1. 

2.8 

2.9 

77.7 

.08 

225.4 

.01 

77.6 

.08 

225. 

1.01 

2.9 

3.       j     78.5 

.07 

235.5 

.02 

78.4 

.07 

235.1 

1.01 

3. 

3  1 

79.2 

.07 

245.5 

02 

79.1 

.07 

245.2 

1.02 

3.1 

3.2 

79.9 

.08 

255.9 

.02 

79.8 

.07 

255.4 

1.02 

3.2 

33 

80.7 

.06 

266.1 

.03 

80.5 

.06 

265.6 

1.02 

3.3 

3.4 

81.3 

06 

276.4 

.03 

81.1 

.07 

275.8 

1.03 

3.4 

3.5 

81.9 

.06 

286.7 

.04 

81.8 

.05 

286.1 

1.03 

3.5 

3.6 

82.5 

06 

297.1 

.04 

82.3 

.06 

296.4 

1.04 

3.6 

3.7 

83.1 

.06 

307  .  5 

1.04 

82.9 

.05 

306.8 

1.03 

3.7 

3.8 

83.7 

.05 

317.9 

1.04 

83.4 

.06 

317.1 

1.04 

3.8 

3.9 

84.2 

.05 

328.3 

1.05 

84. 

.05 

327.5 

1.04 

3.9 

4. 

84.7 

338.8 

84.5 

337.9 

4. 

OPEN    AND    CLOSED    CHANNELS. 


153 


TABLE  26. 

Based  on  Kutter's  formula,  with  n  =  .030.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c \/rs  —  c  X  \/r~  X  \/s~  =  c\/~ X  \/*~~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


vV 

1  in  20000=.  264  ft.  per  mile    | 

1  in  15840  =  .3333  ft.  per  mile 

v/r 

s  =  .00005 

5  =  .0000631  31 

in  feet 

diff. 

y  

diff. 

diff. 

diff. 

in  feet 

c 

.01 

c\/r 

.01 

c 

.01 

Cv/r 

.01 

.4 

19. 

.40 

7.59 

.39 

19.6 

.42 

7.86 

.40 

.4 

.5 

23. 

.38 

11.5 

.46 

23  8 

.38 

11.9 

.47 

.5 

.6 

26.8 

.37 

16.1 

.52 

27.6 

.36 

16.6 

.53 

6 

.7 

30.5 

.34 

21.3 

.58 

31.2 

.34 

21.9 

.58 

.  7 

.8    • 

33.9 

.32 

27.1 

.63 

34.6 

33 

27.7 

.64 

8 

.9 

37.1 

.31 

33.4 

.68 

37.9 

.30 

34.1 

.68 

.9 

1. 

40.2 

.29 

40.2 

.72 

40.9 

.28 

40.9 

.72 

1. 

1.1 

43.1 

.28 

47.4 

.77 

43.7 

.28 

48.1 

.77 

1.1 

1.2 

45.9 

.27 

55.1 

.80 

46.5 

.25 

55.8 

.80 

1.2 

1.3 

48.6 

.25 

63.1 

.84 

49. 

.24 

63.8 

.82 

1.3 

1.4 

51.1 

.24 

71.5 

.88 

51.4 

.24 

72. 

.87 

1.4 

1.5 

53.5 

.23 

80.3 

.90 

53  8 

.22 

80.7 

.89 

1.5 

1.6 

55.8 

.22 

89.3 

.93 

56. 

.21 

89.6 

.92 

1.6 

1.7 

58. 

.21 

98.6 

.96 

58.1 

.21 

98.8 

.95 

1.7 

1.8 

60.1 

.21 

108.2 

.99 

60.2 

.19 

108.3 

.96 

1.8 

1.9 

62.2 

.19 

118.1 

.01 

62.1 

.18 

117.9 

.99 

1.9 

2. 

64.1 

.19 

128.2 

.03 

63.9 

.18 

127.8 

1.01 

2. 

2.1 

66. 

.18 

138.5 

.06 

65.7 

.17 

137.9 

.03 

2.1 

2.2 

67.8 

.17 

149.1 

.06 

67.4 

.16 

148.2 

05 

2.2 

2.3 

69.5 

.17 

159.9 

.08 

69 

.15 

158.7 

.06 

23 

2.4 

71.2 

.16 

170.8 

.11 

70.5 

.15 

169.3 

.10 

24 

2.5 

72.8 

.15 

181.9 

1.13 

72. 

.16 

180.3 

.10 

2.5 

2.6 

74.3 

.14 

193.2 

1.12 

73.6 

.13 

191.3 

.08 

2  6 

2.7 

75.7 

.15 

204.4 

1.19 

74  9 

.13 

202.1 

.12 

2.7 

2.8, 

77.2 

.14 

216.3 

1.17 

76.2 

.13 

213.3 

.13 

28 

2.9 

78.6 

.14 

228. 

1.19 

77.5 

.12 

224.6 

.15 

2.9 

3. 

80. 

.13 

239.9 

1.20 

78.7 

.12 

236.1 

.16 

3. 

3.1 

81.3 

.12 

251.9 

1.21 

79.9 

.11 

247.7 

.16 

3.1 

3.2 

82.5 

.12 

264. 

1.23 

81. 

.12     !  259  3 

1.18 

3.2 

3.3 

83.7 

.12 

276.3 

1.24 

82  2 

.10       271.1 

1.19 

3.3 

3.4 

84.9 

.11 

288.7 

1  24 

83.2 

.11     1  283. 

1.20 

3.4 

3.5 

86. 

.11 

301.1 

1.26    : 

84.3 

.1.0     (295. 

.20 

3.5 

3.6 

87.1 

.11 

313  7 

1.27  j 

85.3 

.10     i  307. 

.21 

3.6 

3.7 

88.2 

.11 

326.4 

1.28 

86.3 

.09     i  319.1 

.22 

3.7 

3.8 

89.3 

.10 

339.2 

1.28  ! 

87.2 

09       331  .  3 

23 

3.8 

3.9 

90.3 

.09 

352. 

1.30 

88.1 

.09 

343.6 

]24 

3.9 

4. 

91.2 

365. 

89. 

356. 

4. 

i 

154 


FLOW    OP    WATER    IN 


TABLE   26. 

Based  on   Kutter's  formula,  with  n  =  .030.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c\S7s    —  c  X  -s/r"  X  \A~  =  c\/r~  X  -N/S~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


v/r 
in  feet 

1  in   10000=.528  ft.  per  mile 

1  in  7500:—  .704  ft.  per  mile 

-v/r 
in  feet 

s  =  .0001 

*  =  .000133333 

c 

diff, 
.01 

c^/r 

diff. 
.01 

c 

diff. 
.01 

cy/r 

diff. 
.01 

A 

20.9 

.42 

8.4 

.42 

21.5 

.43 

8.6 

.43 

.4 

.5 

25.1 

.39 

12.6 

.48 

25.8 

.39 

12.9 

.49 

.5 

.6 

29. 

.36 

17.4 

.54 

29.7 

.36 

17.8 

.55 

.6 

.7 

32.6 

34 

22.8 

.60 

33.3 

.34 

23.3 

.61 

.7 

.8 

36. 

.31 

28.8 

.64 

36.7 

.31 

29.4 

.64 

.8 

.9 

39.1 

.30 

35.2 

.69 

39.8 

.29 

35.8 

.69 

.9 

1. 

42.1 

.27 

42.1 

.72 

42.7 

.27 

42.7 

.72 

1. 

.1 

44.8 

.26 

49.3 

.76 

45.4 

.25 

49.9 

.76 

1.1 

2 

47.4 

.25 

56.9 

.80 

47.9 

.24 

57.5 

.79 

1.2 

.3 

49.9 

.23 

64.9 

.82 

50.3 

.22 

65.4 

.81 

1.3 

.4 

52.2 

.21 

73.1 

.84 

52.5 

.21 

73.5 

.84 

1.4 

.5 

54.3 

.21 

81.5 

.87 

54.6 

.19 

81.9 

.85 

1.5 

.6 

56.4 

.19 

90.2 

.89 

56.5 

.19 

90.4 

.89 

1.6 

.7 

58.3 

.19 

99.1 

.93 

58.4 

.18 

99.3 

.91 

1.7 

1.8 

60.2 

.17 

108  4 

.92 

60.2 

.17 

108.4 

.92 

1.8 

1.9 

61.9 

.17 

117.6 

.96 

61.9 

.15 

117.6 

.92 

1.9 

2. 

63.6 

.16 

127.2 

.97 

63.4 

.15 

126.8 

.95 

2 

2.1 

65.2 

.15 

136.9 

.98 

64.9 

.15 

136.3 

.98 

2.1 

2.2 

66.7 

.14 

146.7 

.99 

66.4 

.13 

146.1 

.96 

2  2 

2.3 

68.1 

.14 

156.6 

1.02 

67.7 

.13 

155.7 

99 

2.3 

2.4 

69.5  !    .13 

166.8 

1.02 

69. 

.13 

165.6 

1.02 

2.4 

2.5 

70.8      .13 

177. 

1.05 

70.3 

.12 

175.8 

1.01 

2.5 

2.6 

72.1  1   .12 

187.5 

1.04 

71.5 

.11 

185.9 

1.01 

2.6 

2.7 

73.3  |   .12 

197.9 

1.07 

72.6 

.11 

196. 

1.04 

2.7 

2.8 

74.5 

.11 

208.6 

1.06 

73.7 

.10 

206.4 

1.02 

2.8 

2.9 

75.6 

.10 

219.2 

1.06 

74.7 

.10 

216.6 

1.05 

2.9 

3. 

76  6 

.11 

229.8 

1.11 

75.7 

.10 

227.1 

1.07 

3. 

3.1 

77.7      .10 

240.9 

1.09 

76.7 

.09 

237.8 

1.05 

3.1 

3.2 

78.7      .09 

251.8 

1.09 

77.6 

.08 

248.3 

1.04 

3.2 

3.3 

79.6      .09 

262.7 

.10 

78.4 

.08 

258.7 

06 

3.3 

3.4 

80.5  i   .09 

273.7 

1.13 

79.2 

.08 

269.3 

.09 

3.4 

3.5 

81.4 

.09 

285. 

.12 

80. 

.08 

280.2 

.08 

3.5 

3.6 

82.3 

.08 

296.2 

.13 

80.8 

.08 

291. 

.09 

3.6 

3.7 

83.1 

.08 

307.5 

.13 

81.6 

.07 

301.9 

.09 

3.7 

3.8 

83.9 

.08 

318.8 

.14 

82.3 

.07 

312.8 

.10 

3.8 

3.9 

84.7 

.07 

330.2 

.15 

83. 

.07 

323.8 

.10 

3.9 

4. 

85.4 

341.7 

83.7 

334.8 

4. 

OPEN    AND    CLOSED    CHANNELS. 


155 


TABLE   26. 

Based  on  Kutter's  formula,  with  n  =  .030.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 


v  =  c-s/fl  =  c  X  ^/r~  X  \/s~  --~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000, 


-v/r 
in  feet 

1  in  5000  =  1.056  ft.  per  mile 

1  in  3333.  3  =  1.584  ft.  per  mile 

Vr 

in  feet 

8  =  .0002 

s  =  .0003 

c 

diff. 
.01 

c\/r 

diff. 
.01 

c 

diff. 
.01 

c\/r 

diff. 
.01 

.4 

22.4 

.43 

8.96      .45 

23.1 

.43           9.24 

.45 

.4 

.5 

26.7 

.42 

13.4 

.50 

27.4 

.40          13.7 

.51 

.5 

.6 

30.7 

.36 

18.4 

.56 

31.4 

.36          18.8 

.57 

.6 

.7 

34.3 

.33 

24. 

.61 

35. 

.32          24.5 

•     .61 

.7 

.8 

37.6 

.30 

30.1 

.64 

38.2 

.30          30.6 

.65 

.8 

.9 

40.6 

.29 

36.5 

.70 

41.2 

.28          37.1 

.69 

.9 

43.5 

.26 

43.5 

.72 

44. 

.26          44. 

.73 

1. 

.1 

46.1 

.24 

50.7 

.75 

46.6 

.24          51.3 

.75 

1.1 

.2 

48.5 

.23 

58.2 

.78 

49. 

.22          58.8 

.78 

1.2 

.3 

50.8 

.21 

66. 

.81 

51.2 

.20          66.6 

.79 

1.3 

.4 

52.9 

.20 

74.1 

.83 

53  2 

.19          74.5 

.82 

1.4 

.5 

54.9 

.19 

82.4 

.85 

55.1 

.18         82.7 

.83 

1.5 

.6 

56.8 

.17 

90.9 

.86 

56.9 

.17          91. 

.86 

1.6 

.7 

58.5 

.17 

99.5 

.89 

58.6 

.16          99.6 

.88 

1.7 

1.8 

60.2 

.16 

108.4 

.90 

60.2 

.15        108.4 

.88 

1.8 

1.9 

61.8 

.14 

117.4 

.90 

61.7 

.14        117.2 

.90 

1.9 

2 

63.2 

.14 

126.4 

.93 

63.1 

.13        126.2 

.90 

2. 

2.1 

64.6 

14 

135.7 

.95 

64.4 

.13        135.2 

.93 

2.1 

2.2 

66 

.12 

145.2 

.94 

65.7 

.12 

144.5 

.94 

2.2 

23 

67.2 

.12 

154.6 

.96 

66.9 

.11 

153.9 

.93 

2.3 

2.4 

68.4 

.12 

164.2 

.98 

68. 

.11 

163.2 

.96 

2.4 

2.5 

69.6 

.11 

174 

.98 

69  1 

.10 

172.8 

.95 

2.5 

2.6 

70.7 

.10 

183.8 

.98 

70.1 

.10 

182.3 

.97 

2.6 

2.7 

71.7 

.10 

193.6 

1. 

71.1 

.09        192. 

.96 

2.7 

2.8 

72.7 

.09 

203.6 

.98 

72. 

.09       201  6 

.98 

2.8 

2.9 

73.6 

.09 

213.4 

1.01 

72.9 

.08     j  211.4 

.97 

2.9 

3. 

74.5 

.09 

223.5 

1.02 

73.7 

.09 

221.1 

1.02 

3. 

3.1 

75.4 

.08 

233.7 

1.01 

74.6 

.09 

231.3 

.97 

3.1 

3.2 

76.2 

.08 

243.8 

1.03 

75.3 

.08 

241. 

1.01 

3.2 

3.3 

77. 

.08 

254.1 

1.03 

76.1 

.07 

251.1 

1.01 

3.3 

3  4 

77.8 

.08 

264.5 

1.04 

76.8 

.07 

261.1 

1. 

3.4 

3.5 

78.6 

.07 

274.9 

1.04 

77.5 

.06 

271.2 

1.01 

3.5 

3.6 

79.3 

.06 

285  3 

1.05 

78.1 

.07 

281.3 

1.01 

3.6 

3.7 

79.9 

.07 

295.8 

1.05 

78.8 

.06 

291.5 

1.02 

3.7 

3.8 

80.6 

.06 

308.3 

1.05 

79.4 

.06 

301.7 

1.02 

3.8 

3.9 

81.2 

.07 

316.8 

1.06 

80. 

.06 

311.9 

1.02 

3.9 

4. 

81.9 

327.4 

80.6 

322.2 

4. 

156 


FLOW    OF    WATER    IN 


TABLE  26- 

Based  on  Kutter's  formula,  with  n  =  .030.     Values  of  the  factors  c  and 
c<\/r  for  use  in  the  formulas 

v  =  c\/r~s  —  c  X  A/r~  X  \/~  =  c^/r~  X  \/«~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


1  in  2500  =  2.114  ft   per  mile 

1  in  1666.7=3.168  ft.  per  mile 

Vr 
in  feet 

Vr 
in  feet 

a  =  .0004 

s  =  .0006 

c 

diff. 
.01 

c^/T 

diff. 
.01 

c 

diff. 
.01 

c<v/r 

diff. 
.01 

.4 

23.5 

.43 

9.4 

.45 

23  9 

.43 

9.6 

.45 

.4 

.5 

27.8 

.40 

13.9 

.52 

28.2 

.40 

14.1 

.52 

.5 

.6 

31.8 

.35 

19.1 

.56 

32.2 

.36 

19.3 

.58 

.6 

.7 

35.3 

.33 

24.7 

.62 

35.8 

.32 

25.1 

.61 

.7 

.8 

38.6 

.30 

30.9 

.65 

39. 

.29 

31.2 

.65 

.8 

.9 

41.6 

.27 

37  4 

.69 

41.9 

.28 

37.7 

.70 

.9 

1. 

44.3 

.25 

44.3 

.72 

44.7 

.24 

44.7 

.71 

1. 

1.1 

46.8 

.24 

51.5 

.75 

47.1 

.23 

51.8 

.75 

1.1 

1.2 

49.2 

.22 

59. 

.78 

49.4 

.22 

59  3 

.78 

1.2 

1.3 

51.4 

.20 

66.8 

.80 

51.6 

.19 

67.1 

.78 

1.3 

1.4 

53.4 

.18 

74.8 

.80 

53.5 

.19 

74.9 

.82 

1.4 

1.5 

55.2 

.18 

82.8 

.84 

55  4 

.17 

83.1 

.83 

1.5 

1.6 

57. 

.17 

91.2 

.86 

57.1 

.16 

91.4 

84 

1.6 

1.7 

58.7 

.15 

99.8 

.86 

58.7 

16 

99.8 

.86 

1.7 

1.8 

60  2 

.14 

108.4 

.86 

60.2 

.14 

108.4 

.86 

1.8 

1.9 

61.6 

.14 

117. 

.90 

61.6 

.13 

117. 

.88 

1.9 

2. 

63. 

.13 

126. 

.90 

62.9 

.13 

125.8 

.90 

2. 

2.1 

64.3 

.12 

135. 

.91 

64.2 

.12 

134.8 

.91 

2.1 

2.2 

65.5 

.12 

144.1 

.93 

65.4 

.11 

143.9 

.91 

2.2 

2.3 

66.7 

.11 

153.4 

.93 

66.5 

.11 

153. 

.94 

2.3 

2.4 

67  8 

.10 

162.7 

.93 

67.6 

.10 

162.4 

.91 

2.4 

2.5 

68.8 

.10 

172. 

.95 

68.6 

.09 

171.5 

.92 

2.5 

2.6 

69.8 

.10 

181.5 

.97 

69.5 

.09 

180.7 

.94 

2.6 

2.7 

70.8 

.09 

191.2 

.96 

70.4 

.09 

190.1 

.95 

2.7 

2.8 

71.7 

.08 

200.8 

,95 

71.3 

.08 

199.6 

.95 

2.8 

2.9 

72.5 

.08 

210.3 

.96 

72.1 

.08 

209.1 

.96 

2.9 

3. 

73  3 

.08 

219.9 

1. 

72.9 

.08 

218.7 

.98 

3. 

3.1 

74.1 

.08 

229.9 

.98 

73.7 

.07 

228.5 

.96 

3.1 

3.2 

74.9 

.07 

239.7 

.98 

74.4 

.07 

238.1 

.97 

3.2 

3.3 

75.6 

.07 

249.5 

.99 

75.1 

.06 

247.8 

.96 

3.3 

3.4 

76.3 

.06 

259.4 

.99 

75.7 

.07 

257.4 

.99 

3.4 

3.5 

76.9 

.07 

269.3 

.99 

76.4 

.06 

267.3 

.98 

3.5 

3.6 

77.6 

.06 

279.2 

1.01 

77. 

.06 

277.1 

.98 

3.6 

3.7 

78.2 

.06 

289.3 

1. 

77.6 

.05 

286.9 

.98 

3.7 

3.8 

78.8 

.06 

299.3 

1.01 

78.1 

.06 

296.8 

.99 

3.8 

3.9 

79.3 

.05 

309  4 

1.01 

78.7 

.05 

306.7 

.99 

3.9 

4. 

79.9 

.06 

319.5 

79.2 

316.7 

4. 

OPEN    AND    CLOSED    CHANNELS. 


157 


TABLE  26. 

Based  on  Kutter's  formula,  with  n  =  .030,     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formula 

v  =  c vV*  =  c  X  \/r~  X  \A~~  =  c\/r~  X  <\A~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 

1  in  1250=4.224  ft.  per  mile 

1  in  1000=5.28  ft.  per  mile 

Vr 

a  =  .0008 

«'=  .001 

in  feet 

diff. 

,—     diff. 

diff. 

diff. 

in  feet 

c 

.01 

cvr    |     .01 

c 

.01 

cVr 

.01 

.4 

24.1 

44 

9.6 

.47 

24.2 

.44 

9.7      .46 

.4 

.5 

28.5 

.39 

14.3 

.53 

28.6 

.39 

14.3 

.52 

.5 

.6 

32.4 

.36 

19.4 

.58 

32.5 

.36 

19.5 

.58 

.6 

.7 

36. 

.32 

25.2 

.62 

36.1      .32 

25.3 

.61 

.7 

.8 

39.2 

.29 

31.4 

.65 

39.3  !    .29 

31.4      .66 

8 

.9 

42.1 

.27 

37.9 

.69 

42.2 

.27 

38.         .69 

.9 

1. 

44.8 

25 

44.8 

.72 

44.9 

.25 

44.9      .72 

1. 

1.1 

47.3 

.23 

52. 

.75 

47.4  !    .23 

52.1       .75 

.1 

1.2 

49.6 

21 

59.5 

.77 

49.7 

.21 

59.6      .77 

.2 

1.3 

51.7 

.19 

67.2 

.78 

51.8 

.19 

67.3 

.79 

.3 

1.4 

53  6 

.18 

75. 

.81 

53.7 

.18 

75.2 

81 

.4 

1.5 

55.4 

.17 

83.1 

.83 

55.5 

.17 

83.3 

.82 

.5 

1.6 

57.1 

.16 

91.4 

.84 

57.2 

.15 

91.5 

.83 

.6 

1.7 

58.7 

.15 

99.8 

.86 

58.7 

.15 

99.8      .86 

.7 

1.8 

60.2 

.14 

108.4 

.86 

60.2 

.14 

108.4      .86 

8 

1.9 

61.6 

.13 

117. 

.88 

61.6 

.13 

117.         .88 

.9  ' 

2. 

62  9 

.12 

125.8 

.88 

62.9 

.12 

125.8      .88 

2 

2.1 

64.1 

.12 

134.6 

.91 

64.1 

.12 

134.6      .89 

2.  1 

2.2 

65.3 

11 

143.7 

.90 

65  3 

.10 

143.7      .88 

2^2 

2.3 

66.4 

10 

152.7 

.91 

66.3 

.11 

152.5 

.93 

2.3 

2.4 

67.4 

.10 

161.8 

.92 

67.4 

.09 

161  8 

.90 

2.4 

2.5 

68.4 

.10 

171. 

.94 

68.3 

.10 

170.8 

.94 

2  5 

2.6 

69  4 

.09 

180.4 

.94 

69.3 

.09 

180.2 

.93 

2.6 

2.7 

70.3 

08 

189.8 

.93 

70.2 

.08 

189.5 

.93 

2.7 

2.8 

71   1 

.08 

199.1 

.94 

71. 

.08 

198.8 

.94 

2.8 

2.9 

71.9 

.08 

208.5 

.96 

71.8 

.08 

208.2 

96 

2.9 

3. 

72.7 

.07 

218.1 

.94 

72.6 

.07 

217.8 

.94 

3. 

3.1 

73.4 

.07 

227.5 

.96 

73.3 

.07 

227.2 

.96 

3.1 

3.2 

74.1 

.07 

237.1  !   .97 

74. 

.06 

236.8 

.94 

3.2 

3.3 

74.8 

.06 

246.8      .96 

74.6 

.07 

246.2 

.98 

3.3 

3.4 

75  4 

07 

256.4 

.98 

75.3 

.06 

256. 

.97 

3.4 

3.5 

76.1 

.06 

266.2 

.98 

75  9 

.06 

265.7 

.96 

3.5 

3.6 

76.7 

.05 

276. 

.98 

76  5 

.05 

275.3 

.98 

3.6 

3.7 

77.2 

.06 

285.8 

.98 

77. 

.06 

285.1 

98 

3.7 

3.8 

77.8 

.05 

295.6 

.98 

77.6 

.05 

294  8 

.98 

38 

3.9 

78.3 

.05 

305.4 

.98 

78.1 

.05 

304.6 

.98 

3.9 

4. 

78.8 

.05 

315.2 

78.6 

.05 

314.4 

4 

158 


FLOW"  OF  WATER  IN 


TABLE  27. 

Based  on  Kutter's  formula,  with  n  =  .035.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  =  c^/rs  =  c  X  Vr~  X  \A~  =  c\/r~  X  N/S~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


•v/r 
in  feet 

1  in  20000=.  264  ft.  per  mile 

1  in  15840=.  3333  ft.  per  mile 

Vr 
in  feet 

s  =  .00005 

s  =  .000063131 

c 

diff. 
.01 

cV'r 

diff. 
.01 

c 

diff. 
.0! 

cVr 

diff. 
.01 

4 

15.6 

34 

6.3 

.32 

16.2 

.34 

6.46 

.34 

.4 

.5 

19. 

.33 

9  5 

.39 

19.6 

.33 

9.8 

.39 

.5 

.6 

22.3 

.31 

13  4 

.44 

22.9 

.31 

13.7 

.45 

.6 

.7 

25.4 

.29 

17.8 

.49 

26. 

.29 

18.2 

.49 

.7 

.8 

28.3 

.28 

22.7 

53 

28.9 

.28 

23.1 

.54 

.8 

.9 

31.1 

.27 

28. 

.58 

31.7 

.26          28.5 

.58 

.9 

1. 

33.8 

.26 

33  8 

62 

34.3 

26 

34.3 

.63 

1. 

1.1 

36.4 

.24 

40 

.66 

36.9 

.24 

40.6 

.65 

1.1 

1.2 

38.8 

23 

46  6 

.69 

39.3 

.22 

47.1 

.69 

1  2 

1.3 

41  1 

23 

53  5 

.73 

41.5 

.22 

54 

.72 

1.3 

1  4 

43.4 

22 

60.8 

75 

43.7 

.21 

61.2 

.75 

1.4 

1  5 

45  6 

.20 

68.3 

.79 

45  8 

20 

68.7 

.78 

1.5 

1.6 

47.6 

.20 

76.2 

81 

47.8 

19 

76.5 

.80 

1.6 

1.7 

49-6 

19 

84.3 

84 

49.7 

19 

84.5 

.83 

1.7 

1.8 

51.5 

19 

92.7 

.87 

51.6 

.17 

92.8 

.85 

1.8 

1.9 

53.4 

17 

101  4 

.88 

53.3 

.17 

101  3 

87 

1.9 

2. 

55  1 

18 

110  2 

.92 

55. 

.16 

110 

.80 

2. 

2.1 

56  9 

.16 

119.4 

.93 

56.6 

16 

118,9 

.91 

2.1 

2  2 

58.5 

.16 

128.7 

.95 

58.2 

.15     i   128 

.91 

2.2 

2.3 

60.1 

15 

138.2 

.97 

59.7 

.14        137.2 

.92 

2.3 

2.4 

61.6 

.15 

147  9 

99 

61.1 

.14 

146.7 

.95 

2.4 

2.5 

63.1 

14 

157.8 

1. 

62.5 

.13 

156.2 

.95 

2  5 

2.6 

64.5 

.14 

167.8 

1.02 

63.8 

13        166            .98 

2.6 

2.7 

65.9 

.14 

178. 

.04 

65  1 

.  13        175  9         99 

2.7 

2.8 

67.3 

.13 

188.4 

.04 

66.4 

.12        185  9 

2.8 

2  9 

68.6 

.12 

198.8 

.06 

67.6 

.12     !   196. 

.01 

2.9 

3. 

69.8 

.12 

209.4 

.09 

68  8 

11 

206.3 

.03 

3. 

3.1 

71. 

.12 

220.3 

.09 

69.9 

11 

216.7 

.04 

3.1 

3.2 

72.2 

.12 

231.2 

10 

71. 

.10 

227  2 

05 

3.2 

3.3 

73.4 

.11 

242  2 

.11 

72. 

.11 

237.8 

.06 

3.3 

3  4 

74  5 

.11 

253.3 

.13 

73.1 

.10 

248  5 

.07 

3.4 

3.5 

75.6 

.10 

264.6 

.13 

74.1 

.09 

259.2 

.07 

3.5 

3.6 

76.6 

.11 

275.9 

15 

75. 

.10 

270.1 

.09 

3.6 

3.7 

77.7 

10 

287.4 

15 

76. 

.09 

282.1 

.10 

3.7 

3.8 

78.7 

.09 

298  9 

.17 

76.9 

.09 

291.1 

.10 

3.8 

3.9 

79  6 

.10 

310.6 

.18 

77.8 

.08 

303  3 

.12 

3.9 

4. 

80.6 

322.4 

78.6 

314.5 

.12 

4. 

OPEN    AND    CLOSED    CHANNELS. 


159 


TABLE  27. 

Based  on  Kutter's  formula,  with  n  =  .035.     Values  of  the  factors  c  and 
c\/r  for  use  in  the  formulae 

v  —  c\/rs  =  c  X  \/r~ X  \/~  =  c\/r~  X  \/s~ 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


v'r 

in  feet 

1  in  10000=0  52S  ft.   per  mile 

1  in  7500=0.704  ft.  per  mile 

Vr 
in  feet 

s  =  .0001 

s=.  000133333. 

c 

diff. 
.01 

cVr 

diff. 
.01 

c 

diff. 
.01 

c\/r 

diff. 
.01 

.4 

17.1 

.36 

6.84 

.36 

17.6      .36    , 

7.04 

.36 

.4 

.5 

20.7 

.83 

10.4 

.40 

21.2 

.34 

10.6 

.42 

.5 

.6 

24. 

.31 

14.4 

.46 

24.6 

.31 

14.8 

.46 

.6 

.7 

27.1 

.29 

19. 

.50 

27.7 

.29 

19.4 

51 

.  7 

.8 

30. 

.27 

24. 

.54 

30.6 

.27 

24.5 

55 

.8 

.9 

32.7 

.26 

29.4 

.59 

33.3 

.25 

30. 

58 

.9 

35.3 

.24 

35.3 

.62 

35.8 

.24 

35  8 

62 

I 

37.7 

.23 

41.5 

.65 

38.2 

23 

42 

66 

!l 

.2 

40 

.22 

48. 

.69 

40.5 

.21 

48.6 

68 

.2 

.3 

42  2 

.21 

54.9 

.71 

42.6 

.20 

55  4 

.70 

.3 

.4 

44.3 

.19 

62. 

.73 

44.6 

.19 

62.4 

74 

.4 

.5 

46  2 

.19 

69.3 

.77 

46.5 

.18 

69.8 

.75 

1.5 

.6 

48.1 

.18 

77. 

.78 

48.3 

17 

77.3 

.77 

1.6 

.7 

49.9 

.17 

84.8 

.81 

50. 

.16 

85. 

.79 

1.7 

.8 

51.6 

16 

92  9 

.82 

51.6 

15 

92  9 

80 

1.8 

1.9 

53  2 

.15 

101.1 

.83 

53  1 

15 

100.9 

.80 

1.9  • 

2. 

54.7 

.15 

109.4 

.86 

54  6 

14 

109  2 

.83 

2. 

2.1 

56  2 

.14 

118. 

.87 

56. 

.13 

117.6 

84 

2.1 

2.2 

57.6 

.13 

126.7 

.88 

57.3 

13 

126  1 

85 

2.2 

2.3 

58.9 

.13 

135.5 

.90 

58  6 

.12 

134.8 

87 

2.3 

2.4 

60.2 

.13 

144  5 

.93 

59  8 

.11 

143.5 

.87 

2.4 

2.5 

61.5 

.12 

153.8 

.92 

60.9 

.12 

152  3 

.88 

2.5 

2.6 

62  7 

.11 

163. 

.93 

62  1 

10 

161  5 

.89 

2.6 

2.7 

63  8 

.11 

172.3 

94 

63  1 

11 

170  4 

.94 

2.7 

2.8 

64.9 

.11 

181.7 

.97 

64  2 

.09 

179.8 

90 

2.8 

2.9 

66. 

10 

191.4 

.96 

65.1 

.10 

188.8 

.95 

2.9 

3. 

67. 

.10 

201 

.98 

66  1 

.09 

198.3 

.94 

3. 

3.1 

68. 

09 

210  8 

.97 

67. 

.09 

207.7 

.96 

3.1 

3.2 

68  9 

09 

220  5 

.98 

67.9 

.08 

217.3 

.94 

3.2 

3.3 

69  8 

.09 

230  3 

01 

68.7 

08 

226  7 

96 

3.3 

3.4 

70.7 

.99 

240  4 

.01 

69  5 

.09 

236  3 

.98 

3.4 

3.5 

71.6 

.08 

250.5 

.01 

70.4 

.07 

246  1 

.97 

3.5 

3.6 

72  4 

08 

260.6 

.02 

71.1 

.07 

255.8 

.99 

3.6 

3.7 

73.2 

.07 

270.8 

.02 

71.8 

.07 

265  7 

.98 

3.7 

3.8 

74. 

.07 

281. 

.04 

72  5 

.07 

275.5 

.99 

3.8 

3.9 

74.7 

.07 

291.4 

.03 

73.2 

.07 

285.4 

1.01 

39 

4. 

75.4 

301.7 

73.9 

295.5 

4. 

160 


FLOW    OF    WATER    IN 


TABLE  27. 

Based  on  Kutter's  formula,  with  n  —  .035.     Values  of  the  factors  c  and 
/F  for  use  in  the  formulae 


=  c  X  \/      X  \/*=  cv"    X 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 

in  feet 

*  =  .0002 

8  =.  . 

0003 

Vr 

in  feet 

c 

diff.           /—      diff. 
.01        c^r         .01 

C 

diff. 
.01 

c\/r~ 

diff. 
.01 

.4 

18.3 

.36           7.32 

.37 

18.8 

.37 

7.52 

38 

.4 

.5 

21  9 

.34          11.         .42 

22  5 

.34 

11.3 

.42 

.5 

.6 

25  3 

.30 

15.2 

.40 

25.9 

.30 

15.5 

.47 

.6 

.7 

28  3      .  30 

19  8      .52           28.9 

.29 

20.2 

.52 

.7 

.8 

31.3  i    .26 

25.         .55           31.8 

.26 

25.4 

.56 

.8 

.9 

33.9      .25 

30.5 

.59     !     34.4 

25 

31 

.59 

.9 

1. 

36  4      .24 

36.4 

.63           36.9 

.23 

36  9 

.62 

1. 

I 

38.8 

.21 

42.7 

64           39  2 

.21 

43.1 

.65 

1.1 

2 

40.9 

.21 

49.1 

68     !      41.3 

.19 

49.6 

.67 

1.2 

.3 

43. 

.19 

55  9        70          43.3 

.19 

56.3 

.70 

1.3 

A 

44.9 

.18 

62.9 

72          45  2 

.17 

63.3 

71 

1.4 

.5 

46.7      .17 

70.1 

.73     i      46.9 

.17 

70.4 

.74 

1.5 

.6 

48.4      .17 

77.4 

.78 

48.6 

15 

77.8 

.74 

1.6 

.7 

50  1       .15 

85.2 

.77 

50  1 

15 

85  2 

.77 

1.7 

.8 

51  6      .14 

92.9 

.78 

51.6 

.14 

92  9 

78 

1.8 

.9 

53 

.14        100  7 

81 

53. 

.13 

100.7 

.79 

1.9 

2. 

54.4      .13     i   108.8 

84 

54.3      .12 

108.6 

.80 

2. 

2.1 

55.7 

13 

117. 

.84 

55.5 

.12 

116.6 

.81 

2.1 

2.2 

57. 

.12 

125.4 

.85           56.7 

11 

124.7 

.82 

2.2 

2.3 

58  2 

.11 

133.9 

.84           57.8 

.11 

132.9 

85 

2.3 

2.4 

59  3 

.11 

142.3 

.87           58.9 

10 

141.4 

84 

2.4 

2.5 

60  4 

.10 

151. 

86      i     59.9 

.10 

149  8 

85 

2.5 

2.6 

61.4 

10 

159.6 

89           60  9 

.09 

158.3 

.86 

2.6 

2.7 

62.4 

.09 

168  5 

.87           61.8 

.09 

166.9 

.87 

2.7 

2.8 

63.3 

.09 

177.2 

.90 

62.7 

,09 

175.6 

.88 

2.8 

2.9 

64  2 

.09 

186.2 

.91 

63.6 

.08 

184.4 

.88 

2.9 

3. 

65  1 

.09 

195.3 

.93 

64.4 

08 

193  2 

89 

3. 

3.1 

66 

.08 

204  6 

.92 

65.2 

.07 

202  1 

88 

3.1 

3.2 

66.8 

.07 

213.8 

90 

65.9 

.08 

210.9 

.92 

3.2 

3.3 

67  5 

.08 

222.8 

94 

66.7 

07 

220.1 

.91 

3.3 

3.4 

68.3 

.07 

232  .  2 

.93 

67.4 

.06 

229.2 

.89 

3.4 

3.5 

69.         .07 

241.5 

.94 

68. 

.07 

238.1 

.91 

3.5 

3.6         69  7      .07 

250.9 

.94 

68.7 

.06 

247.2 

.92 

3.6 

3.7 

70  4      .06 

260.3 

.95 

69  3 

06 

256  4 

.92 

3.7 

3.8 

71.         .06 

269.8 

.95 

69.9 

.06 

265  6 

.92 

3.8 

3.9 

71.6      .06 

279.3 

.96 

70.5 

.05 

274.8 

.93 

3.9 

4. 

72.2 

288.9 

71. 

284.1 

4. 

OPEN    AND    CLOSED    CHANNELS. 


161 


TABLE  27. 

Based  on  Kutter's  formula,  with  %  =  .035.     Values  of  the  factors  c  and 
/r  for  use  in  the  formulse 


=  c  X  \/r    X  \A    =  c\/r    X  VV^- 
All  slopes  greater  than  1  in  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 
in  feet 

1  in  2500=2.112  ft.  per  mile 

1  in  1666.7=3.168  ft.  per  mile 

Vr 
in  feet 

s  —  .0004 

s  =a  .0006 

c 

diff. 
.01 

cvr 

diff. 
.01 

c 

diff. 
.01 

c^r 

diff. 
.01 

.4 

19.1      .37 

7.6 

.38 

19  4 

37 

7.76 

.39 

.4 

.5 

22  8  !    .34 

11.4 

.43 

23  1 

.34 

11.6 

.43 

.5 

.6 

26.2  j    .30 

15.7 

.47 

26.5 

.31 

15.9 

48 

.6 

.7 

29.2  !    .29 

20  4 

.53 

29.6 

.28 

20  7 

52 

.7 

.8 

32.1   |    .26 

25.7 

55 

32.4 

.26 

25.9 

56 

.8 

.9 

34.7      .24 

31.2 

59 

35. 

.24 

31.5 

.59 

.9 

I. 

37.1      .23 

37.1 

.62 

37.4 

.22 

37  4 

.61 

1. 

.1 

39.4      .21 

43.3 

.65 

39.6 

21 

43.5 

.65 

1.1 

.2 

41.5      .20 

49.8 

.68 

41.7 

.19 

50. 

.67 

1.2 

.3 

43.5 

.18 

56.6 

.68 

43.6 

18 

56  7 

.69 

1.3 

.4 

45.3 

.17 

63  4 

.71 

45.4 

17 

63  6 

.71 

1.4 

.5 

47. 

.16 

70  5 

.73 

47.1 

16 

70.7 

.72 

1.5 

.6 

48.6 

.15 

77.8 

.74 

48.7 

.15 

77.9 

.74 

1.6 

.7 

50.1 

.15 

85  2 

.77 

50.2 

.14 

85.3 

.76 

1.7 

1.8 

51.6 

.13 

92  9 

.76 

51.6 

.13 

92.9 

76 

1.8 

1.9 

52.9 

13 

100.5 

.79 

52.9 

.13 

100  5 

.79 

1/9 

o 

54  2 

12 

108.4 

.79 

54  2 

11 

108.4 

.77 

2. 

2*1 

55  4 

.12 

116.3 

.82 

55  3 

12 

116.1 

.82 

2.1 

2  2 

56.6 

.11 

124  5 

.82 

56.5 

10 

124.3 

.80 

2.2 

2*3 

57.7 

.10 

132.7 

.82 

57.5 

.10 

132  3 

.81 

2.3 

2.4 

58.7 

.10 

140.9 

.84 

58.5 

.10 

140.4 

.84 

2.4 

2.5 

59.7 

.10 

149  3 

85 

59.5 

.09 

148.8 

.82 

2.5 

2.6 

60.7 

.09 

157.8 

.85 

60.4 

.09 

157 

.85 

2.6 

2.7 

61  6 

.08 

166.3 

.84 

61.3 

.08 

165.5 

.84 

2.7 

2.8 

62.4 

.08 

174.7 

.86 

62.1 

08 

173.9 

.85 

2.8 

2.9 

63.2 

.08 

183.3 

.87 

62.9 

.08 

182  4 

.87 

2.9 

3. 

64. 

.08 

192. 

.89 

63.7 

.07 

191   1 

85 

3. 

3.1 

64  8 

07 

200  9 

.87 

64.4 

.07 

199.6 

.87 

3.1 

3.2 

65.5 

.07 

209.6 

.89 

65  1 

.06 

208.3 

.85 

3.2 

3.3 

66  2 

.07 

218.5 

.90 

65  7 

.07 

216  8 

.90 

3.3 

3.4 

66.9 

.06- 

227.5 

.89 

66.4 

.06 

225  8 

.87 

3.4 

3.5 

67.5 

.06 

236  4 

.89 

67. 

.06 

234.5 

.89 

3.5 

3.6 

68  1 

.06 

245.3 

.90 

67.6 

.06 

243.4 

.88 

3.6 

3.7 

68.7 

.06 

254.3 

.91 

68.2 

.05 

252.2 

.90 

3.7 

3.8 

69  3 

.06 

263.4 

.91 

68.7 

.06 

261  2 

.89 

3.8 

3.9 

69.9 

.05 

272  5 

.91 

69.3 

05 

270  1 

.90 

3.9 

4. 

70.4 

281.6 

1 

69.8 

279.1 

4. 

11 


162 


FLOW    OF    WATER    IN 


TABLE  27. 

Based  ou  Kutter's  formula,  with  n  =  .035.     Values  of  the  factors  c  and 
for  use  iu  the  formula 


v  ~  c^/r*  =  c  X  \/      X  \/=  ev'      X  \/s~ 
All  slopes  greater  than  1  ia  1000  have  the  same  co-efficient  as  1  in  1000. 


Vr 

1  in  1250=4.224  ft.  per  mile 

1  in  1000—5.28  ft.  per  mile 

Vr 

a  =  .0008 

s  =  .001 

in  feet 

diff.           /— 

diff. 

diff. 

diff. 

in  feet 

c 

.01        cVr 

.01 

c 

.01 

c\/r 

.01 

.4 

19.6 

.37 

7.8 

.39 

19  7 

.37 

7.88 

.39 

.4 

.5 

23.3 

.34 

11.7 

.43 

23.4 

.34 

11.7 

.44 

.5 

.6 

26.7 

.31 

16. 

.49 

26.8 

.31 

16.1 

.48 

.6 

.7 

29.8 

.28 

20.9 

.52 

29.9 

.28 

20.9 

.53 

.7 

.8 

32.6 

.26 

26.1 

.56 

32.7 

.26 

26.2 

.56 

.8 

.9 

35.2 

.24 

31.7 

.59 

35.3 

23 

31.8 

58 

.9 

37.6 

.22 

37.6 

.62 

37.6 

.22 

37.6 

.62 

.1 

39.8 

.20 

43.8       64 

39.8 

.21 

43.8 

.65 

.1 

.2 

41.8 

.19 

50,2 

.66 

41.9 

.19 

50.3 

.66          .2 

.3 

43.7 

.18 

56.8 

.69 

43.8 

.18 

56.9 

.69 

.3 

.4 

45.5 

.17 

63.7 

.71 

45.6 

.16 

63.8 

.70 

.4 

.5 

47.2 

.15 

70  8 

.71 

47.2 

.16 

70.8 

.73 

.5 

.6 

48.7 

.15 

77  9 

.74 

48.8 

.14 

78.1 

.72 

1.6 

.7 

50.2 

.14 

85.3 

.76 

50.2 

.14 

85.3 

.76 

1.7 

1.8 

51.6 

.13 

92.9 

.76 

51.6 

13 

92.9 

.76 

1.8 

1.9 

52.9 

.12 

100.5 

.77 

52.9 

.12 

100.5 

.77 

1.9 

2. 

54.1 

.12 

108.2 

.79 

54.1 

.11 

108.2 

.77 

2. 

2.1 

55.3 

.11 

116  1 

.80 

55.2 

.11 

115.9 

.80 

2.1 

2.2 

56.4 

.10 

124.1 

79 

56.3 

.11 

123.9 

81 

2.2 

2.3 

57.4 

.10 

132 

.82 

57.4 

.10 

132. 

.82 

2.3 

2.4 

58.4 

.10 

140.2 

.83 

58.4 

.09 

140.2 

.81 

2.4 

2.5 

59.4 

.09 

148.5 

.83 

59.3 

.09 

148.3 

.82 

2.5 

2.6 

60.3 

.08 

156.8 

.82 

60.2 

.08 

156  5 

.82 

2.6 

2.7 

61.1 

08 

165. 

.83 

61. 

.08 

164.7 

.83 

2.7 

2.8 

61.9 

08 

173.3 

.85 

61  8 

.08 

173 

.85 

2.8 

2.9 

62.7 

08 

181.8 

.87 

62.6 

.07 

181.5 

.84 

2.9 

3. 

63.5 

.07 

190.5 

85 

63.3 

.07 

189  9 

85 

3. 

3.1 

64.2 

.07 

199. 

.87 

64. 

.07 

198  4 

86 

3.1 

3.2 

64.9 

.06 

207.7 

.85 

64.7 

.07 

207. 

.88 

3.2 

3.3 

65.5 

.06 

216.2 

85 

65.4 

.06 

215.8 

.86 

3.3 

3.4 

66.1 

.06 

224.7 

.89 

66. 

.06 

224  4 

.86 

3.4 

3.5 

66.7 

.06 

233.6 

.88 

66.6 

.06 

233. 

.88 

3.5 

3.6 

67.3 

.06 

242  4 

.88 

67.2 

05 

241  8 

.87 

3.6 

3.7 

67  9 

.05 

251.2 

.88 

67.7 

.05 

250.5 

.88 

3.7 

3.8 

68  4 

.05 

260.0 

.89 

68.2 

.06 

259.3 

.90 

3.8 

3.9 

68.9 

.05 

268.9 

.89 

68.8 

.04 

268.3 

.87 

3.9 

4. 

69.4 

277  8 

69.2 

277. 

4. 

OPEN    AND    CLOSED    CHANNELS. 


163 


TABLE  28. 

Value  of  c\/F  to  be  used  only  in  the  application  of  the  second  type 
of  Bazin's  formula  for  open  channels  with  au  even  lining  of  cut  stone, 
brickwork,  or  other  material  with  surfaces  of  equal  roughness,  exposed  to 
the  flow  of  water.  This  formula  is: — 

v  =  cx/r  X  -\/i" 


where  c  =  V  1  -r-  .000013  f  4.354  4-  _ 


~,^    w 

s£  5U 
-"?£  g 

-*  ~.  P  2 
•    P       Ct 
o 

c\/r 

^    w 

g^BU 

;p| 

5 

cVr 

*h$ 

•:m 

o' 

c\/r 

Hydraulic 
mean 
depth  in 
feet,  r. 

c^r 

.104 

23.710 

.396 

65.756 

1.062 

122.82 

2.250 

187.77 

.125 

27.617 

.417 

68.159 

1.125 

127.05 

2.375 

193.36 

.146 

31.284 

.437 

70.337 

1.187 

131. 

2.500 

198.83 

.167 

34.569 

.458 

72.615 

1.250 

135.03 

2.750 

209.31 

.187 

38.147 

.479 

74.764 

1.312 

138.93 

3. 

219.36 

.208 

41.327 

.500 

76.907 

1  .  375 

142.79 

3.250 

228.98 

.229 

44.484 

.562 

83.048 

1.437 

146.42 

3.500 

238.18 

250 

47  430 

.625 

88.772 

1.500 

149.90 

3.750 

246.96 

.271 

50.267 

.687 

94.315 

1.625 

156.83 

4. 

255.58 

292 

53.077 

.750 

99.573 

1  .  750 

163.46 

4.250 

263.81 

.312 

55.783 

.812 

104.53 

1.875 

169.80 

4.500 

271.87 

.333 

58.346 

.875 

109.35 

2. 

175.99 

4.750 

279.78 

.354 

60.898 

.937 

114. 

2.125 

182.02 

5. 

287.30 

.375 

63.336 

1. 

118.50 

164 


FLOW    OF    WATER    IN 


TABLE  29. 

Giving   the   length  of  two  side  slopes    of  a  trapezoidal  channel, 
side  slopes  plus  the  bed  width  are  equal  to  the  perimeter. 


The 


Depth 
in 

Feet 

1  to  1 

1  to  1 

1J  to  1 

2  to  1 

.5 

1.118 

1.414 

1.803 

2.236 

.75 

1.677 

2.121 

2.704 

3.354 

1. 

2.236 

2.828 

3.606 

4.472 

1.25 

2.795 

3.535 

4.507 

5.590 

1.5 

3.354 

4  .  242 

5.408 

6.708 

1.75 

3.913 

4.949 

6.310 

7.826 

2. 

4.472 

5.656 

7  212 

8.944 

2.25 

5.031 

6.345 

8.112 

10.062 

2.5 

5.590 

7.070 

9.014 

11.181 

2.75 

6.149 

7.778 

9.916 

12.299 

3 

6.708 

8.484 

10.816 

13.417 

3.25 

7.267 

9.192 

11.718 

14  535 

3.5 

7.816 

9.899 

12.618 

15.653 

3.75 

8.385 

10.606 

13.522 

16.771 

4. 

8.944 

11.312 

14.422 

17.889 

4.25 

9.503 

12.021 

15.324 

19.006 

4.5 

10.062 

12.728 

16.226 

20.124 

4.75 

10.621 

13.435 

17.126 

21.242 

5. 

11.180 

14.142 

18.028 

22.360 

5.25 

11.739 

14.849 

18.930 

23.478 

5.5 

12.298 

15.556 

19.830 

24.596 

5.75 

12.857 

16.263 

20.732 

25.714 

6. 

13.416 

16.970 

21  634 

26  833 

6.25 

13.975 

17.678 

22.536 

27.951 

6.5 

14.534 

18.385 

23.436 

29.069 

6.75 

15.093 

19.092 

24.338 

30.187 

7. 

15.652 

19.800 

25.240 

31.306 

7.25 

16.211 

20.506 

26.140 

32.423 

7.5 

16.770 

21.213 

27.042 

33.542 

7.75 

17.329 

21.920 

27.944 

34.660 

8, 

17.888 

22.627 

28.844 

35.778 

8.25 

18.447 

23.334 

29.746 

36.896 

8.5 

19.006 

24.042 

30.648 

38.014 

8.75 

19.565 

24.749 

31.550 

39.132 

9. 

20.124 

25.456 

32.450 

40  250 

10. 

22  360 

28.284 

36,  056 

44.720 

11. 

24.596 

31.112 

39.662 

49.  194 

12. 

26.832 

33.941 

43.268 

53-  664 

13. 

29.068 

36.769 

46.872 

58.  139 

14. 

31.304 

39.598 

50.748 

62.611 

15. 

33.540 

42.626 

54.080 

67.083 

16. 

35.776 

45.254 

57-690 

71  555 

OPEN    AND    CLOSED    CHANNELS. 


165 


TABLE  30. 

Giving  velocities   and   discharges   of    trapezoidal   channels   in   earth, 
according  to  Bazin's  formula  (37),  for  channels  in  earth: — 


»  =  \/t-*-  .00035  (.2438  +  -1  \ 


Side  Slopes  1  to  1 .     v  —  mean  velocity  in  feet  per  second,  and  Q  =  dis- 
charge in  cubic  feet  per  second. 

(Professional  Papers  on  Indian  Engineering,  Volume  V,  Second  Series.) 


Depth 
in 
feet. 

Slope 
lin 

Bed  width  3  ft. 

Bed  width  4  ft. 

Bed  width  5  ft. 

Bed  width  6  ft. 

v             Q             v 

Q 

. 

Q 

v 

Q 

2500 

.679       2.72       .721 

3.61 

.752 

4.51 

.776 

5.43 

, 

2857 

.635        2.54       .675 

3.37 

.704 

4  22 

.726 

5.08 

t 

3333 

.588        2.35       .625 

3.12 

.651 

3.91 

.672 

4.70 

4000 

.537        2.15 

.570 

2.85 

.595 

3.57 

.613 

4.29 

5000 

.480        1.92 

.510 

2.55 

.532 

3.19 

.549 

3  84 

6666 

.416        1.66 

.442 

2.20 

.461 

2.76 

.475 

3.33 

.5 

2500 

.899        6.07  1     .959 

7  92 

1.01 

9.81 

1.04 

11.73 

.5 

2857 

.841 

5.68 

.897 

7  40 

.941 

9.17 

.976 

10:97 

5 

3333 

.779 

5.26 

.831 

6.85 

.871 

8.49 

.903 

10.16 

.5 

4000 

.711        4.80 

.758 

6.26 

.795 

7.75 

824 

9.28 

.5 

5000 

.636 

4.29 

.678 

5.60 

.711 

6.93 

.737 

8.30 

.5 

G66G 

.511 

3.72 

.588 

4.85 

616 

6.01 

.639 

7-.  18 

2 

2500 

1.09 

10.91 

1.16 

13.96 

1.22 

17.11 

1.27 

20.32 

2 

2857 

1.02 

10.20 

1.09 

13.06  1 

1.14 

16.01 

1.19 

19.01 

2.' 

3333 

.945 

9.45 

1.01 

12.09  j 

1.06 

14.82 

1.10 

17.60 

2. 

4000 

.862 

8.62 

.920 

11.04 

.966 

13.53 

1. 

16.07 

2. 

5000 

.771 

7.71 

.823 

9  88 

.864 

12.10 

.898 

14.37 

2. 

6666 

668 

6.68 

.713 

8.55 

.749 

10.48 

.778 

12.44 

2.5 

2500 

1.26 

17.39 

1.35 

21.88 

1  41 

26.52 

1.47 

31.26 

2.5 

2857 

1.18 

16.27 

1.26 

20.47 

1.32 

24.80 

1.38 

29  23 

2.5 

3333 

1.09 

15.06 

1  17 

18.95 

1.22 

22.96 

1.27 

27.07 

2.5 

4000 

1. 

13.74 

1.06 

17.30 

1.12 

20.96 

1.16 

24  71 

2.5 

5000 

.894 

12.29 

.952 

15.47 

1. 

18.75 

1.04 

22.10 

2.5 

6666 

.774 

10.65 

.825 

13.40 

.866 

16.24 

.901 

19.14 

3. 

2500 

1.43 

25.65 

1.51 

31.79 

1.59 

38.13 

1.65 

44  60 

3. 

2857 

1.35 

23.99 

1.42 

29.74 

1.40 

35.67 

1.55 

41.72 

3. 

3333 

1.23 

22.21 

1.31 

27.54 

1.38 

33.02 

1.43 

38.64 

3 

4000 

.13 

20.27 

.20 

25.14 

1.26 

30.15 

1.31 

35  26 

3. 

5000 

.01 

18.13 

.07 

22.49 

1.12 

26.97 

1.17 

31.54 

3. 

6666 

.873 

15.71 

.927 

19.47 

973 

23.35 

1..01 

27.3-2 

3.5 

2500 

.58 

35.87 

.67 

43.86 

1.75 

52.08 

1.82 

60.51 

3.5 

2857 

.47 

33.50 

.56 

41.02 

.64 

48.72 

1  70 

56.60 

3.5 

3333 

.37 

31  07 

.45 

37.98 

.52 

45  11 

1.58 

52.40 

3.5 

4000 

.25 

28.36 

.32 

34.70 

.38 

41.18 

1.44 

47.83 

3  5 

5000 

.12 

25.37 

.18 

31.01 

.24 

36  83 

1.29 

42.79 

3.5 

6666 

.966 

21.97 

.02 

26.86 

.07 

31.89 

1.11 

37.05 

166 


FLOW    OF    WATER    IN 


TABLE  30. 

Giving   velocities   and   discharges    of    trapezoidal   channels   in   earth, 
according  to  Bazin's  formula  (37),  for  channels  in  earth: — 


v  =  V  1-i-  .00035 


(.2438  +  -! 


Side  Slopes  1  to  1.     v  —  mean  velocity  in  feet  per  second,  and  Q  =  dis- 
charge in  cubic  feet  per  second.  , 


Depth 
in 
feet. 

Slope 
lin 

Bed  width  7  ft. 

Bed  width  8  ft. 

Bed  width  9  ft. 

Bed  width  10  ft. 

! 

i    " 

Q 

V 

Q 

V 

Q 

V 

Q 

2500 

.795 

6.36 

.810 

7.29 

.823 

8.23 

.834 

9.17 

2857 

.744 

5.95 

.758 

6.82 

.770 

7.70 

.780 

8.58 

3333 

.688 

5.51 

.702 

6.32 

.713 

7.13 

.722 

7.94 

4000 

.628 

5.03 

.641 

5.77 

.651 

6.51 

.659 

7.25 

't 

5000 

.562 

4.50 

.573 

5.16 

.582 

5.82 

.590 

6.48 

6666 

.487 

3.89 

.496 

4.47 

.504 

5.04 

.511 

5.62 

.5 

2500 

1.07 

13.68 

1.10 

15.65 

1.12 

17  63 

1.14 

19.63 

.5 

2857 

1. 

12.79 

1.03 

14.64 

1.05 

16.49 

1.06 

18.35 

.5 

3333 

.929 

11.85 

.942 

13.55 

.970 

15.27 

.985 

17. 

.5 

4000 

.848 

10.82 

.869 

12.37 

885 

13.93 

.899 

15.52 

.5 

5000 

.759 

9.68 

.777 

10.08 

.792 

12.47 

.804 

13.88 

.5 

6666 

.657 

8.38 

.673 

9.59 

.686 

10.80 

.697 

12.02 

2. 

2500 

1.31 

23.58 

1.34 

26.87 

1  37 

30.20 

1.40 

33.56 

2. 

2857 

1.23 

22.06 

1.26 

25  13 

1.28 

28.25 

1.31 

31.39 

2. 

3333 

1.13 

20.42 

1.16 

23.27 

1.19 

26  16 

1.21 

29.06 

2. 

4000 

1.04 

18.64 

1.06 

21.24 

1.09 

23.88 

1.11 

26  53 

2 

5000 

.926 

16.68 

.950 

19.01 

.971 

21.36 

.989 

23.73 

2. 

6666 

.802 

14.44 

.823 

16.46 

.841 

18.50 

.856 

20.55 

2.5 

2500 

1.52 

36.07 

56 

40.95 

1.60 

45.88 

1.63 

50.85 

2.5 

2857 

1.42 

33.74 

.46      38.30 

1.49 

42.91 

1.52 

47.57 

2.5 

3333 

1.32 

31.24 

.35      35  46 

1  38 

39.73 

1.41 

44.04 

2.5 

4000 

1.20 

28.51 

.23 

32.37 

26 

36.27 

1.29 

40.20 

2.5 

5000 

1.07 

25.51 

.10 

28.96 

1.13 

32.44 

1.15 

35.9(3 

2.5 

6666 

.930 

22.09 

.955 

25.08 

.977 

28.10 

.997 

31.14 

3. 

2500 

1.71 

51.21 

.76 

57.90 

.80 

64.66 

.83 

71.48 

3. 

2857 

1.60 

47.90 

.64 

54.15 

.68 

60.48 

.71 

06.86 

3. 

3333 

1.48 

44.35 

.52 

50.14 

.56 

55.99 

.59 

01.90 

3. 

4000 

1.35 

40.48 

.39 

45.77 

.42 

51.12 

.45 

56.51 

3. 

5000 

1.21 

36.21 

.24 

40.94 

.27 

45.72 

.30 

50.54 

3. 

6666 

1  05 

31.36 

.07 

35.45 

.10 

39.59 

.12 

43.77 

3.5 

2500 

1.88 

69.07 

.93 

77.77 

1.98 

86.57 

.02 

95.46 

3.5 

2857 

1.76 

64.61 

.81 

72.74 

.85 

80.97 

.89 

89.29 

3.5 

3333 

1.63 

59.82 

.67 

67.35 

.71 

74.79 

.75 

82.67 

3.5 

4000 

1.49 

54.60 

.53 

61.48 

.56     68.44 

.60 

75.46 

3.5 

5000 

1.33 

48.84 

.37 

54.90 

.40     61.21 

.43 

67.50 

3.5 

6666 

1.15 

42.30 

.18 

47.62 

.21  i  53.01  j 

.24 

58.45 

OPEN    AND    CLOSED    CHANNELS. 


167 


TABLE  30. 

Giving   velocities   and    discharge^    of     trapezoidal    channels    in    earth, 
according  to  Bazin's  formula  (37),  for  channels  in  earth: — 


•o  =  ]l  -T-  .00035     .243 


(  .2438  + 


Sides  Slopes  1  to  1 .     v  =  mean  velocity  in  feet  per  second,  and  Q  =  dis- 
charge in  cubic  feet  per  second. 


II                             1 

Bed  width  11  ft. 

Bed  width  12  ft.    !    Bed  width  13  ft. 

Bed  width  14  ft. 

Depth 

in 

Slope 

feet. 

lin 

V 

Q 

V               Q 

V 

Q 

V 

Q 

1. 

•2500 

.843 

10.11 

.  850 

11.06 

.858 

12.01 

.864 

12.95 

1. 

2857 

.788 

9.46 

.796 

10.34 

.802 

11.23 

.808 

12.12 

3333 

.730 

8.76 

.737 

9.58 

.743 

10.40 

.748 

1  1  .  22 

4000 

.666 

8. 

.673 

8.74 

.678 

9.49 

.683 

10.24 

5000 

.596 

7.15 

.602 

7.82 

.606 

8.49 

.611 

9.16 

6666 

.516 

G.19 

.521 

6.77 

.525 

7.35 

.529 

7.93 

5 

2500 

1.15 

21  63 

1.17 

23.64 

1.18 

25.65 

1.19 

27.67 

.5 

2857 

1.08 

20.23 

1.10 

22.11 

1.10 

23.99 

1.11 

25.88 

.5 

3333 

.999 

18.73 

1.01 

20.47 

1.02 

22.21    !   1.03 

23.96 

.5 

4000 

.912 

17.10 

.923 

18.69 

.932 

20.28 

.941 

21.87 

.5 

5000 

.816 

15.29 

.825 

16.71 

.834 

18.14 

842 

19.57 

.5 

6666 

.706 

13.24 

.715 

14.47 

.722 

15.71 

.729 

16.94 

2. 

2500 

1.42 

36.92 

1.44 

40.31 

1.46 

43.71 

1.47 

47.12 

2. 

2857 

1.33 

34.54 

1.35 

37.70 

1.36 

40.88 

1.38 

44.07 

2 

3333 

1.23 

31.98 

1.25 

34.91 

1.26 

37.85 

1.28 

40.81 

2. 

4000 

1.12 

29.19 

1.14 

31.87 

1.15 

34.55 

1.16 

37.25 

2 

5000 

1. 

26.11 

1.02 

28.50 

1.03 

30  91 

1.04 

33.32 

2 

6666 

.870 

22.61 

.882 

24.68 

.892 

26.76 

.902 

28.85 

2.5 

2500 

.65 

55  .  84 

1.68 

60.89 

1.70 

65.95 

1.72 

71.03 

2.5 

2857 

.55 

52.24 

.57 

56.90 

1.59 

61  69 

1.61 

66  44 

2.5 

3333 

.43 

48.36 

.45 

52.73 

1.47 

57.11 

1.49 

61.51 

2.5 

4000 

.31 

44.15 

.33 

48.14 

1.35 

52.13 

1.36 

56.15 

2.5 

5000 

.17 

39.49 

.19 

43.06 

1.20 

46  63 

1.22 

50.23 

2.5      6666 

.01 

34.20 

.03 

37.29 

1.04 

40.39 

1.05 

43.49 

3. 

2500 

.87 

78.36 

.90 

85.28 

1.92 

92.24 

1.95 

99.23 

3. 

2857 

.75 

73.29 

.77 

79.77 

1.80 

86.28 

1.82 

92.82 

3. 

3333 

.62 

67.86 

.64 

73.85 

1.66 

79.88 

1.69 

85.94 

3. 

4000 

.48 

61.95 

.50 

67.42 

1.52 

72.92 

1.54 

78.45 

3. 

5000 

.32 

55.41 

.34 

60.30 

1.36 

65.23 

.38 

70.17 

3. 

6666 

.14 

47.99 

.16 

52.22 

1   18 

56.49 

.19 

60.77 

3.5 

2500 

.06 

104.42 

2.09 

113.44 

2.12 

122.53 

2.15 

131.66 

3.5 

2S57 

92 

97.67 

.96 

106.11 

1.98 

114.61 

2.01 

123.15 

3.5 

3333 

.78 

90.43 

.81 

98.24 

1.84 

106.11 

.86 

114.01 

3.5 

4000 

.63 

82  .  55 

.65 

89.68 

1.68 

96.86 

.70 

104.08 

3.5 

5000 

.45 

73.84 

.48 

80  22. 

1.50 

86.64 

.52 

93.10 

35 

6666 

.26 

63.94 

.28 

69.47 

1.30 

75.03 

.32 

80.62 

168 


FLOW    OF    WATER    IN 


TABLE  30. 

Giving   velocities    and    discharges    of   trapezoidal    channels    in    earth, 
according  to  Baziii's  formula  (37),  for  channels  in  earth: — 


V==Yl-*-  .00035  ( .2438  -f  _L  \  X  >/rs 


Side  Slopes  1  to  1.     v  —  mean  velocity  in  cubic  feet  per  second,  and  Q 
discharge  in  cubic  feet  per  second. 


Depth 
in 
feet. 

Slope 
1  in 

Bed  width  15  ft.       Bed  width  16  ft. 

:    Bed  width  18  ft.  :    Bed  width  20  ft. 

V 

Q            v 

Q 

V 

Q 

v 

Q 

1.5 

2500 

1.20 

29.69 

1.21 

31.72 

1.22 

35.78 

1  .  24 

39.85 

1.5 

2857 

1  .  12 

27.77 

1.13 

29.67 

1.14 

33.47 

1.16 

37.28 

1.5 

3333 

1.04 

25.71 

1.05 

27.47 

1.06 

30.99 

1.07 

34.52 

1.5 

4000 

.948 

23.47 

.955 

25.08 

.967 

28.29 

.977 

31.51 

1.5 

5000 

.848 

21. 

.854 

22.43 

.865 

25.30 

.874 

28.18 

1.5 

6666 

.735 

18.18 

.740 

19.42 

.749 

21.91 

.757 

24.41 

2. 

2500 

.49 

50.54 

1.50 

53.96 

1.52 

60.84 

1.54 

67.74 

2. 

2857 

.39 

47.27 

1  40 

50.48 

1.42 

56.91 

1.44 

63.36 

2. 

3333 

.29 

43.77 

1.30 

46  74 

1  .  32 

52.69 

1.33 

58.66 

2. 

4000 

.18 

39.95 

1.19 

42.66 

1.20 

48.09 

1.22 

53.55 

2. 

5000 

.05 

35.74 

1.06 

38.16 

1.08 

43.02 

1.09 

47.90 

2. 

6666 

.910 

30.95 

.918 

33.04 

.931 

37.26 

.943 

41.48 

2.5 

2500 

.74 

76.13 

1.76 

81.24 

.79 

91.50 

1.81 

101.80 

2.5 

2857 

.63 

71.21 

1.64 

75.99 

.67 

85.58 

1.69 

95.22 

25 

3333 

1.51 

65.93 

1.50 

70.36 

.55 

79.24 

1.57 

88.16 

2.5 

4000 

1.38 

60.18 

1.39 

64  23 

.41 

72.33 

1.43 

80.48 

2.5 

5000 

1.23 

53.83 

1.24 

57.45 

.26 

64.70 

1.28 

71.98 

2.5 

6666 

1.07 

46.62 

1.08 

49.75 

.09 

56.03 

1.11 

62.34 

3. 

2500 

1.97 

106.26 

1.99 

113.30 

.02 

127.46 

2.05 

141.68 

3. 

2857 

1.84 

99.40 

1.86 

105.98 

.89 

119.22 

1.92 

132.53 

3. 

3333 

1.70 

92.02 

1.72 

98.12 

.75 

110.38 

1.78 

122.70 

3. 

4000 

1.56 

84. 

1.57 

89.57 

.60 

100.76 

1.62 

112.01 

3. 

5000 

1.39 

75.14 

1.41 

80.12 

.43 

90.13 

1.45 

100.19 

3. 

6666 

1.21 

65.07 

1.22 

69.38 

1.24 

78.05 

1.26 

86.76 

3.5 

2500 

2.17 

140.82 

2.20 

150.03 

2.24 

168.54 

2.28 

187.15 

3.5 

2857 

2.03 

131.72 

2.06 

140.34 

2.09 

157.64 

2.13 

175.05 

3.5 

3333 

1.88 

121.95 

1.90 

129.93 

1.94 

145.95 

1.97 

162.07 

3.5 

4000 

1.72  1111.33 

1.74 

118.61 

1.77 

133.24 

1.80 

147.95 

3.5 

5000 

1.54 

99.58 

1.55 

106.09 

1.58 

119.17 

1.61 

132.33 

3.5 

6666 

1.33 

86.23 

1.35 

91.87 

1.37 

103.21 

1.39 

114.60 

4. 

2500 

2.37 

179.77 

2.39 

191.34 

2  44 

214.61 

2.48 

238.03 

4. 

2857 

2.21 

168.15 

2  24 

178.97 

2.28 

200.74 

2.32 

222.64 

4. 

3333 

2  05 

155.68 

2.07 

165.70 

2.11 

185.86 

2.15 

206.13 

4. 

4000 

1.87 

142.12 

1.89 

151.26 

1.93 

169.66 

1.96 

188.17 

4. 

5000 

1.67 

127.12 

1.69 

135.30       1.72 

151  76 

1.75 

168.31 

4. 

6666 

1.45 

110.08 

1.46 

117.17       1.49 

131.42 

1.52 

145.76 

OPEN    AND    CLOSED    CHANNEIS. 


169 


TABLE  31. 

Velocities    and   discharges   in  trapezoidal  channels  based   on  Kutter's 
formula  with  n=  .025.     Side  slopes  1  horizontal  to  1  vertical. 


BED  WIDTH  30  FEET. 

BED  WIDTH  40  FEET. 

Depth  in 
feet. 

Slope 
lin 

Velocity 
in 
feet  per 

Discharge 
in 
cubic  feet 

Depth  in 
feet. 

Slope 
lin 

Velocity 
In 
feet  per 

Discharge 
in 
cubic  feet 

second. 

per 
second. 

second. 

per 

second. 

2 

1500 

2.203 

141. 

2 

1500 

2.242 

188.3 

2 

2000 

1.905 

121.9 

2 

2000 

1.941 

163. 

2 

3000 

1.539 

98.5 

2 

3000 

1.574 

132.2 

2 

5000 

1.231 

78.8 

2 

5000 

1.215 

102.1 

3 

1500 

2.856 

282.7 

3 

1500 

2.923 

377. 

3 

2000 

2.471 

244  6 

3 

2000 

2.535 

327. 

3 

3000 

2.013 

199.3 

3 

3000 

2.062 

266. 

3 

5000 

1.556 

154. 

3 

5000 

1.596 

205.9 

4 

1500 

3.396 

461.8 

4 

1500 

3.497 

615.4 

4 

2000 

2.936 

399.3 

4 

2000 

2.982 

524.8 

4 

3000 

2.401 

326.6 

4 

3000 

2.473 

435.2 

4 

5000 

1.858 

252.7 

4 

5000 

1.889 

332.5 

5 

1500 

3.859 

675.3 

5 

1500 

4.112 

925.2 

5 

2000 

3.334 

585  2 

5 

2000 

3.454 

777.1 

5 

3000 

2.736 

478.8 

5 

3000 

2.826 

635.8 

5 

5000 

2.123 

371.5 

5 

5000 

2.194 

493.6 

BED  WIDTH  50  FEET. 

BED  WIDTH  60  FEET. 

2 

1500 

2.268 

235.8 

2 

1500 

2.294 

284.4 

2 

2000 

1.965 

204.4 

2 

2000 

1.979 

245.4 

2 

3000 

1.765 

183.5 

2 

3000 

1.611 

199.7 

2 

5000 

1.229 

127.8 

2 

5000 

1.238 

153.5 

3 

1500 

2.968 

472. 

3 

1500 

3 

567. 

3 

2000 

2.570 

408.6 

3 

2000 

2.600 

491.4 

3 

3000 

2.096 

333.2 

3 

3000 

2.127 

402. 

3 

5000 

1.618 

257.3 

3 

5000 

1.638 

309.6 

4 

1500 

3.559 

768.7 

4 

1500 

3.607 

923.4 

4 

2000 

3.085 

666.3 

4 

2000 

3.123 

799.5 

4 

3000 

2.537 

548. 

4 

3000 

2.553 

653.5 

4 

5000 

1  953 

421.8 

4 

5000 

1.980 

506  .  9 

5 

1500 

4.068 

1118.7 

5 

1500 

4.136 

1344.2 

5 

2000 

3.528 

970.2 

5 

2000 

3.582 

1164.1 

5 

3000 

2.887 

793.9 

5 

3000 

2.935 

953.8 

5 

5000 

2.243 

616.8 

5 

5000 

2.277 

740. 

170 


FLOW    OF    WATER    IN 


TABLE   31. 

Velocities  and  discharges  in  trapezoidal  channels   based   on   Kutter's 
formula  with  n  =0.25.     Side  slopes  1  horizontal  to  1  vertical. 


BED  WIDTH  70  FEET. 

BED  WIDTH  80  FEET. 

Depth  in 
feet. 

Slope 
liu 

Velocity 
in 
feet  per 

Discharge 
in 
cubic  feet 

Depth  in 
feet. 

Slope 
lin 

Velocity 
in 
feet  per 

Discharge 
in 
cubic  feet 

second 

per 
second. 

second. 

per 
second. 

3 

2000 

2.622 

574.2 

3 

2000 

2.637 

656.6 

3 

3500 

1.976 

432.7 

3 

3500 

1.989 

495.2 

3 

7500 

1.344 

294.3 

3 

7500 

1.353 

336.9 

3 

10000 

1.163 

254.7 

3 

10000 

1.169 

291.1 

4 

2000 

3.152 

933. 

4 

2000 

3.175 

1066.8 

4 

3500 

2.387 

706.5 

4 

3500 

2.404 

807.7 

4 

7500 

1  .  635 

483.9 

4 

7500 

1.648 

553.7 

4 

10000 

1.418 

419.7 

4 

10000 

1.429 

480.1 

5 

2000 

3.621 

1357.9 

5 

2000 

3.653 

1552.5 

5 

3500 

2.746 

1029.7 

5 

3500 

2.77 

1177.2 

5 

7500 

1.89 

708.7 

5 

7500 

1.909 

811.3 

5 

10000 

1.643 

616.1 

5 

10000 

1.657 

704.2 

6 

2000 

4.040 

1842.2 

6 

2000 

4.080 

2105.3 

6 

3500 

3.066 

1398.1 

6 

3500 

3.099 

1599. 

6 

7500 

2.121 

967.1 

6 

7500 

2.144 

1106.3 

6 

10000 

1.848 

842.7 

6 

10000 

1.869 

964.4 

BED  WIDTH  90  FEET. 

BED  WIDTH   100  FEET. 

3 

2000 

2.649 

739.1 

3 

2000 

2.657 

821. 

3 

3500 

1.998 

557.4 

3 

3500 

2.004 

619.2 

3 

7500 

1  .  359 

379.1 

3 

7500 

1.364 

421.4 

3 

10000 

1.175 

327.8 

3 

10000 

1.180 

364.6 

4 

2000 

3.196 

1201.7 

4 

2000 

3.208 

1334.5 

4 

3500 

2.419 

909.5 

4 

3500 

2.431 

1011.3 

4 

7500 

1.658 

623.4 

4 

7500 

1.667 

693.4 

4 

10000 

1.439 

541.1 

4 

10000 

1.446 

601.5 

5 

2000 

3.677 

1746.6 

5 

2000 

3.702 

1943.5 

5 

3500 

2.79 

1325.2 

5 

3500 

2.806 

1473.1 

5 

7500 

1  .  923 

913.4 

5 

7500 

1.935 

1015.8 

5 

10000 

1.670 

793.2 

5 

10000 

1.682 

883. 

6 

2000 

4.120 

2373.1 

6 

2000 

4.140 

2633. 

6 

3500 

3.122 

1798.2 

6 

3500 

3.143 

1998.9 

6 

7500 

2  161 

1244.7 

6 

7500 

2.176 

1383.9 

6 

10000 

1.888 

1087.5 

6 

10000 

1.898 

1199.8 

OPEN    AND    CLOSED    CHANNELS. 


171 


TABLE  32. 

Velocities  and  discharges  in  trapezoidal  channels   based   on  Kutter's 
formula,  with  n  =  .03.     Sides  slopes  \  horizontal  to  1  vertical. 


BED  WIDTH  1  FOOT. 

BED  WIDTH  2  FEET. 

Depth  in 
feet. 

Slope 
1  iu 

Velocity 
iu 
feet  per 

Discharge 
III 
cubic  feet 

Depth  in 
leet. 

Slope 
lin 

Velocity 
in 
feet  per 

Discharge 
cubic  feet 

second. 

per 
second. 

second 

per 
second. 

1.5              266 

j 

.625 

.5 

380 

1 

1.125 

1.5 

66 

2 

1.25 

.5 

95 

2 

2.25 

1.5 

30 

3 

1.875 

.5 

42 

3 

3.375 

1.5 

17 

4 

2.5 

.5 

24 

4 

4.5 

542 

1 

1.5 

1. 

870 

1 

25 

135 

2 

3. 

1. 

217 

2 

5. 

60 

3 

4.5 

1. 

97 

3 

7-5 

34 

4 

6. 

1. 

54 

4 

10, 

^5 

911 

1 

2.625 

1.5 

1340 

1 

4.125 

.5 

228 

2 

5.25 

1.5 

335 

2 

8.25 

.5 

101 

3 

7.875 

1.5 

149 

3 

12-375 

1.5 

57 

4 

10.5 

1.5 

84 

4 

16.5 

2 

1752 

1 

6. 

2] 

438 

2 

12. 

2. 

194 

3 

18. 

2. 

110 

4            24. 

BED  WIDTH  3  FEET. 

BED  WIDTH  4  FEET. 

.5 

448. 

1 

1.625 

1.             1195              1 

4.5 

.5 

112 

2 

3.25 

1  .              300             2 

9. 

.5 

50 

3 

4.875 

1.               133              3 

13.5 

.5 

28 

4 

.6.5 

1.                75             4 

.18. 

1. 

1070 

1 

3.5 

.25 

1536              1 

5.8 

1. 

268 

2 

7. 

25 

387              2 

11.6 

119 

3 

10.5 

.25 

172 

3 

17.3 

67 

4 

14. 

.25 

97 

4 

23.1 

'5 

1657 

1 

5.625 

.5          1859              1 

71 

1.5 

414 

2 

11.25 

.5 

473              2            14.2 

1.5 

184 

3 

16.875 

1.5 

210 

3 

21.4 

1.5 

104 

4 

22.5 

1.5 

118 

4 

28.5 

2. 

2216 

1 

8. 

2. 

2570 

1 

10. 

2. 

554 

2 

16. 

2. 

660             2       |     20. 

2 

246 

3 

24. 

2. 

293              3 

30. 

2. 

138 

4 

32. 

2 

165 

4 

40. 

2.5 

2790 

1 

10.62 

2^5 

3188 

1 

13.1 

2.5 

698 

2 

21.25 

2.5 

822 

2 

26.3 

2  5 

310 

3 

31.88 

2.5 

365 

3 

39.4 

2.5              174 

4 

42.5 

2.5 

206 

4 

52.5 

172 


FLOW    OF    WATER    IN 


TABLE  32. 

Velocities  and    discharges  in  trapezoidal  channels  based  on  Kutter's 
formula,  with  n  =  .03.     Side  slopes  J  horizontal  to  1  vertical. 


BED  WIDTH  6  FEET. 


BED  WIDTH  8  FEET. 


Depth  in 
feet. 

Slope 
lin 

Velocity 
in 
feet  per 
second. 

Discharge 
in 
cubic  feet 
per 
second. 

Depth  in 
feet. 

Slope 
lin 

Velocity 
in 
feet  per 
second. 

Discharge 
in 
cubic  feet 
per 
second. 

1. 

1380 

1 

6.5 

1. 

1459 

1 

8.5 

1. 

348 

2 

13. 

1. 

373 

2 

17. 

1. 

155 

3 

19.5 

1. 

166 

3 

25.5 

1. 

87 

.     4 

26. 

1. 

93 

4 

34. 

1.25 

1798 

1 

8.3 

1.25 

1984 

1 

10.8 

1.25 

457 

2 

16.6 

1.25 

504 

2 

21.6 

1.25 

203 

3 

24.8 

1.25 

224 

3 

32.3 

.25 

114 

4 

33.1 

.25 

126 

4 

43.1 

.5 

2230 

1 

10.1 

.5 

2433 

1 

13.1 

.5 

570 

2 

20.2 

.5 

624 

2 

26.3 

.5 

253 

3 

30.4 

.5 

277 

3 

39.4 

.5 

142 

4 

40.5 

.5 

156 

4 

52.5 

.75 

2671 

1 

12. 

.75 

2947 

1 

15.5 

.75 

680 

9 

24. 

.75 

758 

2 

31. 

.75 

302 

3 

36.1 

1.75 

337 

3 

46.5 

.75 

170 

4 

48.1 

1.75 

190 

4 

62.1 

2. 

3101 

1 

14. 

2. 

3451 

1 

18. 

2. 

800 

2 

28. 

2. 

889 

2 

36. 

2. 

356 

3 

42. 

2. 

395 

3 

54. 

2. 

200 

4 

56. 

2. 

222 

4 

72. 

2.25 

3533 

1 

16. 

2.25 

3886 

1 

20.5 

2  25 

912 

2 

32. 

2.25 

1006 

2 

41. 

2.25 

405 

3 

48. 

2.25 

447 

3 

61.6 

2.25 

228 

4 

64.1 

2.25 

252 

4 

82.1 

2.5 

3895 

1 

18.1 

2.5 

4385 

1 

23.1 

2.5 

1006 

2 

36.2 

2.5 

1134 

2 

46.2 

2.5 

447 

3 

54.4 

2.5 

504 

3 

69.4 

2.5 

252 

4 

72.5 

2.5 

283 

4 

92.5 

2.75 

4292 

1 

20.3 

2.75 

4906 

1 

25.8 

2.75 

1107 

2 

40.6 

2.75 

1266 

2 

51.6 

2.75 

492 

3 

60.8 

2.75 

563 

3 

77.3 

2.75 

277 

4 

80.1 

2.75 

317 

4 

103.1 

3. 

4672 

1 

22.5 

3. 

5348 

1 

28.5 

3. 

1213 

2 

45. 

3. 

1382 

2 

57. 

3. 

539 

3 

67  5 

3. 

615 

3 

85.5 

3. 

303 

4 

90. 

3. 

346 

4 

114. 

OPEN    AND    CLOSED    CHANNELS. 


173 


TABLE   32. 

Velocities   and   discharges    in  trapezoidal  channels  based  on  Kutter's 
formula,  with  n  =  .03.     Side  slopes  J  horizontal  to  1  vertical. 


BED  WIDTH  10  FEET. 

BED  WIDTH  12  FEET. 

Depth  in 

S'ope 

Velocity 
in 

Discharge 
in 

Depth  in 

Slope 

Velocity 
in 

Discharge 
in 

feet. 

lin 

feet  per 

cubic  feet 

feet. 

lin 

feet  pet- 

cubic  feet 

second. 

per 
second. 

second. 

per 
•  second. 

'                    \ 

1.0 

2651 

1 

16.1 

.5 

2803 

1 

19.1 

1.5 

680 

2 

32.3 

.5 

718 

2 

38.3 

1.5 

302 

3 

48.4 

.5 

319 

3 

57.4 

1.5 

170 

4 

64.5 

.5 

180 

4 

76.5 

1.75 

3190 

1 

19. 

.75 

3368 

1 

22.5 

1.75 

822 

2 

58 

.75 

866 

2 

45.1 

1.75 

365 

3 

57.1 

.75 

385 

3 

67.6 

1.75 

206 

4 

76.1 

.75 

217 

4 

90.1 

2. 

3731 

1 

22. 

2 

3953 

1 

26. 

2. 

958 

2 

44. 

2. 

1030 

2 

52. 

2. 

426 

3 

66. 

2. 

458 

3 

78. 

2. 

239 

4 

88. 

2. 

258 

4 

104. 

2.25 

4275 

1 

25. 

2.25 

4586 

1 

29.5 

2.25 

1107 

2 

50. 

2.25 

1186 

2 

59.1 

2.25 

492 

3 

75.1 

2.25 

528 

3 

88.6 

2.25 

277 

4 

100.1 

2.25 

297 

4 

118.1 

2.5 

4826 

1 

28.1 

2.5 

5128 

1 

33.1     . 

2.5 

1237 

2 

56.3 

2.5 

1323 

2 

66.2 

2.5 

551 

3 

84.4 

2.5 

588 

3 

99.4 

2.5 

310 

4 

112.5 

2.5 

331 

4 

132.5 

2.75 

5352 

1 

31.3 

2.75 

5728 

1 

36.8 

2.75 

1383 

2 

62.6 

2.75 

1467 

2 

73.6 

2.75 

615 

3 

93.8 

2.75 

655 

3 

110.3 

2.75 

346 

4 

125.1 

2.75 

368 

4 

147.1 

3. 

5945 

1 

34.5 

3. 

6328 

1 

40.5 

3. 

1528 

2 

69. 

3. 

1625 

2 

81. 

3. 

682 

3 

103.5 

3. 

725 

3 

121.5 

3. 

384 

4 

138. 

3. 

408 

4 

162. 

3.25 

6503 

**  1 

37.8 

3.25 

7023 

1 

44.3 

2.25 

1658 

2 

75.6 

3.25 

1794 

2 

88.6 

3.25 

740 

3 

113.3 

3.25 

800 

3 

132.8 

3.25 

416 

4 

151.1 

3.25 

450 

4 

177.1 

3.5 

6992 

1 

41.1 

3.5 

7577 

1 

48.1 

35 

1793 

2 

82.2 

3.5 

1930 

2 

96.2 

3.5 

800 

3 

123.4 

3.5 

864 

3 

144  4 

3.5 

450 

4 

164.5 

3.5 

486 

4 

192.5 

174 


FLOW    OF    VvATER    IN 


TABLE   32. 

Velocities   and  discharges  in  trapezoidal   channels  based  on   Kutter's 
formula,  with  n  —  .03.     Side  slopes   \  horizontal  to  1  vertical. 


BED  WIDTH  14  FEET. 

BED  WIDTH  16  FEET. 

Depth  in 

Slope 

Velocity 
in 

Discharge 
in 

Depth  in 

Slope 

Velocity 
in 

Discharge 
in 

feet. 

lin 

feet  per 

cubic  feet 

feet. 

lin 

f^et  per 

cubic  feet 

second. 

per 
second. 

second. 

per 
second. 

1.5 

2859 

1 

21.1 

.5 

2948 

1 

25.1 

1.5 

738 

2 

44.2 

.5 

758 

2 

50.2 

1.5 

328 

3 

66.3 

.5 

337 

3 

75.3 

1.5 

185 

4 

88.5 

.5 

189 

4 

100.5 

1.75 

3472 

1 

26. 

.75 

3623 

1 

29.5 

1.75 

889 

2 

52. 

1.75 

935 

2 

59. 

1.75 

395 

3 

78. 

.75 

415 

3 

88,5 

1.75 

222 

4 

104. 

1,75 

234 

4 

118.1 

2. 

4120 

1 

30. 

2. 

4293 

1 

34. 

2. 

1060 

2 

60. 

2. 

1110 

2 

68. 

2. 

470 

3 

90. 

2. 

492 

3 

102. 

2. 

264 

4 

120. 

2. 

277 

4 

136. 

2.25 

4678 

1 

34. 

2^25 

4898 

1 

38.5 

2.25 

1210 

2 

68. 

2.25 

1266 

2 

77. 

2.25 

539 

3 

102. 

2.25 

563 

3 

115.5 

2.25            303 

4 

136.1 

2.25 

317 

4 

154.1 

2.5 

5364 

1 

38.1 

2.5 

5552 

1 

43.1 

2.5 

1383 

2 

76.2 

2.5 

1433 

2 

86.2 

2.5 

615 

3 

114.3 

2.5 

637 

3 

129.3 

2.5 

346 

4 

152.5 

2.5 

359 

4 

172.5 

2.75 

6064 

1 

42.3 

2.75 

6325 

1 

47.  S 

2.75 

1559 

2 

84.6 

2.75 

1622 

2 

95.6 

2.75 

696 

3 

126.8 

2.75 

726 

3 

143  3 

2.75 

392 

4 

169.1 

2.75 

408 

4 

191.1 

3. 

6732 

1 

46.5 

3. 

7023 

1 

52.5 

3 

1723 

2 

93. 

S. 

1794 

2 

105. 

3. 

770 

3 

139.5 

3. 

800 

3 

157.5 

3. 

433 

4 

186. 

3. 

450 

4 

210. 

3.25 

7427 

1 

50.8 

3.25 

7730 

1 

57.3 

3.25 

1896 

2 

101.6 

3.25 

1964 

2 

114.6 

3.25 

848 

3 

152.3 

3  .  25 

880 

3 

171.8 

3.25 

477 

4 

203.1 

3.25 

495 

4 

229.1 

3.5 

8013 

I 

55.1 

3.5 

8331 

1 

62.1 

3.5 

2045 

2 

110.2 

3.5 

2120 

2 

124.2 

3.5 

914 

3 

165.3 

3.5 

949 

3 

186.  3 

3.5 

514 

4 

220.5 

3.5 

534 

4 

248.5 

OPEN    AND    CLOSED    CHANNELS. 


175 


TABLE   32. 

Yelocities  and  discharges  in  trapezoidal   channel.;  based  on  Kutter's 
formula,  with  n  =  .03.     Side  slopes   £  horizontal  to  1  vertical. 


BED  WIDTH  18  FEET. 


BED  WIDTH  20  FEET. 


Depth  in 
feet. 

Slope 
1  in 

Velocity 
in 
feet  per 
second. 

Discharge 
in 
cubic  feet 
per 
second. 

Depth  in 
feet. 

Slope 
1  in 

Velocity 
in 
feet  per 
second. 

Discharge 
in 
cubic  feet 
per 
second. 

1.5 

3124 

1 

28.1 

1.5 

3022 

1 

31.1 

1.5 

779 

2 

56.2 

1.5 

779 

2 

62.3 

1.5 

348 

3 

84.4 

1.5 

346 

3 

93.3 

1.5 

195 

4 

112.5 

1.5 

195 

4 

124.5 

1.75 

3713 

1 

33. 

1.75 

3713 

1 

36.5 

1.75 

958 

2 

66. 

1.75 

958              2 

73. 

1.75 

426 

3 

99.1 

1.75 

426 

3 

109.6 

1.75 

240 

4 

132.1 

1.75 

240 

4 

146.1 

2. 

4385 

1 

38. 

2. 

4492 

1 

42 

2 

1130 

2 

76. 

2. 

1157 

2 

84. 

2 

504 

3 

114. 

2. 

515 

3 

126. 

2 

284 

4 

152. 

2. 

290 

4 

168. 

2^25 

5114 

1 

43. 

2.25 

5245 

1 

47.5 

2.25 

1320 

2 

86. 

2.25 

1352 

2 

95. 

2.25 

589 

3 

129.1 

2.25 

602 

3 

142.6 

2.25 

331 

4 

172.1 

2.25 

338 

4 

190. 

2.5 

5825 

1 

48.1 

2.5 

5935 

1 

53.1 

2.5 

1500 

2 

96.2 

2.5 

1528 

2 

106.2 

2.5 

668 

3 

144.4 

2.5 

682 

3 

159.3 

2.5 

376 

4 

192.5 

2.5 

384 

4 

212.5 

2.75 

6585 

1 

53.3 

2.75 

6737 

1 

58.8 

2.75 

1692 

2 

106.6 

2.75 

1726 

2 

117.6 

2.75 

755 

3 

159.8 

2.75 

770 

3 

176.3 

2.75 

425 

4 

213.1 

2.75 

433 

4 

235.1 

3. 

7285 

1 

58.5 

3. 

7427 

1 

64.5 

3. 

1862 

2 

117. 

3. 

1897 

2 

129. 

3. 

832 

3 

175.5 

3. 

848 

3 

193. 

3. 

468 

4 

234. 

3. 

477 

4 

258. 

3.25 

8028 

1 

63.8 

3.25 

8163 

1 

70.3 

3.25 

2056 

2 

127.6 

3.25 

2083 

2 

140.6 

3.25 

914 

3 

191.3 

3.25 

931 

3 

210.8 

3.25 

514 

4 

255.1 

3  25 

524 

4 

281.1 

3.5 

8807 

1 

69.1 

3.5 

8966 

1 

76.1 

3.5 

2251 

2 

138.2 

3.5 

2282 

2 

152.2 

3.5 

1000 

3 

207.4 

3.5 

1018 

3 

228.3 

3.5 

563 

4 

276.5 

3.5 

573 

4 

304.5 

176 


FLOW    OP    WATER    IN 


TABLE  32. 

Velocities  and  discharges  in   trapezoidal   channels   based  on  Kutter's 
formula,  with  ?i  =  .03.     Side  slopes  -J  horizontal  to  1  vertical. 


tfED    WIDTH    2£>    1'EET. 

13ED    WIDTH    3U   JttEET. 

Depth  in 
feet. 

Slopo 
1m 

Velocity 
iu 
feet  per 

Discharge 
in 
cubic  feet 

Depth  in 
feet. 

Slopo 
1  iu 

Velocity 
in 
feet  per 

Discharge 
in 
cubic  feet 

second. 

per 
second. 

second. 

per 
second. 

2. 

4697  ' 

1 

52. 

2. 

4797 

1 

62. 

2. 

1212 

2 

104. 

2. 

1237 

2 

124. 

2. 

541 

3 

156. 

2. 

551 

3 

186. 

2. 

304 

4 

208. 

2. 

310 

4 

248. 

•2.25 

5489 

1 

58.8 

2.25 

5589 

1 

70. 

2.25 

1408 

2 

117.6 

2.25 

1435 

2 

140. 

2.25 

628 

3 

176.3 

2.25 

641 

3 

210. 

2  25 

353 

4 

235.1 

2.25 

361 

4 

280. 

2.5 

6197 

1 

65.6 

2.5 

6448 

1 

78.1 

2.5 

1586 

2 

131.2 

2.5 

1657 

2 

156.2 

2.5 

711 

3 

196.8 

2.5 

740 

3 

234  3 

2.5 

400 

4 

262.5 

2.5 

416 

4 

312.5 

2.75 

6992 

1 

72.5 

2.75 

7310 

1 

86.3 

2.75 

1792 

2 

145. 

2.75 

1866 

2 

172.6 

2.75 

800 

3 

217.6 

2.75 

832 

3 

258.8 

2.75 

450 

4 

290.1 

2.75 

468 

4 

345.1 

3. 

7878 

1 

79.5 

3. 

8108 

1 

94.5 

3. 

2008 

2 

159. 

3. 

2084 

2 

189. 

3. 

897 

3 

238.5 

3. 

931 

3 

283.5 

3. 

504 

4 

318. 

3. 

523 

4 

378. 

3.5 

9651 

1 

93.6 

3.5 

10007 

1 

111.1 

3.5 

2450 

2 

187.2 

3.5 

2531 

2 

222.2 

3.5 

1091 

3 

280.9 

3.5 

1127 

3 

333.3 

3.5 

614 

4 

374.5 

3.5 

634 

4 

444.5 

4. 

11308 

i 

108. 

4. 

11952 

1 

128. 

4. 

2840 

2 

216. 

4. 

2958 

2 

256. 

4. 

1263 

3 

324. 

4. 

1323 

3 

384. 

4. 

708 

4 

432. 

4. 

745 

4 

512. 

4.5 

13185 

1 

122  6 

4.5 

13831 

1 

145.1 

4.5 

3285 

2 

245.2 

4.5 

3436 

2 

290.2 

4.5 

1454 

3 

367.9 

4.5 

1522 

3 

435.3 

4.5 

818 

4 

490.5 

4.5 

856 

4 

580.5 

OPEN    AND    CLOSED    CHANNELS. 


177 


TABLE  32. 

Velocities   and  discharges   in  trapezoidal  channels  based  on  Kutter's 
formula,  with  n  =  .03.      Side  slopes  •£  horizontal  to   1  vertical. 


BED  WIDTH  35  FEET. 

BED  WIDTH  40  FEETT 

Depth  in 
feet. 

Slope 
lin 

Velocity 
in 
feet  per 

Discharge 
in 
cubic  feet 

Depth  in 
feet. 

Slope 
lin 

Velocity 
in 
feet  per 

Discharge 
in 
cubic  feet 

second. 

per 
second. 

second. 

per 
second. 

2. 

4886 

1 

72. 

2. 

5012 

1 

82. 

2. 

1266 

2 

144. 

2. 

1294 

2 

164. 

2. 

563 

3 

216. 

2. 

576 

3 

246. 

2. 

317 

4 

288. 

2. 

324             4 

328. 

2.25 

5706 

1 

81.3 

2.25 

5853              1 

92.5 

2.25 

1465 

2 

162.6 

2.25 

1504             2 

185. 

2.25 

655 

3 

243.8 

2.25 

668 

3 

277.6 

2.25 

368 

4 

325.1 

2.25 

376 

4 

370.1 

2.5 

6601 

1 

90.6 

2.5 

6732             1 

103.1 

2.5 

1691 

2 

181.2 

2.5 

1725 

2 

206.3 

2.5 

754 

3 

271.9 

2.5 

770 

3 

309.4 

2.5 

425 

4 

362.5 

2.5 

433 

4 

412.5 

2.75 

7261 

1 

100. 

2.75 

7725             1 

113.8 

2.75 

1935 

2 

200. 

2.75 

1969             2 

227.6 

2.75 

864 

3 

300. 

2.75 

880             3 

341.3 

2.75 

486 

4 

400. 

2.75 

495     !         4 

455.1 

3. 

8479 

1 

109.5 

3. 

8642 

1 

124.5 

3. 

2158 

2 

219. 

3. 

2199 

2 

249.  . 

3. 

965 

3 

328.5 

3. 

982 

3 

373.5 

3. 

543 

4 

438. 

3. 

552 

4 

498. 

3.5 

10381 

1 

128.6 

3.5 

10751 

1 

146.1 

3.5 

2630 

2 

257.2 

3.5 

2705 

2 

292.2 

3.5 

1164 

3 

385.8 

3.5 

1203 

3 

438.3 

3.5 

654 

4 

514.4 

3.5 

677 

4 

584.5 

4. 

12515 

1 

148. 

4. 

12776 

1 

168. 

4. 

3125 

2 

296. 

4. 

3163 

2 

336. 

4. 

1380 

3 

444. 

4. 

1406 

3 

504. 

4. 

782 

4 

592. 

4. 

791             4 

672. 

4.5 

14505 

1 

167.6 

4.5 

14997 

1 

190.1 

4.5 

3591 

2 

335.2 

4.5 

3701 

2 

380.3 

4.5 

1591 

3 

502.9 

4.5 

1640 

3 

570.4 

4.5 

895 

4 

670.5 

4.5 

922 

4 

760.5 

12 


178 


FLOW    OF    WATER    IN 


TABLE  32. 

Velocities   and  discharges  in  trapezoidal  channels  based  on  Kutter's 
formula,  with  n  =  .03.      Side  slopes   J  horizontal  to  1   vertical. 


BED  WIDTH  45  FEET. 

BED  WIDTH  50  FEET. 

Depth  in 
feet. 

Slope 
1  in 

Velocity 
in 
feet  per 

Discharge 
in 
cubic  feet 

Depth  in 
feet. 

Slope 
1  m 

Velocity 
in 
feet  per 

Discharge 
in 
cubic  feet 

second. 

per 
second. 

second. 

per 
second. 

2. 

5013 

1 

92. 

2. 

5128 

1 

102. 

2. 

1294 

2 

184. 

2. 

1322 

2 

204. 

2. 

576 

3 

276. 

2 

589 

3 

306. 

2. 

324 

4 

368. 

2 

331 

4 

408. 

2.25 

5951 

1 

103.8 

2  25 

6086 

1 

115. 

2.25 

1527 

2 

207.6 

2.25 

1557 

2 

230. 

2.25 

682 

3 

311.3 

2.25 

697 

3 

345. 

2.25 

384 

4 

415.1 

2.25 

392 

4 

460. 

2.5 

6864 

1 

115.6 

2.5 

6999 

1 

128.1 

2.5 

1759 

2 

231.3 

2.5 

1794 

2 

2.36.3 

2.5 

785 

3 

346.9 

2.5 

800 

3 

384.4 

2.5 

442 

4 

462  5 

2.5 

450 

4 

512.5 

2.75 

7886 

1 

127.5 

2.75 

8039 

1 

141.3 

2  75 

2012 

2 

255. 

2.75 

2034 

2 

282.6 

2.75 

897 

3 

382.6 

2.75 

914 

3 

423.9 

2.75 

504 

4 

510.1 

2.75 

514 

4 

565.1 

3. 

8800 

1 

139.5 

3. 

8969 

1 

154  .  5 

3. 

2239 

2 

279. 

3. 

2275 

2 

309. 

3. 

998 

3 

418.5 

3. 

1018 

3 

463.5 

3. 

562 

4 

558. 

3. 

573 

4 

618. 

3.5 

10930 

1 

163.6 

3.5 

14130 

1 

181.1 

3.5 

2751 

2 

327.3 

3.5 

2796 

2 

362.2 

3.5 

1223 

3 

490.9 

3.5 

1243 

3 

543.4 

3.5 

688 

4 

654.5 

3.5 

699 

4 

724.5 

4. 

13180 

i 

188. 

4. 

13410 

1 

208. 

4. 

3272 

2 

376. 

4. 

3331 

2 

416. 

4. 

1454 

3 

564. 

4. 

1477 

3 

624. 

4. 

821 

4 

752. 

4. 

830 

4 

832. 

4.5 

15230 

1 

212.6 

4.5 

15707 

1 

235.1 

4.5 

3751 

2 

425.3 

4.5 

3866 

2 

470.2 

4.5 

1661 

3 

637.9 

4.5 

1707 

3 

705.4 

45 

935 

4 

850.5 

4.5 

960 

4 

940.5 

OPEN    AND    CLOSED    CHANNELS. 


179 


TABLE   32. 

Velocities   and   discharges  in  trapezoidal  channels  based  on   Kutter's 
formula,  with  n  =  .03.      Side  slopes  -J  horizontal  to   1  vertical. 


BED  WIDTH  60  FEET. 

BED  WIDTH  70  FEET. 

Depth  in 
feet. 

Slope 
1  in 

Velocity 
in 
feet  per 

Discharge 
in 
cubic  feet 

Depth  in 
feet. 

Slope 
liu 

Velocity 
in 
feet  per 

Discharge 
in 
cubic  feet 

_ 

second. 

per 
second. 

second. 

per 
second. 

3. 

2317                2 

369. 

3. 

2356 

2 

429. 

3. 

1035             3 

553.5 

3. 

1050 

3 

643.5 

3. 

583 

4 

738. 

3. 

593 

4 

858. 

3. 

373 

5 

922.5 

3. 

378 

5 

1072.5 

3.25 

2623 

2 

400,6 

3.25 

2661 

2 

465.6 

3.25 

1163 

3 

600.8 

3.25 

1183 

3 

698.4 

3.25 

654 

4 

801.1 

-     3.25 

665 

4 

931.1 

3.25 

419 

5 

1001.4 

3.25 

426 

5 

1163.9 

3.5 

2893 

2 

432.3 

3.5 

2949 

2 

502.3 

3.5 

1286 

3 

648.4 

3.5 

1305 

3 

753.4 

3.5 

723 

4 

864.5 

3.5 

734 

4 

1004.5 

3.5 

464 

5 

1080.6 

3.5 

470 

5 

1255.6 

4. 

3435 

2 

496. 

4. 

3488 

2 

576. 

4. 

1522 

3 

744. 

4. 

1544 

3 

864. 

4. 

856 

4 

992. 

4. 

869 

4 

1152. 

4. 

548 

5 

1240. 

4. 

556 

5 

1440. 

4.5 

3988 

2 

560.3 

4.5 

4094 

2 

650.3 

4.5 

1759 

3 

840.4 

4.5 

1807 

3 

975.4 

4.5 

989 

4 

1120.5 

4.5 

1017 

4 

1300.5 

4.5 

633 

5 

1400.6 

4.5 

651 

5 

1625.6 

5. 

4602 

2 

625. 

5. 

4653 

2 

725. 

5. 

2020 

3 

937.5 

5. 

2045 

3 

1087.5 

5. 

1133 

4 

1250. 

5. 

1148 

4 

1450. 

5. 

723 

5 

1562  .  5 

5. 

734 

5 

1812.5 

6. 

5785 

2 

756. 

6. 

5963 

2 

876. 

6. 

2538 

3 

1134. 

6. 

2584 

3 

1314. 

6. 

1406 

4 

1512. 

6. 

1440 

4 

1752. 

6. 

900 

5 

1890. 

6. 

922 

5 

2190. 

180 


FLOW    OF    WATER    IN 


TABLE  32. 

Velocities   and   discharges  in  trapezoidal  channels,  based  on  Kutter's 
formula,  with  n  —  .03.      Side  slopes  \  horizontal  to  1  vertical. 


BED  WIDTH  80  FEET. 

BED  WIDTH  90  FEET. 

Depth  in 

Slope 

Velocity 
in 

Discharge 
in 

Depth  in 

Slope 

Velocity 
in 

Discharge 
in 

feet. 

lin 

feet  per 

cubie  feet 

feet. 

lin 

feet  per 

cubic  feet 

second. 

per 
second. 

(second. 

per 
second. 

3. 

2404 

2 

489. 

3. 

2403 

2 

549. 

3. 

1070 

3 

733.5 

3. 

1074 

3 

823.5 

3. 

603 

4 

978. 

3. 

603 

4 

1098. 

3. 

386 

5 

1222.5 

3. 

386 

5 

1372.5 

3.25 

2661 

2 

530.6 

3.25 

2704 

2 

595.6 

3  25 

1183 

3 

795.8 

3.25 

1203 

3 

893.3 

3.25 

665 

4 

1061.1 

3.25 

677 

4 

1191.1 

3.25 

426 

5 

1326.4 

3.25 

433 

5 

1488.9 

3.5 

2946 

2 

572.3 

3.5 

2982 

2 

642.3 

3.5 

1305 

3 

858.4 

3.5 

1326 

3 

963.4 

3.5 

734 

4 

1144.5 

3.5 

746 

4 

1284.5 

3.5 

470 

5 

1430.6 

3.5 

477 

5 

1605.6 

4. 

3541 

2 

656. 

4. 

3596 

2 

736. 

4. 

1567 

3 

984. 

4. 

1590 

3 

1104. 

4. 

882 

4 

1312. 

4. 

895 

4 

1472. 

4. 

564 

5 

1640. 

4. 

573 

5 

1840. 

4.5 

4167 

2 

740.3 

4.5 

4221 

2 

830.3 

4.5 

1835 

3 

1110.4 

4.5 

1859 

3 

1245.4 

4.5 

1030 

4 

1480.5 

4.5 

1045 

4 

1660.5 

4.5 

660 

5 

1850.6 

4.5 

668 

5 

2075.6 

5. 

4792 

2 

825. 

5. 

4833 

2 

925. 

5. 

2104 

3 

1237.5 

5. 

2139 

3 

1387.5 

5. 

1178 

4 

1650. 

5. 

1194 

4 

1850. 

5. 

754 

5 

2062.5 

5. 

764 

5 

2312.5 

6. 

6079 

2 

996. 

6. 

6175 

2 

1116. 

6. 

2649 

3 

1494. 

6. 

2682 

3 

1674. 

6. 

1477 

4 

1992. 

6. 

1488 

4 

2232. 

6. 

943 

5 

2490. 

6. 

952 

5 

2790. 

OPEN    AND    CLOSED    CHANNELS. 


181 


TABLE  32. 

Velocities  and  discharges  in  trapezoidal  channels,  based    on  Kutter's 
formula,  with  n  —  .03.      Side  slopes  J  horizontal  to   1  vertical. 


BED  WIDTH  100  FEET. 

BED  WIDTH  120  FEET. 

Depth  in 
feet. 

Slope 
liii 

Velocity 
in 
feet  per 
second. 

Discharge 
in 
cubic  feet 
per 
second. 

Depth  in 
feet. 

Slope 
1  in 

Velocity 
in 
feet  per 
second. 

Discharge 
in 
cubic  feet 
per 
second. 

3. 

2443 

2 

609. 

6. 

6462 

2 

1476. 

3. 

1090 

3 

913.5 

6. 

2796 

3 

2214. 

3. 

614 

4 

1218. 

6. 

1554 

4 

2952. 

3. 

393 

5 

1522.5 

6. 

986 

5 

3690. 

3.25 

2748 

2 

660.6 

7. 

7914 

2 

1729. 

3.25 

1223 

3 

990.8 

7. 

3389 

3 

2593.5 

3.25 

688 

4 

1321.1 

7. 

1879 

4 

3458. 

3.25 

440 

5 

1651.4 

7. 

1195 

5 

4322.5 

3.5 

3029 

2 

712.3 

8. 

9595 

2 

1984. 

3.5 

1346 

3 

1068.4 

8. 

4034 

3 

2976. 

3.5 

757 

4 

1424.5 

8. 

2231 

4 

3968. 

3.5 

485 

5 

1780.6    |       8. 

1412 

5 

4960. 

4. 

3650 

2 

816. 

4. 

1614 

3 

1224. 

BED  WIDTH  140  FEET. 

4. 

908 

4 

1632. 

4. 

581 

5 

2040. 

4. 

3701 

2 

1136. 

4. 

4221 

2 

920.3 

4. 

1640 

3 

1704. 

4. 

1859 

3 

1380.4 

4. 

921 

4 

2272.    ' 

4. 

1045 

4 

1840.5 

4. 

589 

5 

2840. 

4. 

668 

5 

2300.6 

5 

5051 

2 

1425. 

5. 

4913 

2 

1025. 

5. 

2217 

3 

2137.5 

5. 

2161 

3 

1537.5 

5. 

1241 

4 

2850. 

5. 

1210 

4 

2050. 

5. 

794 

5 

3562.5 

5. 

774 

5 

2562  .  5 

6. 

6533 

2 

1716. 

6. 

6231 

2 

1236. 

6. 

2811 

3 

2574. 

6. 

2714 

3 

1854. 

6. 

1568 

4 

3432. 

6. 

1512 

4 

2472. 

6. 

997 

5 

4290 

6. 

963 

5 

3090. 

7. 

8109 

2 

2009. 

BED  WIDTH  120  FEET. 

7. 

7. 

7- 

3462 
1925 
•  1001 

3 
4 

3013.5 
4018. 

4. 

3652 

2 

976. 

. 
8. 

i^ZL 

9795 

2 

5022  .  5 
2304. 

4. 

1612 

3 

1464. 

8. 

4116 

3 

3456. 

4. 

906 

4 

1952. 

8. 

2278 

4 

4608. 

4. 

580 

5 

2440. 

8. 

1443 

5 

5760. 

5. 

4989 

2 

1225. 

9. 

11453 

2 

2601. 

5. 

2190 

3 

1837.5 

9. 

4822 

3 

3901.5 

5. 

1224 

4 

2450. 

9. 

2632 

4 

5202. 

5. 

784 

5 

3062.5 

9. 

1633 

5 

6502.5 

182 


FLOW    OP    WATER    IN 


TABLE  33. 

Giving  fall  in  feet  per  mile;  the  distance  on  slope  corresponding  to  a 
fall  of  one  foot,  and  also  the  values  of  s  and  s/^ 

s=  —  =siiie  of  slope  —  fall  of  water  surface  (h),  in  any  distance  (I), 

6 

divided  by  that  distance. 


Fall  in 
iuches 
per 
mile. 

Slope 
1  in 

s 

V» 

Fall  in 
feet  per 
mile. 

Slope 
1  in 

s 

3  — 
\/s 

2 

31680 

.000031565 

.005618 

.25 

21120 

.000047349 

.006881 

2* 

25344 

.000039457 

.006281 

.50 

10560 

.000094697 

.009731 

31 

18103 

.000055240 

.007432 

.75 

7040 

.000142045 

.011918 

4 

15840 

.000063131 

.007945 

1. 

5280 

.000189393 

.013762 

4| 

14080 

.000071023 

.008427 

1.25 

4224 

.000236742 

.015386 

5 

12672 

.000078913 

.008883 

1.5 

3520 

.000284091 

.016854 

5| 

11520 

.000086805 

.009317 

1.75 

3017 

.000331439 

.018205 

6| 

9748 

.000102588 

.010129 

2. 

2640 

.000378788 

019463 

7 

9051 

.000110479 

,010511 

2^25 

2347 

.  000426076 

.020641 

71 

8448 

.000118371 

.010880 

2.5 

2112 

.000473485 

.021760 

8 

7920 

.000126261 

.011237 

2.75 

1920 

.000520833 

.022822 

8* 

7454 

.000134154 

.011583 

3. 

1760 

.000568182 

.023837 

9-i 

6670 

.000149937 

.012245 

3.25 

1625 

.000615384 

.024807 

10 

6336 

.000157828 

.012563 

3.5 

1508 

.000663130 

.025751 

10| 

6034 

.000165720 

.012873 

3.75 

1408 

.000710227 

.026650 

11 

5760 

.000173598 

.013176 

4. 

1320 

.000757576 

.  027524 

HI 

5510 

.000181502 

.013472 

5. 

1056 

.000946970 

.030773 

12 

5280 

.000189393 

.013762  : 

6. 

880. 

.001136364 

.03371 

12| 

5069 

.000197285 

.014016 

7. 

754.3 

.001325732 

.036416 

12| 

4969 

.000201231 

.014185 

8. 

660. 

.001515152 

.038925 

13 

4874 

.000205182 

.014324 

9. 

586.6 

.001704445 

.041286 

13| 

4693 

.  000213068 

.014597 

10. 

528. 

.001893939 

.043519 

13| 

4608 

.000217014 

.014732 

11. 

443.6 

.002083333 

.  045643 

14 

4526 

.  000220960 

.014865 

12. 

440. 

.002272727 

.047673 

141 

4425 

.  000225989 

.015033 

13. 

406,1 

.002462121 

.  04962 

14| 

4370 

.000228851 

.015128 

14. 

377.1 

.002651515 

.051493 

14| 

4271 

.000234137 

.015301 

15. 

352. 

.002840909 

.0533 

15| 

4088 

.000244634 

.015641 

16. 

330. 

.003030303 

.055048 

16 

3960 

000252525 

.015891 

17. 

310.6 

.003219696 

.056742 

161 

3840 

.000260411 

.016137 

18. 

293.3 

.003409090 

.058388 

17 

3727 

.000268308 

.016381 

19. 

277.9 

.003598484 

.059988 

17| 

3621 

.000276199 

.016619 

20. 

264. 

.003787878 

.061546 

18| 

3425 

.000291982 

.017087 

21. 

251.4 

.003977272 

.063066 

19 

3335 

.000299874 

.017317 

22. 

240. 

.004166667 

.064549 

19* 

3249 

.000307765 

.017543 

23. 

229.6 

.004356060 

.066 

20 

3168 

.000315656 

.017767 

24. 

220. 

.004545454 

.067419 

20  1 

3091 

.000323548 

.017987 

25. 

211.2 

.004734848 

.06881 

21| 

2947 

.000339331 

.018421 

26. 

203.1 

.  004924242 

.070173 

22 

2880 

.000347222 

.018634 

27. 

195.2 

.005113636 

.07151 

22J 

2816 

.000355114 

.018844 

28. 

188.6 

.005303030 

.072822 

23 

2755 

.000363005 

.019052 

29. 

182.1 

.005492424 

.074111 

23  1 

2696 

.000370896 

.019259 

30. 

176. 

.005681818 

.075373 

OPEN    AND    CLOSED    CHANNELS. 


183 


TABLE  33. — SLOPES. 


Slope 
1  in 

Fall  in 
feet  per 

s 

Slope 
1  in 

Fall  in 
feet  per 
milo 

»• 

Vs 

Q1110* 

4 

1320. 

.25 

.5 

51 

103.5 

.019607843 

.  140028 

5 

1056. 

.2 

.447214 

52 

101.5 

.019230769 

.  138676 

6 

880. 

.  166666666 

.408248  I 

53 

99.62 

.018867925 

.137361 

7 

754.3 

.142857143 

.377978 

54 

97.78 

.018518519 

.  136085 

8 

660. 

.125 

.  353553 

55 

96. 

.018181818 

.  134839 

9 

586.7 

.111111111 

.  333333 

56 

94.29 

.017850143 

.  133630 

10 

528. 

.1 

.316228 

57 

92.65 

.017543860 

.  132453 

11 

480 

.090909090 

.301511 

58 

91.03 

.017241379 

.131305 

12 

440. 

.083333333 

.288675 

59 

89.49 

.016949153 

.  130189 

13 

406.2 

.076923077 

.277350 

60 

88. 

.016666667 

.  129100 

14 

377.1 

.071428571 

.267261 

61 

86.56 

.016393443 

.  128037 

15 

352. 

.066666667 

.258199 

62 

85.16 

.016129032 

.  127000 

16 

330. 

.0625 

.25 

63 

83.81 

.015873010 

.  125988 

17 

310.6 

.058823529 

.  242536 

64 

82.50 

.015625 

.125 

18 

293.3 

.055555555 

.235702 

65 

81  23 

.015384615 

.  124035 

19 

277.9 

.052631579 

.229416 

66 

80. 

.015151515 

.  123091 

20 

264. 

.05 

.223607 

67 

78.81 

.014925353 

.122169 

21 

251.4 

.047619048 

.218218 

68 

77.65 

.014705882 

.  121286 

22 

240. 

.  045454545 

.213200 

60 

76.52 

.014492754 

.  120386 

23 

229.6 

.043478261 

.208514 

70 

75.43 

.014285714 

.119524 

24" 

220. 

.041066667 

.204124 

71 

74.36 

.014084507 

.118678 

25 

211.2 

.04 

.2 

72 

73.33 

.013888889 

.117851 

26 

203.1 

.038461538 

.196116 

73 

7  2  33 

.013688630 

.117041 

27 

195.6 

.  037037037 

.  192450 

74 

7l!36 

.013513514 

.116248 

28 

188.6 

.035714286 

.  188982 

75 

70.40 

.013333333 

.115470 

29 

182.1 

.  034452759 

.  185695 

76 

69.47 

.013157895 

.114708 

30 

176. 

.  033333333 

.  182574 

77 

68.57 

.012987013 

.113961 

31 

170.3 

.032258065 

.  179605 

78 

67.69 

.012820513 

.113228 

32 

165. 

.03125 

.176777 

70 

06.84 

.012658228 

.112509 

33 

160. 

.030303030 

.  174077 

80 

66. 

.0125 

.111803 

34 

155.3 

.029411765 

.171499 

81 

65.18 

.012345679 

.111111 

35 

150.9 

.028571429 

.  169031 

82 

04.39 

.012195122 

.110431 

36 

146.7 

.027777778 

.  166667 

83 

63.62 

.012048193 

.  109764 

37 

142.7 

.027027027 

.  164399 

84 

62.80 

.011904762 

.  109109 

38 

138.9 

.026315789 

.  1G2221 

85 

62.12 

.011764706 

.  108465 

39 

135.4 

.025641028 

.  160125 

86 

61.40 

.011627907 

.107833 

40 

132. 

.025 

.158114 

87 

60.69 

.011494253 

107211 

41 

128.8 

.  024390244 

.  156174 

88 

60. 

.011363636 

.  106600 

42 

•125.7 

.  023809524 

.  154303 

89 

59.32 

.011235955 

.  106000 

43 

122.8 

.0232,55814 

.  152490 

90 

58.66 

.011111111 

.  105409 

44 

120. 

.022727273 

.  15075G 

91 

58.02 

.010989011 

.  104828 

45 

117.3 

.022222222 

.  149071 

92 

57.39 

.  010869565 

.  104257 

46 

114.8 

.021739130 

.  147444 

93 

56.78 

.010752688 

.  103695 

47 

112.3 

.021276600 

.U5865 

94 

56.17 

.010638298 

.  103142 

48 

110. 

.020833333 

.144337  ! 

95 

55.58 

.010526316 

.  102598 

49 

107.8 

.020408163 

.142857  1 

96 

55. 

.010416667 

.  102062 

50 

105.6 

.02 

.141421 

97 

£4.43 

.010309278 

.  101535 

184 


FLOW    OF    WATER    IN 


TABLE  33.— SLOPES. 


Fall  in 

Fall  in 

Slope 
1  in 

feet  per 
mile. 

s 

V* 

Slope 
;  1  in 

feet  per 
mile. 

s 

v~ 

98 

53.88 

.010204082 

.101015 

145 

36.41 

.006896552 

.083046 

99 

53.34 

.010101010 

.  100504 

146 

36.16 

.006849315  .OS2760 

100 

52.8 

.010 

.1 

147 

35.92 

.006802721  .082479 

101 

52.28 

.  009900990 

.099504 

148 

35.68 

.  006756757 

.082199 

102   51.76 

.009803922 

.099015 

149 

35.44 

.006711409 

.081923 

103   51.26 

.009708738 

.098533 

150 

35.20 

.006666667 

.081650 

104   50.77 

.009615385 

.098058 

151 

34.97 

.006622517 

.081379 

105   50.29 

.009523810 

.  097590 

152 

34.74 

.006578947 

.081111 

106   49.81 

.009433962 

.097129 

153 

34.51 

.  006535948 

.080845 

107 

49.35 

.009345794 

.  096674 

154 

34.29 

.  006493506 

.080582 

108 

48.89 

.  009259259 

.096225 

155 

34.06 

.006451613 

.08)0322 

109 

48.44 

.009174312 

.095783 

156 

33.85 

.006410256 

.080065 

110 

48. 

.009090909 

.095346 

157 

33.63 

.006369427 

.079809 

111 

47.57 

.009009009 

.094916 

158 

33.42 

.006329114 

.079556 

112 

47.14 

.008928571 

.094491 

159 

33.21 

.  006289308 

.  079305 

113 

46.72 

.008849558 

.094072 

160 

33. 

.00625 

.079057 

114 

46.31 

.008771930 

.093659 

161 

32.8 

.006211180 

.078811 

115 

45.91 

.008695692 

.093250 

162 

32.59 

.006172840 

.078568 

116 

45.52 

.  008620690 

.092848 

163 

32.39 

.006134969 

.078326 

117 

45.13 

.008547009 

.092450 

164 

32.20 

.006097561 

.078087 

118 

44.75 

.008474576 

.092057 

165 

32. 

.  006060606 

.  077850 

119 

44.37 

.008403361 

.091669 

166 

31.81 

.006024096 

.077615 

120 

44. 

.008333333 

.091287 

167 

31.62 

.005988024 

.077382 

121 

43.64 

.008264463 

.090909 

168 

31.43 

.005952381 

.077152 

122 

43.28 

.008196721 

.090536 

169 

31.24 

.005917160 

.076923 

123 

42.93 

.008130081 

.090167 

170 

31.06 

.005882353 

.076697 

124 

42.58 

.008064516 

.  089803 

171 

30.88 

.  005847953 

.076472 

125 

42.24 

.008 

.  089442 

172 

30.7 

.005813953 

.  076249 

126 

41.91 

.007836508 

.089087 

173 

30.52 

.  005780347 

.  076029 

127 

41.58 

.  007874016 

.088736 

174 

30.34 

.005747126 

.075810 

128 

41.25 

.0078125 

.088388 

175 

30.17 

.005714286 

.075593 

129 

40.93 

.007751938 

.088045 

176 

30. 

.005681818 

.075378 

130 

40.62 

.007692308 

.087706 

177 

29.83 

.005649718 

.075164 

131 

40.31 

.007633588 

.087370 

178 

29.66 

.005617978 

.074953 

132 

40. 

.007575758 

.087039 

179 

29.50 

.005586592 

.074744 

133 

39.70 

.007518797 

.086711 

180 

29.33 

.005555556 

.074536 

134 

39.40 

.007462687 

.  086387 

181 

29.17 

.005524862 

.074329 

135 

39.11 

.007407407 

.086066 

182 

29.01 

.005494505 

.074125 

136 

38.82 

.007352941 

.085749 

183 

28.85 

.  005464481 

.073922 

137 

38.54 

.007299270 

.085436 

184 

28.70 

.  005434783 

.073721 

138 

38.26 

.007246377 

.085126 

185 

28.54 

.  005405405 

.073521 

139 

37.98 

.007194245 

.084819 

186 

28  .  39 

.  005376344 

.073324 

140 

37.71 

.007142857 

.084516 

187 

28.24 

.005347594 

.073127 

141 

37.45 

.007092199 

.084215 

188 

28.09 

.005319149 

.072932 

142 

37.18 

.  007042254 

.083918 

189 

27.94 

.005291005 

.072739 

113 

36.92 

.006993007 

.083624 

190 

27.79 

.005263158 

.072548 

144 

36.67 

.006944444 

.083333 

191 

27.64 

.005235602 

.072357 

OPEN    AND    CLOSED    CHANNELS. 


185 


TABLE  33. — SLOPES. 


Slope 
1  iii 

Fall  in 
feet  pel- 
mile. 

s 

\/s 

Slope 
1  in 

Fall  in 
feet  per 
mile. 

s 

x/a 

192 

27.50 

.005208333 

.072169 

395 

13.37 

.002531646 

.050315 

193 

27.36 

.005181347 

.071982 

.  400 

13.20 

.002500000 

.050000 

194 

27.22 

.005154639 

.071796 

405 

13.04 

.002469136 

.049690 

195 

27.08 

.005128205 

.071612 

410 

12  88 

.  002439024 

.049387 

196 

26.94 

.005102041 

.071429 

415 

12.72 

.002409639 

.049088 

197 

26.80 

.005076142 

.071247 

420 

12.57 

.002380952 

.048795 

198 

26.67 

.005050505 

.071067 

425 

12.42 

.002352941 

.048507 

199 

26.53 

.005025126 

.070888 

430 

12.28 

.002325581 

.048224 

200 

26.40 

.005 

.070710 

435 

12.14 

.002298851 

.047946 

205 

25.76 

.004878049 

.069843 

440 

12. 

.002272727 

.047673 

210 

25.14 

.004761905 

.069007 

445 

11.87 

.002247191 

.047404 

215 

24.56 

.004651163 

.068199 

450 

11.73 

.002222222 

.047140 

220 

24. 

004545454 

.067419 

455 

11.60 

.002197802 

.046880 

225 

23.47 

.004444444 

.066667 

460 

11.48 

.002173913 

.046625 

230 

22.96 

.004347826 

.065938 

465 

11.35 

.002150538 

.046374 

235 

22.48 

.004255319 

.065233 

470 

11.24 

.002127660 

.046126 

240 

22. 

.004166667 

.064549 

475 

11.12 

.002105263 

.045883 

245 

21.55 

.004081623 

.063885 

480 

11. 

.002083333 

.045644 

250 

21.12 

.004000000 

.063246 

.  485 

10.89 

.002061856 

.045407 

255 

20.71 

.003921569 

.062620 

490 

10.78 

.002040816 

.045175 

260 

20.31 

.003846154 

.062018 

495 

10.67 

.002020202 

.044947 

265 

19.92 

.003773585 

.061430 

500 

10.56 

.002000000 

.044721 

270 

19.56 

.003703704 

.060858 

505 

10.46 

.001980198 

.044499 

275 

19.20 

.  003633634 

.  060302 

510 

10.35 

.001960784 

.044281 

280 

18.86 

.003571429 

.059761 

515 

10.25 

.001941748 

.044065 

285 

18  53 

.003508772 

.059235 

520 

10.15 

.001923077 

.043853 

290 

18.20 

.003448276 

.058722 

525 

10.06 

.001904763 

.043644 

295 

17.90 

.003389831 

.  058222 

530 

9.962 

.001886792 

.043437 

300 

17.60 

.  003333333 

.057735 

535 

9.870 

.001869159 

.043234 

305 

17.31 

.  003278689 

.057260 

540 

9.778 

.001851852 

.043033 

310 

17.03 

.003225806 

.056796    545 

9.688 

.001834862 

.042835 

315 

16.76 

.003174603 

056344 

550 

9.600 

.001818182 

.042640 

320 

16.50 

.003125000 

.055902 

555 

9.513 

.001801802 

.042448 

325 

16.25 

.  003076923 

.055470 

560 

9.428 

.001785714 

.  042258 

330 

16. 

.003030303 

.055048 

565 

9.345 

.001769912 

.042070 

335 

15.76 

.002985075 

.054636 

570 

9.263 

.001754386 

.041885 

340 

15.53 

.002941176 

.054232 

575 

9.182 

.001739130 

.041703 

345 

15.30 

.002898551 

.053838 

580 

9.103 

.001724138 

.041523 

350 

15.09 

.002857143 

.053452 

585 

9.026 

.001709420 

.041345 

355 

14.87 

.002816901 

.053074 

590 

8.949 

.001694915 

.041169 

360 

14.67 

.062777778 

.052705 

595 

8.874 

.001680672 

.040996 

365 

14.47  1.002739726 

.052342 

600 

8.800 

.001666667 

.040825 

370 

14.27  .002702703 

.051988 

605 

8.727 

.001652893 

.040656 

375 

14.08  i.  002666667 

.051640 

610 

8.656 

.001639344 

.040489 

380 

13.90 

.  002631579 

.051299 

615 

8.585 

.001626016 

.040324 

385 

13.71 

.002597403 

.050965 

620 

8.516 

.001612903 

.040161 

390 

13.54 

.002504103 

.050637 

625 

8.448 

.001600000 

.040000 

186 


FLOW    OF    WATER    IN 


TABLE  33.— SLOPES. 


Slope 
1  in 

Fall  in 
feet  per 
mile. 

s 

V~ 

Slope 
1  in 

Fall  in 
feet  per 
mile. 

s 

%/« 

630 

8.381 

.001587302 

.039841  , 

865 

6.104 

.001156069 

.034001 

635 

8.317 

.001574803 

.039684 

870 

6.069 

.001149425 

.  033903 

640   8.250 

.001562500 

.  039528 

875 

6.034 

.001142857 

.  033800 

645 

8.186 

.001550388 

.039375 

880 

6. 

.001136364 

.033710 

650 

8.123 

.001538462 

.039223 

885 

5.966 

.001129944 

.033614 

655 

8.061 

.001526718 

.039073 

890 

5.932  i.  001  123597 

.033520 

660 

8. 

.001515152  1.038925 

895 

5.900  1.001117318 

.033426 

665 

7.940 

.001503759 

.038778 

900 

5.867  .0011,11111 

.033333 

670 

7.881 

.001492537 

;  038633 

905 

5.834 

.001104972 

!  033241 

675 

7.822 

.001481481 

.038490 

910 

5.802 

.001100110 

.033108 

680 

7.765 

.001470588 

.038348 

915 

5.770 

.001093896 

.033059 

685 

7.708 

.001459854 

.038208 

920 

5.739 

.001086957 

.032969 

690 

7.652 

.001449275 

.038069  ! 

925 

5.708 

.001081081 

.032879 

695 

7.597 

.001438849 

.037932  I 

930 

5.677 

.001075269 

.032791 

700 

7.543 

.001428571 

.037796  i 

935 

5.648 

.001069519 

.  032703 

705 

7.490 

.001418440 

.037662  ! 

940 

5.617 

.001063830 

.032616 

710 

7.437 

.001408451 

.037529 

945 

5.587 

.001058201 

.032530 

715 

7.385 

.001398601 

.037398 

950 

5.558 

.001052632 

.032444 

720 

7.333 

.  001388889 

.037268 

955 

5.528 

.001047120 

.  032359 

725 

7.283 

.001379310 

.037139 

960 

5.500 

.001041667 

.  032275 

730 

7.233 

001369863 

.037012 

965 

5.472 

.001036269 

.032191 

735 

7.184 

.001360544 

.036885 

970 

5.434 

.001030928 

.032108 

740 

7.135 

.001351351 

.036761 

975 

5.415 

.001025641 

.032026 

745 

7.087 

.001342282 

.036637 

980 

5.388 

.001020408 

.031944 

750 

7.040 

.001333333 

.  036515 

985 

5.360 

.001015228 

.031863 

755 

G.993 

.001324503 

.036394 

990 

5.333 

.001010101 

.031782 

760 

6.948 

.001315789 

.036274 

995 

5.306 

.001005025 

.031702 

765 

6.902 

.001307190 

036155 

1000 

5.280 

.001000000 

.031623 

770 

6.857 

.001298701 

.036038 

1005 

5.253 

.000985025 

.031544 

775 

6.812 

.001290323 

.035921 

1010 

5.228 

.00099099 

.031466 

780 

6.769 

.001282051 

.035806 

1015 

5.202 

.  000985222 

.031388 

785 

6.726 

.001273885 

.035691 

1020 

5.176 

.000980392 

.031311 

790 

6.684 

.001265823 

.  035578 

1025 

5.151 

.000975610 

.031235 

795 

6.642 

.  001257862 

.035466 

1030 

5.126 

.000970873 

.031159 

800 

6.600 

.001250000 

.035355 

1035 

5.101 

.000966184 

.031083 

805 

6.559 

.001242236 

.035245 

1040 

5.077 

.000961538 

.031009 

810 

6.518 

.001234568 

.035136 

1045 

5.053 

.000956938 

.030934 

815 

6.478 

.001226994 

.035028 

1050 

5.029 

.000952381 

.030861 

820 

6.439 

.001219512 

.  034922 

1055 

5.005 

.000947867 

.  030787 

825 

6.400 

.001212121 

.034816 

1060 

4.981 

.000943396 

.030715 

830 

6.362 

.001204819 

.034710 

1065 

4.958 

.000938967 

.030643 

835 

6.324 

.001197605 

.034606 

1070 

4.935 

.000934579 

.030571 

840 

6.2S6 

.001190476 

.034503 

1075 

4.912 

.  000930233 

.030499 

845 

6.248 

.001183432 

.034401 

1080 

4.889 

.000925926 

.030429 

850 

6.212 

.001176471 

.034300 

1085 

4.866 

.000921659 

.030359 

855 

0.175 

.001169591 

.034199 

1090 

4.844 

.000917431 

.030289 

860 

6.140 

.001162791 

.034099 

1095 

4.822 

.000913242 

.030220 

OPEN    AND    CLOSED    CHANNELS. 


187 


TABLE  33.— SLOPES. 


Slope 
1  in 

Fall  in 
feet  per 
mile. 

s 

r  |  Slope 
Vt)     1  in 

Fall  in 
feet  per 
mile. 

s 

•N/r 

1100 

4.800 

.000909090 

.030151  [I  1335 

3.955 

.000749064 

.  027369 

1105 

4.778 

.000904159 

.  030069 

i  1340 

3.940 

.000746268 

.027318 

1110 

4.757 

.  000900900 

.030015 

1345 

3.926  .000743420 

.027267 

1115 

4.735 

.000896861 

.029948 

1350 

3.911  .000740741 

.027217 

1120 

4.714 

.000892857 

.029881 

1355 

3.897 

.000738007 

.027166 

1125 

4.693 

.  000888888 

.029814 

1360 

3.882 

.000735294 

.027116 

1130 

4.673 

.000884956 

.029748 

1365 

3.868 

.000732601 

.027067 

1135 

4.652 

.  000881057 

.029683 

1370 

8.854 

.000729927 

.027017 

1140 

4.632 

.000877193 

.029617 

1375 

3.840 

.000727273 

.026968 

1145 

4.611 

.000873365 

.029553 

1380 

3.826 

.  000724638 

.026919 

1150 

4.591 

.000869566 

.029488 

1385 

3.812 

.  000722022 

.026870 

1155 

4.571 

.000865801 

.029425 

1390 

3.799 

.000719424 

.026822 

1160 

4.552 

.000862069 

.029361 

1395 

3.785 

.000716846 

.026774 

1165 

4.532 

.000858370 

.029298 

1400 

3.771 

.000714286 

.  026726 

1170 

4.513 

.000854701 

.029235 

1405 

3.758 

.000711744 

.026679 

1175 

4.494 

.000851064 

.029173 

1410 

3.745 

.000709220 

.026631 

1180 

4.475 

.000847458 

.029111 

1415 

3.731 

.000706714 

.026584 

1185 

4.456 

.000843882 

.029049 

1420 

3.718 

.  000704225 

.026537 

1190 

4.437 

.000840336 

.028988 

1425 

3.705 

.000701754 

.026491 

1195 

4.418 

.000836820 

.028928 

1430 

3.692 

.000699300 

.026444 

1200 

4.400 

.000833333 

.028868 

1435 

3.680 

.000696864 

.026398 

1205 

4.382 

.000829875 

.028808 

1440 

3.667 

.000694444 

.026352 

1210 

4.364 

.000826446 

.028748 

1445 

3.654 

.000692042 

.026307 

1215 

4.346 

.000823045 

.028689 

1450 

3.641 

.  000689655 

.026261 

1220 

4.328 

.000819672 

.028630 

1455 

3.629 

.000687285 

.026216 

1225 

4.310 

.000816326 

.028571 

1460 

3.617 

.  000684931 

.026171 

1230 

4.293 

.000813008 

.028513 

1465 

3.604 

.000682594 

.026126 

1235 

4.275 

.000809717 

.028455 

1470 

3.592 

.000680272 

.026082 

1240 

4.258 

.000806452 

.028398 

1475 

3.580 

.000677966 

.026038 

1245 

4.241 

.000803213 

.028341 

1480 

3.568 

.000675676 

.025994 

1250 

4.224 

.000800000 

.028284 

1485 

3.556 

.000673401 

.  025950 

1255 

4.207 

.000796813 

.028228 

1490 

3.544 

.000671141 

.025907 

1260 

4.190 

.000793651 

.028172 

1495 

3.532 

.000668896 

.025803 

1265 

4.174 

.000790514 

.028116 

1500 

3.520 

.000666666 

.025820 

1270 

4.157 

000787402 

.028061 

1505 

3.508 

.000664452 

.025777 

1275 

4.141 

000784314 

.028006 

1510 

3.497 

,000662252 

.025734 

1280 

4.125 

000781250 

.027951 

1515 

3.485 

.000660066 

.025691 

1285 

4.109 

000778210 

.027896 

1520 

3.474 

.000657895 

.  025649 

1290 

4.093 

000775116 

027841 

1525 

3.462 

.000655737 

.025607 

1295 

4.077 

000772201 

027789 

1530 

3.451 

.000653595 

.  Q25566 

1300 

4.062 

000769231 

027735 

1535 

3.440 

.000652117 

.025524 

1305 

4.046 

000766283 

027682 

1540 

3.429 

.000649351 

025482 

1310 

4.031 

000763359 

027629 

1545 

3.417 

.000647275 

025441 

1315 

4.015 

000760456 

027576 

1550 

3.407 

.000645161 

.025400 

1320 

4. 

000757576 

027524 

1555 

3.396 

.000643087 

025359 

1325 

3.985 

000754717 

027472 

1560 

.  3.385 

.000641025 

025318 

1330 

3.970 

000751880 

.  027420 

1565 

3.374 

.000638978 

025278 

188 


FLOW    OF    WATER    IN 


TABLE  33.— SLOPES. 


Slope 
1  iii 

Fall  in 
feet  per 
mile. 

s 

S/.S 

Slope 
1  in 

Fall  in 
feet  per 
mile. 

s 

v/« 

1570 

3.363 

.000636943 

.025238 

1805 

2.925 

.000554017 

.023538 

1575 

3.352 

.000634921 

.025198 

1810 

2.917 

.000552486 

.  023505 

1580 

3.342 

.  0006329  1J 

.025158 

1815 

2.909 

.000550964 

.023473 

1585 

3.331 

.000630915 

.025118 

1820 

2.901 

.000549451 

.023440 

1590 

3.321 

.000628931 

.025078 

1825 

2.893 

.  000547945 

.023408 

1595 

3.310 

.000626959 

.  025039 

1830 

2.885 

.000546448 

.023376 

1600 

3.300 

.000625000 

.  025000 

1835 

2.877 

.000544949 

.023344 

1605 

3.290 

.  000623053 

.024961 

1840 

2.870 

.000543478 

.023313 

1610 

3.280 

.000621118 

.024922 

1845 

2.862 

.000542005 

.023281 

1615  ]  3.269 

.000619195 

.024884 

1850 

2.854 

.000540541 

.023250 

1620 

3.259 

.000617284 

.  024845 

1855 

2.847 

.000539084 

.023218 

1625 

3  249 

.000615384 

.024807 

1860 

2.839 

.000537633 

.023187 

1600 

3.239 

.000613497 

.  024769 

1865 

2.831 

.000536193 

.023156 

1635 

3.229 

.000611621 

.  024731 

1870 

2.824 

.000534759 

.023125 

1640 

3.220 

.000699756 

.024693 

1875 

2.816 

.000533333 

.  023094 

1645 

3.210 

.000607900 

.024656 

1880 

2.809 

.000531915 

.023063 

1650 

3.200 

.000606060 

.024618 

1885 

2.801 

.000530504 

.023033 

1655 

3.190 

.  000604230 

.024581 

1890 

2.794 

.000529101 

.023002 

1660 

3.181 

000602409 

.024544 

1895 

2.786 

.000527705 

.022972 

1665 

3.171 

.000600601 

.  024507 

1900 

2.779 

.000526316 

.022942 

1670 

3.162 

.000598802 

.024470 

1905 

2.772 

.000524934 

.022911 

1675 

3.152 

.000597015 

.  024434 

1910 

2.764 

.000523500 

.022881 

1680 

3.143 

.000595238 

.024398 

1915 

2.757 

.000522193 

.  022852 

1685 

3.134 

.000593102 

.  024354 

1920 

2.750 

.000520833 

.022822 

1690 

3.124 

.000591717 

.024325 

1925 

2.743 

.000519481 

.022792 

1695 

3.115 

.000589971 

.024290 

1930 

2.736 

.000518135 

.022763 

1700 

3  106 

.000588235 

.  024254 

1935   2.729 

.000516796 

.022733 

1705 

3.097 

.009586510 

.024218 

1940   2.722 

.000515464 

-.022704 

1710 

3.088 

.  000584795 

.024183 

1945 

2.715 

.000514139 

.  022G75 

1715 

3.079 

.  000583090 

.024147 

1950 

2.708 

.000512821 

.022646 

1720 

3.070 

.000581395 

.024112 

1955 

2.701 

.000511509 

.022616 

1725 

3.061 

.000579710 

.024077 

1960 

2.694 

.000510204 

.022588 

1730 

3.052 

.000578035 

.  024042 

19G5 

2.687 

.000508906 

.022559 

1735 

3.042 

.000576369 

.024008 

1970 

2.680 

.000507614 

.022530 

1740 

3.035 

.000574712 

.023973 

1975 

2.673 

.  OC0506329 

.  022502 

1745 

3.026 

.  000573066 

.023939 

1980 

2.667 

.000505051 

.022473 

1750 

3.017 

.000571429 

.023905 

1985 

2.660 

.000503778 

.  022445 

1755 

3.009 

.000569801 

.023871 

1990 

2.653 

.000502513 

.022417 

1760 

3. 

.000568182 

.023837 

1995 

2.647 

.000501253 

.022388 

1755 

2.992 

.000566572 

.023803 

2000 

2.640 

.000500000 

.022301 

1770 

2.983 

.000564972 

.  023769 

2005 

2.633 

.000498753 

.022333 

1775 

2.975 

.  000563380 

.023736 

2010 

2.627 

.000497512 

.  022305 

1780 

2.966 

.000561798 

.023702 

2015 

2.620 

.000496278 

.022277 

1785 

2.958 

.000560224 

.023669 

2020 

2.614 

.  000495050 

.022250 

1790 

2.950 

.000558659 

.023636 

2025 

2.607 

.000493827 

022222 

1795 

2.942 

.000557103 

.023603 

2030 

2.601 

.000492611 

.022195 

1800 

2.933 

.000555555  |.  023570 

2035 

2.595 

.  000491400 

.022168 

OPEN    AND    CLOSED    CHANNELS. 


189 


TABLE  33.— SLOPES. 


Slope 
1  in 

Fall  in 
feet  per 
mile. 

s 

v/s 

\  Slope 
1  in 

Fall  in 
feet  per 
mile. 

s 

Vs 

2040 

2.588 

.000490196 

.022140 

2265 

2.331 

.000441501  '.  021012 

2045 

2.582 

.000488998 

.022113 

2270 

2.326 

.000440529 

.020989 

2050 

2  576 

.000487805 

.022086 

2275 

2.321  .000439560 

.010966 

2055 

2.569 

.000486618 

.022059 

2280 

2.316  i.  000438597 

.020943 

2060 

2.563 

.  000485437 

.022033 

2285 

2.311 

.000437637 

.  020920 

2065 

2.557 

.000484213 

.  022005 

2290 

2.306 

.000436681 

.020897 

2070 

2.551 

.000483093 

.021979 

2295 

2.301 

.  000435730 

.  020874 

2075 

2  .  545 

.000481928 

.021953 

2300 

2.296 

.000434783 

.020853 

2080 

2  538 

.  000480769 

.021926 

2305 

2.291 

.  000433839 

.020829 

2085 

2.532 

.000479616 

.021900 

2310 

2.286 

.000432900 

.  020806 

2090 

2.526 

.  000478469 

.021874 

2315 

2.281 

.000431965 

.020784 

2095 

2.520 

.000477327 

.021848 

2320 

2.276 

000431034 

.020761 

2100 

2.514 

.000476190 

.021822 

2325 

2.271  .000430108 

.020740 

2105 

2.508 

.000475059 

.021796 

2330 

2.266  .000429185 

.020717 

2110 

2.502 

.000473934 

.021770 

2335 

2.261  .000428266 

.  020694 

2115 

2.496 

.000472813 

.021744 

2340 

2.256  .000427350 

.020672 

2120 

2.491 

.000471698 

.021719 

2345 

2  252  .000426439 

.020650 

2125 

2.485 

.  000470588 

.021693 

2350 

2.247  .000425532 

.020628 

2130 

2.479 

.  000469484 

.021668 

2355 

2.242  .000424629 

.020607 

2135 

2.473 

.000468384 

.021642 

2360 

2.237  .000423729 

.020585 

2140 

2.467 

.000467290 

.021617 

2365 

2.233  .000422833 

.020563 

2145 

2.462 

.000466200 

.021592 

2370 

2.228  1.000421941 

.020541 

2150 

2.456 

.000465116 

.021567 

2375 

2.223  j.  00042  1053 

.020520 

2155 

2.450 

.000464037 

.021542 

2380 

2.219  j.000420168 

.020498 

2160 

2.444 

.000462963 

.021517 

2385 

2.214  1.000419287 

.020477 

2165 

2.439  i.  00046  1894 

.021492 

2390 

2.209  000418410 

.020455 

2170 

2.433 

.000460829 

.021467 

2395 

2.205  .000417534 

.020434 

2175 

2.428 

.  000459770 

.021442 

2400 

2.200 

.000416667 

.020412 

2180 

2.422 

.000458716 

.021418 

2405 

2.195 

.000415801 

.020391 

2185 

2.416 

.000457666 

.021393 

2410 

2.191  !.  0004  14938 

.020370 

2190 

2.411 

.000456621 

.021369 

2415 

2.186 

.000414079 

.020349 

2195 

2.405 

.000455581 

.021344 

2420 

2.182 

.000413223 

.020328 

2200 

2.400 

.000454545 

.021320 

2425 

2.177  .000412371 

.  020307 

2205 

2  .  395 

.000453515 

.021296 

2430 

2.173 

.000411523 

.020286 

2210 

2.389 

.  000452489 

.021272 

2435 

2.168 

.000410678 

.020265 

2215 

2.384 

.000451467 

.021248 

2440 

2.164 

.000409836 

.020244 

2220 

2.378 

.000450450 

.021224 

2445 

2.160  .500408998 

.020224 

2225 

2.373 

.000449438 

.021200 

2450 

2.155  .000408163 

.020203 

2230 

2.368 

.000448430 

.021176 

2455 

2.151 

.000407332 

.020182 

2235 

2.362 

.000447427 

.021152 

2460 

2.146 

.000406504 

.020162 

2240 

2.357 

.000446429 

.021129 

2465 

2.142 

.000405680 

.020141 

2245 

2.352 

.000445434 

.021105 

2470 

2.138 

.000404858 

.020121 

2250 

2.347 

.000444444 

.021082 

2475 

2.133 

.  000404040 

.020101 

2255 

2.341 

.000443459 

.021058 

2480 

2.129 

.000403226 

.020080 

2260 

2.336 

.000442478 

.021035 

2485 

2.125 

.000402414 

.020060 

190 


FLOW    OF    WATER    IN 


TABLE  33.— SLOPES. 


Slope 
1  in 

Fall  in 
feet  per 
mile. 

s 

vA" 

Slope 
1  in 

Fall  in 
feet  per 
mile. 

s 

V* 

2490 

2.120 

.000401606 

.  020040 

2715 

1.945 

.  000368324 

.019192 

2495 

2.116 

.000400802 

.  020020 

!  2720 

1.941 

.  000367647 

.019174 

2500 

2.112 

.  000400000 

.020000 

2725 

.938 

.000366972 

.019156 

2505 

2.108 

.000399202 

.019980 

2730 

.934 

.000366300 

.019139 

2510 

2.104 

.000398406 

.019960 

2735 

.931 

.000365631 

.019121 

2515 

2.099 

.000397614 

.019940 

2740 

.927 

.000364964 

.019104 

2520 

2.095 

.000396825 

.019920 

2745 

.923 

.000364299 

.019086 

2525 

2.091 

.  000396039 

.019901 

2750 

.920 

.000363636 

.019069 

2530 

2.087 

.000395257 

.019881 

2755 

.916 

.000362972 

.019052 

2535 

2.083 

.000394477 

.019861 

2760 

.913 

.000362319 

.019035 

2540 

2.079 

.000393701 

.019842 

!  2765 

.910 

.000361664 

.019017 

2545 

2.075 

.000392927 

.019822 

2770 

1.906 

.000361011 

.019000 

2550 

2.071 

.000392157 

.019803 

2775 

1.903 

.000360360 

.018983 

2555 

2.066 

.000391389 

.019784 

i  2780 

1.900 

.000359712 

.018966 

2560 

2.063 

.  000390625 

.019764 

2785 

1.896 

.000359066 

.018949 

2565 

2.058 

.000389864 

.019745 

1  2790 

1.892 

.  000358423 

.018932 

2570 

2.054 

.000389105 

.019726 

2795 

1.889 

.  000357782 

.018915 

2575 

2.050 

.000388349 

.019706 

2800 

.886 

.000357143 

.018898 

2580 

2.047 

.000387697 

.019687 

2805 

.882 

.000356506 

.018881 

2585 

2.042 

.000o86847 

.019668 

2810 

.879 

.000355871 

.018865 

2590 

2.039 

.000386100 

.019649 

2815 

.875 

.000355279 

.018848 

2595 

2.035 

.000385357 

.019630 

2820 

.872 

.000354610 

.018831 

2600 

2.031 

.000384615 

.019612 

2825 

.869 

.  000353982 

.018814 

2605 

2.027 

.000383877 

.019593 

2830 

.866 

.  000353357 

.018797 

2610 

2.023 

.000383142 

.019574 

2835 

.862 

.000352733 

.018781 

2615 

2.019 

.000382410 

.019555 

2840 

1.859 

.000352113 

.018764 

2620 

2.015 

.000381679 

.019536 

2845 

1.856 

.000351423 

.018746 

2025 

2.011 

.000380952 

.019518 

2850 

1.852 

.  000350877 

.018731 

2630 

2.008 

.000380228 

.  019499 

2855 

1.849 

.000350877 

.018715 

2635 

2.004 

.000379507 

.019481 

2860 

1.846 

.  000349650 

.018699 

2640 

2. 

.000378787 

.019462 

2865 

1.843 

.  000349040 

.018682 

2645 

1.996 

.000378072 

.019444 

2870 

.839 

.000348432 

.018666 

2650 

1.992 

.000377359 

.019426 

2875 

.836 

.000347827 

.018650 

2655 

1.989 

.000376648 

.019407 

2880 

.833 

.000347222 

.018634 

2660 

1.985 

.000375940 

.019389 

2885 

.830 

.000346662 

.018617 

2665 

1.981 

.000375235 

.019371 

2890 

.827 

.000346021 

.018602 

2670 

1.977 

.000374532 

.019353 

2895 

.824 

.  000345427 

.018585 

2675 

1.974 

.000373832 

.019334 

2900 

.820 

.  000344827 

.018569 

2680 

1.970 

.000373134 

.019316 

2905 

.817 

.000344234 

.018554 

2685 

1.966 

.000372437 

.019298 

2910 

.814 

.000343643 

018537 

2690 

1.963 

.000371747 

.019281 

2915 

.811 

.000343057 

.018521 

2695 

1.959 

.000371058 

.019263 

2920 

.808 

.  000342456 

.018506 

2700 

1.956 

.  000370370 

.019245 

2925 

.805 

.900341880 

018490 

2705 

1.952 

.  000369686 

.019228 

2930 

1.802 

.000341297 

.018474 

2710 

1.949 

.000369004 

.019209 

2935 

1.799 

.000340716 

018456 

OPEN    AND    CLOSED    CHANNELS. 


191 


TABLE  33.— SLOPES. 


Slope 
1  in 

Fall  in 
feet  per 
mile. 

s 

jr 

Slope 
1  in 

Fall  in 
feet  per 
mile. 

s 

V~ 

2940 

1.796 

.  000340136 

.018442 

3460 

1.526 

.000289017 

.017000 

2945 

1.793 

.  000339559 

.018427 

3480 

1.517 

.000287356 

.016951 

2950 

.790 

.000338983 

.018414 

3500 

1.509 

000285714 

.016903 

2955 

.787 

.000338409 

.018396 

3520 

1.500 

.000284091 

.016855 

2960 

.784 

.  000337838 

.018380 

3540 

1.491 

.000282486 

.016807 

2965 

.781 

.000337268 

.018264 

3560 

1.483 

.000280899 

.016760 

2970 

.778 

.000336700 

.018349 

35SO 

1.475 

.000279329 

.016713 

2975 

.775 

.000336134 

.018334 

3600 

1.467 

.000277778 

.016667 

2980 

.772 

.000335571 

.018319 

3620 

.459 

.000276243 

.016620 

2985 

.769 

.060335008 

.018303 

3640 

.450 

.000274725 

.016575 

2990 

.766 

.  000334482 

.018288 

3660 

.442 

.000273224 

.016530 

2995 

.763 

.  000333890 

.018272 

3680 

.435 

.000271739 

.016484 

3000 

.760 

.000333333 

.018257 

3700 

.427 

.000270270 

.016440 

3010 

.754 

.000332226 

.018227 

3720 

.420 

.000268817 

.016395 

3020 

.748 

.000331129 

.018197 

3740 

.412 

.000267380 

.016352 

3030 

.742 

.000330033 

.018667 

3760 

1.404 

.000265958 

.016308 

3040 

.737 

.  000328947 

.018137 

3780 

1  .  397 

.000264550 

.016265 

3050 

1.731 

.000327869 

.018107 

3800 

1.390 

.000263158 

.016222 

3060 

1.725 

.000326797 

.018077 

3820 

1.382 

.000261780 

.016180 

3070 

1.720 

.000325733 

.018048 

3840 

1.375 

.000260417 

.016138 

3080 

1.715 

.000324675 

.018019 

3860 

1.368 

.000259067 

.016095 

3090 

1.709 

.OOC323625 

.017989 

3880 

.361 

000257732 

.016054 

3100 

1.703 

.000322581 

017960 

3900 

.354 

.000256410 

.016013 

3110 

1.698 

.000321543 

.017932 

3920 

.347 

.000255102 

.015972 

3120 

1.692 

.000320513 

.017903 

3940 

.340 

.000253807 

.015931' 

3130 

1.687 

000319489 

.017874 

3960 

.333 

.000252525 

.015891 

3140 

1.682 

.000318471 

.017845 

3980 

1.327 

.000251256 

.015851 

3150 

1.676 

.000317460 

.017817 

4000 

1.320 

000250000 

015811 

3160 

1.671 

.000316456 

.017789 

4020 

1.313 

.000248756 

.015772 

3170 

1.666 

.000315457 

.017761 

4040 

1.307 

.000247525 

.015733 

3180 

1.660 

.000314465 

.017733 

4060 

1.300 

.000246306 

.015694 

3190 

1.655 

.000313480 

.017705 

4080 

.294 

.000245098 

.015655 

3200 

.650 

.  000312500 

.017677 

4100 

.288 

.000243903 

.015617 

3220 

.640 

000310559 

.017622 

4120 

.282 

.000242718 

.015580 

3240 

.629 

.000308641 

.017568 

4140 

.275 

.000241546 

.015542 

3260 

.620 

.000306748 

.017514 

4160 

.269 

.000240382 

.015505 

3280 

.610 

.000304878 

.017461 

4180 

.263 

.000239235 

.015467 

3300 

.600 

.000303030 

.017408 

4200 

1.257 

.  000238095 

.015430 

3320 

.590 

.000301205 

.017355 

4220 

1.251 

.000236967 

.015394 

3340 

.581 

.000299401 

.017303 

4240 

1.245 

.000235849 

.015358 

3360 

.571 

.000297619 

.017251 

4260 

1.239 

.  000234742 

.015322 

3380 

.562 

.000295858 

.017200 

4280 

1.234 

.000233645 

.  015286 

3400 

1.553 

.000294113 

.017150 

4300 

1.228 

.  000232558 

.015250 

3420 

1.544 

.  000292398 

.017100 

4320 

1.222 

.000231482 

.015215 

3440 

1.535 

.  000290688 

.017050 

4340 

1.217 

.000230415 

.015180 

192 


FLOW    OF    WATER    IN 


TABLE  33. — SLOPES. 


Slope 
1  in 

Fall  in 
feet  per 
mile. 

s 

\/s 

Slope 
1  in 

Fall  in 
feet  per 
mile. 

s 

V^ 

4360 

1.211 

.000229716 

.015145 

6000 

.880 

.000166667 

.012910 

4380 

.205 

.000228311 

.015110 

6080 

.868 

.000164474 

.012820 

4400 

.200 

.000227273 

.015076 

61CO 

.857 

.000162338 

.012741 

4420 

.194 

.000226244 

.015041 

6240 

.846 

.000160256 

.012659 

4440 

.189 

.000225225 

.015007 

6320 

.836 

.000158228 

.012579 

4460 

.184 

.000224215 

.014974 

6400 

.825 

.000156250 

.012500 

4480 

.179 

.000223214 

.014940 

6480 

.815 

.000154321 

.012422 

4500 

.173 

.000222222 

.014907 

6560 

.805 

.000152439 

.012347 

4520 

.J68 

.000221239 

.014874 

6640 

.795 

.000150602 

.012272 

4540 

.163 

.000220264 

.014841 

6720 

.786 

.000148810 

.012199 

4560 

.158 

.000219298 

.014808 

6800 

.777 

.000147059 

.012127 

4580 

.153 

.000218341 

.014776 

6880 

.767 

.000145349 

.012056 

4600 

.148 

.000217391 

.014744  1 

6960 

.759 

.000143678 

.011986 

4620 

.143 

.000216450 

.014712 

7000 

.754 

.000142857 

.011952 

4640 

.138 

.000215517 

.014681 

7040 

.750 

.000142045 

.011919 

46GO 

.133 

.000214592 

.014649 

7120 

.742 

.000140449 

.011851 

4680 

1.128 

.000213675 

.014617 

7200 

.733 

.000138889 

.011785 

4700 

1.124 

.000212766 

.014586 

7280 

.725 

.000137363 

.011720 

4720 

1.119 

.000211864 

.014557 

7360 

.718 

.000135869 

.011656 

4740 

1.114 

.000210970 

.014524 

7440 

.710 

.000134408 

.011594 

4760 

1.109 

.000210084 

.014492 

7500 

.704 

.000133333 

.011547 

4780 

1.104 

.  000209205 

.014464 

7520 

.702 

.000132979 

.011532 

4800 

1.100 

.000208333 

.014434 

7600 

.695 

.000131579 

.011471 

4820 

.096 

.  000207469 

.014404 

7680 

.687 

.000130208 

.011411 

4840 

.091 

.000206612 

.014374 

7760 

.680 

.000128866 

.011352 

4860 

.0^7 

.000205761 

.014344 

7840 

.673 

.000127551 

.011293 

4880 

.082 

.000204918 

.014315 

7920 

.667 

.000126263 

.011237 

4900 

.078 

.000204081 

.014285 

8000 

.660 

.000125000 

.011180 

4920 

.073 

.  000203252 

.014256 

8080 

.653 

.000123763 

.011125 

4940 

.069 

.  000202429 

.014227 

8160 

.647 

.000122549 

.011070 

4960 

.065 

.000201613 

.014199 

8240 

.64.1 

.000121359 

.011016 

4980 

.060 

.000200803 

.014170 

8320 

.635 

.000120192 

.010963 

5000 

.056 

.  000200000 

.014142 

8400 

.629 

.000119048 

.010911 

5040 

.048 

.000198570 

.014086 

8480 

.623 

.000117925 

.010860 

5120 

.031 

.000195313 

.013975 

8560 

.617 

.000116823 

.010809 

5200 

.015 

.000192308 

.013888 

8640 

.611 

.000115741 

.010759 

5280 

1. 

.000189394 

.013862 

8720 

.605 

.000114679 

.010709 

5360 

.985 

.000186567 

.013659 

8800 

.600 

.000113636 

.010660 

5440 

.971 

.000183824 

.013558 

8880 

.595 

.000112613 

.010612 

5520 

.957 

.000181160 

.013460 

8960 

.585 

.000111607 

.010565 

5600 

.943 

.000178572 

.013363 

9000 

.587 

.000111111 

.010541 

5680 

.930 

.000176056 

.013268 

9040 

.584 

.000110620 

.010518 

5760 

.917 

000173611 

.013176 

9120 

.579 

.000108649 

.010472 

5840 

.904 

.000171233 

.013085 

9200 

.574 

.000108696  ' 

.010427 

5920 

.892 

.000168919 

.012997 

9280 

.569 

.000107759 

.010380 

OPEN    AND    CLOSED    CHANNELS. 


193 


TABLE  33.— SLOPES. 


Q1     Fall  in 

^r-r 

s 

•vA 

Slope 
1  in 

Fall  in 
feet  per 
mile. 

s     \  Vs' 

9360   .564 

.000106838 

.010336 

12880 

.410  1.000077640 

.008811 

9440 

.559 

.000105932  1.010293 

12960 

.407  |.  00007  7  160 

.008784 

9520 

.555 

.000105042  1.  010249 

13000 

.406 

.  000076923 

.008771 

9600 

.550 

.000104167  ,010206 

13040 

.405 

.  000076687 

.008757 

9680 

.545 

.000103306 

.010164 

13120 

.402 

.000076220 

.008730 

9760 

.541 

000102459 

.010122 

13200 

.400 

.000075758 

.008704 

9840 

.537 

.000101626 

.010081 

13280 

.398 

.000075301 

.008678 

9920 

.532 

.000100807 

.010040 

13360 

.395 

.  000074850 

.008651 

10000 

.528 

.000100000 

.010000 

13440 

.393 

.000074405 

.008625 

10080 

.524 

.000099206 

.009960 

13520 

.390 

.000073965 

.008600 

10160 

.520 

.000098425 

.009921 

13600 

.388 

.000073530 

.008575 

10240 

.516 

.000097656 

.009882 

13680 

.386 

.000073100 

.008550 

10320 

.512 

.  000096924 

.  009844 

13750 

.384 

.  000072675 

.008525 

10400 

.508 

.000096154  .009806 

13840 

.382 

.000072254 

.008500 

10480 

.504 

.000095420  .009768 

13920 

.379 

.000071839 

.008476 

10560 

.500 

.000094697  .009731 

14000 

.377 

.000071429 

.008452 

10640 

.496 

.000093985  .009695 

14080 

.375 

.000071023 

.008428 

10720 

.492 

.000093284 

.  009658 

14160 

.373 

.000070622 

.008404 

10800 

.489 

.  000092593 

.009623 

14240 

.371 

.  000070225 

.008380 

10880 

.485 

.000091912 

.009587 

14320 

.369 

.  000069832 

.008357 

10960 

.482 

.000091241 

.009552 

14400 

.367 

.  000069445 

.008334 

11000 

.480 

.000090909 

.009534 

14480 

.365 

.000069061 

.008310 

11040 

.478 

.000090580 

.009518 

14560 

.363 

.  000068681 

.008288 

11120 

.475 

.000089928 

.009483 

14640 

.361 

.000068306 

.008265 

11200 

.471 

.000089286 

.  009449 

14720 

.359 

.000067935 

.008242 

11280 

.468 

.  000088653 

.009416 

14800 

.357 

.000067568 

.  008220 

11360 

.465 

.  000088028 

.  009382 

14880 

.355 

.  000067204 

.008198 

11440 

.462 

.000087412 

.009350 

14960 

.353 

.  000066848 

.008176 

11520 

.458 

.000086806 

.009317 

15000 

.352 

.  000066667 

.OOG165 

11600 

.455 

.000086207 

.  009285 

15040 

.351 

.000066490 

.008154 

11680 

.452   .000085617 

.009253 

15120 

.349 

.000066138 

.008133 

11760 

.449  j  .  000085034 

.009221 

15200 

.347 

.  000065790 

.008111 

11840 

.446   .000084459 

.009190 

15280 

.346 

.  000065445 

.008090 

11920 

.443 

.000083893 

.009160 

15360 

.344 

.000065104 

.008069 

12000 

.440 

.  000083333 

.009129 

15440 

.342  1.000064767 

.  008048 

12080 

.437   .000082782 

.009099  i 

15520 

.  340  .  000064433 

.008027 

12160 

.434 

.  000082237 

.009069  i 

15600 

.339  .000064103 

.008007 

12240 

.431 

.000081699 

.009039 

15680 

.337  1.000063776 

.007986 

12320 

.429 

.000081169 

.009010  i 

15760 

.335  .000063452 

.007966 

12400 

.426 

.000080645 

.008980 

15840 

.333  .000063131 

.007946 

12480 

.423 

.000080128 

.008951 

15920  1   .332  .000062814 

.007926 

12560 

.420 

.000079618 

.008923 

16000   .330  :.  000062500 

007906 

12640  I   .418 

.000079114 

.  008895  ' 

16080    .328  .000062189  .007886 

12720  j   .415 

.000078616  .008867   16160   .327  .000061881  .007867 

12800  !   .413 

.000078125  .008839  1  16240  j   .325  .000061577  1.007847 

13 


194 


FLOW    OF    WATER    IN 


TABLE  33.— SLOPES. 


Fall  in 

^  ftr 

s 

N/T 

1  Slope 
1  in 

Fall  in 
feet  per 
mile. 

s 

V* 

16320  i  .324   .000061275 

.007828 

18800 

.281 

.000053191 

.007293 

16400 

.  322   .  000060976 

.007809 

18880 

.280 

.000052966 

.007278 

16480 

.320 

.000060680 

.007790 

18960 

.279 

.000052742 

.  007262 

16560 

.319 

.000060387 

.007771 

19000 

.280 

.  000052632 

.007255 

16640 

.317 

.000060096 

.007753 

I  19040 

.277 

.000052521 

.007246 

16720 

.316 

.000059809 

.  007734 

1  19120 

.276 

.000052301 

.007232 

16800 

.314 

.  000059524 

.007715 

I  19200 

.275 

.  000052083 

.007217 

16880 

.313 

.  000059242 

.007697 

!  19280 

.274 

000051867 

.007202 

16960 

.311 

.000058962 

007679 

19360 

.273 

.000051653 

.007187 

17000 

.311 

.  000058824 

.007670 

j  19440 

.272 

.000051440 

.007172 

17040 

.310 

.000058686 

.007661 

19520 

.271 

.000051229 

.007157 

17120 

.308 

.000058411 

.  007643 

S  19600 

.269 

.000051020 

.007142 

17200 

.307 

.000058140 

.  007625 

!  19680 

268 

000050813 

.007128 

17280 

.306 

.000058146 

.  007608 

19760 

.267 

.  000050607 

.007114 

17360 

.304 

.  000057604 

.  007590 

19840 

.266 

.  000050403 

.007100 

17440 

.303  1.000057429 

.007573 

19920 

.265 

.000050201 

.007085 

17520 

.301  1.000057078 

.  007555 

!  20000 

.264 

.000050000 

.007071 

17600 

.300  j.  0000568  18 

.007538 

i  20080 

.263 

.000049800 

.007057 

17680 

.299   .000056561 

.007520 

20160 

.262 

.  000049603 

.  OC7043 

17760 

.297  i  .  000056306 

.  007504 

20240 

.261 

.  000049407 

.  007029 

17840 

.296 

.000056054 

.007487 

i  20320 

.260 

.000049212 

.007015 

17920 

.295  1.000055804 

.  007470 

20400 

.259 

.  000049020 

.007001 

18000 

.293  ;.  000055555 

.  007454 

\  20480 

.258 

.000048828 

.  006987 

18080 

.292   .000055310 

.  007437 

i  20560 

.257 

.000048638 

.006974 

18160 

.291   .000055066 

.007421 

20640 

.256 

.000048447 

.  006960 

18240 

.289   .000054825  .007404 

i  20720 

.255 

.000048263 

.006947 

18320 

.288   .000054585 

.007388 

20800 

.254 

.000048077 

.006934 

18400 

.287  i.  000054348 

.007372 

!  20880 

.253 

.  000047893 

.  006920 

18480 

.286   .000054112 

.007356 

20960 

.252 

.000047710 

.006907 

18560 

.285   .000053879  .007340 

!  21040 

.251  j.  000047529 

.006894 

18640 

.283 

.000053648  .007324 

21120 

250 

.000047348 

.00688) 

18720 

.282 

.000053419 

.007308 

OPEN    AND    CLOSED    CHANNELS.  195 

Article  14.     Formulae  for  Mean  Velocity  in  Pipes, 
Sewers,  Conduits,  etc. 

In  continuation  of  the  formulae  for  mean  velocity  in 
open  channels,  given  at  page  8,  the  following  collection 
of  formulae  is  given  for  finding  the  mean  velocity  in 
pipes,  sewers,  conduits,  etc.  As  already  stated,  it  is 
believed  that  such  a  collection  will  be  useful,  not  only 
for  reference,  but  also  for  comparison  with  the  most 
modern  and  accurate  formulae.  This  list  contains  al- 
most all  the  formula)  in  use  in  different  countries,  in 
modern  times,  and  it  is  the  most  complete  collection  of 
formulae,  relating  to  the  Flow  of  Water  in  Open  and 
Closed  Channels,  ever  before  gathered  together  in  a  sin- 
gle work. 

Some  of  the  formulae  for  open  channels,  already  given, 
have  also  been  used  for  pipes,  sewers,  conduits,  etc. 
These  will  not  be  reproduced  here.  They  will,  how- 
ever, be  denoted  by  the  numbers  already  given  to  them. 
The  same  symbols  are  used  here  as  already  given  at 
page  6.  We  have  also,  in  addition: — 

d  =  diameter  of  pipe  in  feet,  if  not  otherwise  stated. 

The  formulae  already  used  for  open  channels,  and 
which  have  also  been  used  for  pipes,  sewers  conduits, 
etc.,  are: — 

D'Aubisson's,  Taylor's,  Downing's,  Beardmore's,  Les- 
lie's, Pole's,  formula  (1);  D'Aubisson's  (5);  Beardmore's 
(7);  Eytelwein's  (8);  Neville's  (12);  Dwyer's  (13); 
Young's  (16);  Dubuat's  (17);  De  Prony's  (21);  St.  Ve- 
nant's  (23);  Provis's  (25);  Fanning's  (28);  Kutter's 
(40). 

The  following  formulae  are  also  applicable  to  pipes, 
sewers  and  conduits: — 


196  FLOW    OF    WATER    IN 

D'Arcy's  formula  for  clean  iron  pipes  under  pressure 
is:  — 

(  rs  Y 

v  =  --)  M61)7726  +  ..OOOOOT62  >    .............  (51) 

(  r          ) 

Flynn's  modification  of  D'Arcy's  formula  is:  — 
155256 


D'Arcy's  formula  as  given  by  J.  B.  Francis,  C.  E., 
for  old  cast-iron  pipe,  lined  with  deposit,  and  under  pres- 
sure is:  — 

144 

(53) 


Flynn's  modification  of  D'Arcy's  formula  for  old  cast- 
iron  pipe  is:  — 

70243.  9 


Molesworth's  modification    of   Kutter's    formula   (40) 
with  n  =  .013  is:  — 

181  + 


»=  026,  00281  \  X  ^V8 (55) 

1+v/Tv41'6+^~) 

Flynii's    modification    of    Kutter's    formula    is    (see 
Article   20,  in  which  are  given  values  of  K  and  \/r  ): — 


=      1  +  (44.41  X  - 

\  | 

Lampe's  formula  is: — 


X  \/TS (56) 


(57) 


OPEN    AND    CLOSED     CHANNELS.  197 

Weisbach's  formula  is: — 

i 

(58) 

.016921 


:   j  1.505  +CX--J 


where  c  =  .01439  + 

vz 

Prony's  formula  is: — 

v  =  97  v/^  —.08  nearly (59) 

Eytelwein's  formula  is: — 

v=  108  v/r«  —  -13  nearly (60) 

Another  formula  of  Eytelwein  is: — 

)* (6D 


D'Aubisson's  formula  is:  — 

v=  98i/rs—  .1  ...........................  (62) 

Hawksley's  formula  is:  — 

o  =  48.05(    ^*      \*  ....................  (63) 

V  *  +  64  a  / 

Poncelet's  formula  is:  — 

....................  (64) 


Blackwell's  formula  is:  — 

v  =  47.913  (^_V  .......................  (65) 

Neville's  formula  is:  — 

(h  r  \i  /r*n\ 

_  i     ................  (66) 
.0234/-H--  0001085  l) 

Hughes'  modification  of  Eytelwein's  formula  (61)  is:  — 


-_ 

2.112 


198  FLOW    OP    WATER    IN 

BlackwelFs  modification  of  Eytelwein's  formula  (61) 


Kirkwood's  formula  for  tuberculated  pipes  is:  — 

v  =  80  v/rs  ................................  (69 

Article  15.     Remarks  on  the  Formulae. 

For  the  purpose  of  comparison,  the  formula  of 
D'Arcy  and  Lampe,  for  the  diameters  given  in  Table  34, 
have  been  changed  into  the  form:  — 


and  the  values  of  c  are  given  in  Table  34. 

For  the  same  purpose  of  comparison  the  formulae  of 
Kutter  (40),  is  given  in  the  same  table.  Kirkwood's 
formula  (69),  also  given,  is  modern,  but  it  has  a,  constant 
co-efficient.  Also  three  of  the  old  formulae  are  given, 
namely,  BlackwelPs  (65),  Pronv's  (59),  and  Downing's 

(i). 

Almost  all  the  old  formulae  have  constant  co-efficients. 
It  was  well  known  to  many  engineers,  that  these  co- 
efficients gave  too  high  a  velocity  for  small  channels, 
and  too  low  a  velocity  for  large  channels.  To  remedy 
this,  Leslie  (see  page  8),  gave  a  co-efficient  of  100, 
formula  (1),  for  large  and  rapid  rivers,  and  a  co-efficient 
of  68,  formula  (2),  for  small  streams.  In  the  same  way 
Stevenson  gave  a  co-efficient  of  96,  formula  (3),  for 
streams  discharging  over  2,000  cubic  feet  per  minute, 
and  69,  formula  (4),  for  streams  discharging  under 
2,000  cubic  feet  per  minute.  There  was  no  easy  curve 
from  one  co-efficient  to  another.  It  was  a  sudden  in- 
crease. It  is  evident  that  this  cannot  be  correct.  An 
inspection  of  the  old  formulas  will  show  that  their  co- 


OPEN    AND    CLOSED    CHANNELS.  199 

efficients  were  constant,  arid,  according  to  the  different 
authorities,  varied  from  92.3  to  100. 

The  modern  and  more  accurate  formulae  have  varying 
co-efficients,  whose  value  increases  with  the  me^ease  of 
the  hydraulic  mean  depth,  r. 

The  value  of  the  co-efficient  in  D'Arcy's  formula  (51), 
depends  on  the  hydraulic  mean  depth,  r,  and  is  not 
affected  by  the  slope;  and  it  is  the  same  with  Lampe's 
formula  (57). 

In  Kutter's  formula  (40),  the  co-efficient  depends  not 
only  on  the  hydraulic  mean  depth,  r,  but  also,  to  a  less 
extent,  on  the  slope,  s. 

The  co-efficients  of  the  modern  formulae  increase  very 
much  from  the  small  diameters  to  the  large  ones,  where- 
as, the  old  formulae  have  the  same  co-efficients  for  all 
diameters,  being  too  high  for  diameters  under  one  foot, 
and  too  low  for  diameters  exceeding  one  foot.  For 
diameters  larger  than  6  feet  there  is  very  little  change 
in  D'Arcy's  co-efficient,  and  for  very  large  pipes  it  does 
not  exceed  113.8. 

For  diameters  greater  that  10  feet  D'Arcy's  co-efficient 
is  almost  constant.  It  increases  very  little  more  than 
113.5,  even  for  a  diameter  of  16  feet  or  more,  but  Kut- 
ter's co-efficient  continues  to  increase  until  such  a 
diameter  is  reached  as  is  never  likely  to  be  required  in 
practice. 

Now,  the  experiments  on  which  D'Arcy's  formula  is 
based  were  made  011  clean  pipes,  of  the  diameters  us- 
ually adopted  in  practice,  flowing  under  pressure,  and 
under  conditions  somewhat  similar  to  pipes  in  actual 
use,  and,  therefore,  as  the  experiments  were  conducted 
with  great  accuracy,  the  results  are  entitled  to  the  con- 
fidence of  engineers.  D'Arcy's  experiments  did  not, 
however,  include  pipes  of  a  very  large  hydraulic  mean 
radius.  In  one  respect  he  differs  from  most  of  the  mod- 


200  FLOW    OF    WATER    IN 

ern  authorities,  inasmuch  as  the  slope  has  110  effect  011 
the  value  of  the  co-efficient  of  his  formula. 

Kutter;s  formula  is  derived,  not  only  from  experi- 
ments made  on  channels  with  small  hydraulic  radius, 
but  also  on  channels  with  large  hydraulic  radius,  and 
his  co-efficients  for  very  large  pipes  are,  therefore,  more 
likely  to  agree  with  the  actual  discharge  than  D'Arcy's 
constant  co-efficient  of  113.5  for  very  large  pipes.  But 
again,  Kutter's  formula  is  open  to  the  objection  that  it 
is  based  011  experiments  made  on  open  channels.  I  may 
here  remark,  although  it  is  only  remotely  connected 
with  pipe  discharge,  that  Major  Allan  Cunningham 
states,  as  the  result  of  his  extensive  experiments  for  four 
years  on  the  Ganges  Canal,  that  Kutter's  formula  alone, 
of  all  those  tried  by  him,  was  found  generally  applica- 
ble to  all  conditions  of  discharge,  and  that  it  gave 
nearer  results  to  the  actual  velocity  than  any  of  the 
other  formula)  tried  by  him.  It  gave  results  with  a  dif- 
ference from  the  actual  velocity  seldom  exceeding  5  per 
cent.,  and  usually  much  less  than  that.  When  we  con- 
trast the  wide  divergence  of  the  old  formulae  under 
varying  flow  from  the  actual  velocity,  with  the  results 
obtained  by  Kutter's  formula,  it  will  be  seen  that  the 
latter  is  the  most  accurate  formula  for  channels  with 
large  hydraulic  mean  radius. 

With  reference  to  D'Arcy's  co-efficients  not  being  af- 
fected by  the  slope,  Neville  states: — 

"  As  long  as  the  diameter  of  a  long  pipe  continues 
constant,  the  velocity  (by  D'Arcy's  formula)  is  always 

represented  by  a  given  fixed  multiple  of  }/rs,  110  mat- 
ter how  small  or  great  the  declivity  of  the  pipe  may  be. 
For  an  inch  pipe  this  multiplier  for  feet  measures  is 
80.3.  ****** 

"  In  the  excerpt  proceedings  of  the  Institution  of  Civil 
Engineers,  p.  4,  6th  Feb.,  1855,  James  Simpson,  Presi- 


OPEN    AND    CLOSED    CHANNELS.  201 

dent,  in  the  chair,  there  is  given  for  the  "  Colinton 
pipe  "  16  inches  diameter,  eight  or  nine  years  in  use, 
three  observations. 

First,  29,580  feet  long,  a  head  of  420  feet,  an^ardis- 
charge  of  571  cubic  feet  per  minute.  These  give  v  = 

6.816  feet  =  99.2  i/rJTnearly.  Secondly,  a  length  of 
25,765  feet,  a  head  of  184  feet,  and  a  discharge  of  440 
cubic  feet  per  minute;  these  give  v  --=  5.252  feet  =  96.3 
\/rs.  And  thirdly,  a  length  of  3.815  feet,  a  head  of  184 
feet,  and  a  discharge  of  1.215  cubic  feet  per  minute; 
these  give  v  ==  14.5  feet  =  115  \/rs  nearly.  In  these 
three  examples  the  diameter,  castings  and  age  of  the 
pipes,  are  the  same.  Yet  it  is  seen,  clearly,  that  the  in- 
clination affects  the  multiplier  of  \/rs  which  increases 
with  the  inclination,  s,  although  M.  D'Arcy's  formula 
would  make  the  multiplier  the  same  in  each  case,  and 
for  all  inclinations,  viz.:  v  =  110  \/r8." 

In  the  formulae  of  Lampe  and  Kutter  the  co-efficients 
have  a  steady  increase  with  the  increase  of  the  diameter'. 

K utter' s  formula  has  the  great  advantage  of  being 
easily  adapted  to  a  change  in  the  surface  of  the  pipe 
exposed  to  the  flow  of  water,  by  a  change  in  the  value  of 
n.  It  will  be  seen  that  the  co-efficients  of  Lampe  agree 
somewhat  with  Kutter  with  n  =  .011.  Now,  very  few 
engineers,  even  with  the  smoothest  pipe,  use  Kutter 
with  n  =  .011.  It  is  more  usual  to  use  n  =  .013,  to 
provide  for  the  future  deterioration  of  the  surface  ex- 
posed to  the  flow  of  water. 

The  48-inch  Glasgow  water  pipes  mentioned  at  page 
218  gave  at  first  a  discharge  more  than  that  given  by  the 
old  formula),  but  it  gradually  diminished,  though  the 
pipes  still  continued  to  discharge  more  than  the  quan- 
tity given  by  the  old  formulae. 

An    inspection    of    Table    34   will    show    that    for   all 


202  FLOW    OF    WATER    IN 

diameters  greater  than  1  foot  6  inches,  Lampe's  co- 
efficients are  very  much  greater  than  D'Arcy's,  for  clean 
pipes,  and  than  Kutter  with  n  =  .013.  It  is,  therefore, 
evident  that,  for  old  pipe,  Lampe's  formula  gives  too 
high  a  discharge. 

The  48-inch  pipe  given  as  an  example  at  page  234 
has,  by  D'Arcy's  formula  for  clean  pipes  (52),  a  co-effi- 
cient =  112.6,  and  in  Table  34  we  find  that  for  this 
pipe,  Kutter,  with  n  =  .013,  has  a  co-efficient  of  116.5. 
As  the  pipe  gradually  deteriorated  D'Arcy's  co-efficient 
112.6,  represented  the  maximum  flow.  For  this  pipe 
Lampe  gives  a  co-efficient  =  139.0,  being  sixteen  per 
cent,  in  excess  of  the  maximum  co-efficient  found  by 
experiment. 

Comparing  D'Arcy's  and  Kirkwood's  formulae  for 
tuberculated  pipe,  the  co-efficients  of  the  latter  are  the 
greater  for  all  the  diameters  given.  As  in  the  case  of 
clean  pipe,  D'Arcy's  co-efficient  for  tuberculated  pipe 
increases  very  little  for  the  large  diameters. 


OPEN    AND    CLOSED    CHANNELS. 


203 


TABLE  34.     Giving  the  value  of  c  iu  the  formula  v  =  c^/rs  in  ten  dif- 
ferent formulas: 


VALUE  OF  CO-EFFICIENT  c. 


s 

y 

H 

.    W 

.    W 

.    W 

_  w 

S 

b       Tuberculated 

p" 

1 

fjf 

5! 

II 

8| 

8-| 

II 

3 

0     - 

1 

fa, 

-—    05 

!» 

o  " 

H    -o 

Hf       ^ 

o"* 

<-s 

1 

cc" 

CfQ 

Sgf 

g-g; 

3' 

B  p 

II 

§  ii 

g 

I  II 

jf 

t-j 

B 

GO 
l-h 

•     o 

'So 

»*« 

0 

STb 

^2 

^b 

H^» 

O 

d 

| 

00* 

^& 

'tr  2. 

,®S 

0* 

M 

4*-  •-"'"' 
•7-  co 

"gjo 

|£ 

O5 

Hj 

1 

1 

1 

VI 

s 

ft.  in. 

i      0 

•    p 

| 

•      il 

:    II 

:    II 

:   p1 

? 

p" 

:   ? 

1 

80.3 

65.1      47.l! 

95.8 

97. 

100. 

54.1 

80. 

2 

92.9 

74.8 

61.5 

95.8 

97. 

100. 

62.5 

80. 

4 

101.7 

85.4 

77.4: 

95.8 

97. 

100. 

68.  4 

80. 

6 

105.3 

92.8 

87.4:     77.5 

69.5 

95.8 

97. 

100. 

70.8 

80. 

1 

109.3 

106.2 

105.  7!     94.6 

85.3 

95.8 

97. 

100. 

73.5 

80. 

1  6 

110.7 

115. 

116.1!  104.3 

94.4 

95.8 

97. 

100. 

74.5 

80. 

2 

111  5 

128.5 

123.6 

111.3 

101.1 

95.8 

97. 

100. 

74.9 

80. 

3 

112.2 

133.2 

133.6 

120.8 

110.1 

95.8 

97. 

100. 

75.5 

80. 

4 

112.6 

139. 

140.4 

127.4 

116.5 

95.8 

97. 

100. 

75.7 

80. 

5 

112.8 

145.2 

145.4 

132.3 

121  .  1    95  8 

97. 

100. 

75.9 

80. 

6 

113. 

150.4 

149.4 

136.1 

124.8    95.8 

97. 

100. 

76. 

80. 

7 

113.1 

155. 

152.7 

139.2 

127.9 

95.8 

97. 

100. 

76.1 

80. 

8 

113.2 

159.1 

155.4 

141.9 

130.4 

95.8 

97. 

100 

76.1 

80. 

9 

113.2 

162.7 

157.7 

144.1 

132.7    95.8 

97. 

100. 

76.2 

80. 

10 

113.3 

166.1 

159.7 

146. 

134.5    95.8 

97. 

100. 

76.2 

80. 

11 

113.3 

169.2 

161.5 

147.8 

136.  2i  95.8 

97. 

100. 

76.2 

80. 

12 

113.3 

172.1 

163. 

149  3 

137.7    95.8 

97. 

100. 

76.2 

80. 

14 

113.4 

177.3 

165.8 

152 

140.4 

95.8 

97. 

100. 

76.3 

80. 

16 

113.4    182.9 

168. 

154  2 

142.1 

95.8 

97. 

100.      76.3 

80. 

18 

113.5    186.1 

169.9    156.1 

144.4 

95.8 

97. 

100.      76.3 

80. 

20 

113.5;   190. 

171  61  157.7 

146. 

95.8 

97. 

100. 

76.4 

80. 

i             i 

204 


FLOW    OP    WATER    IN 


Article  16.     Values  of  c  and  c  \/r  for  Circular  Channels 
Flowing  Full.     Slopes  Greater  than  i  in  2640. 

According  to  Kutter's  formula,  the  value  of  c,  the 
co-efficient  of  discharge,  is  the  same  for  all  slopes  greater 
than  1  in  1000,  that  is,  within  these  limits,  c  is  constant. 
We  further  find  that  up  to  a  slope  of  1  in  2640  the  value 
of  c  is,  for  all  practical  purposes,  constant,  and  even  up 
to  a  slope  of  1  in  5000  the  difference  in  the  value  of  c  is 
very  little.  This  is  well  exemplified  in  Table  35,  which 
is  compiled  from  Table  19. 

TABLE  35.     Giving  the  value  of  c  for  different  values  of  \/r  and  s  in 
Kutter's  formula,  with  n  =  .013 


SLOPES. 

1  iu  1000 

1  in  2500     1  in  3333.  3 

1  in  5000 

c 

c           c 

c 

.6 

93.6 

91.5         90.4 

8S.  4 

1. 

116.5 

115.2        113.2 

113.  C 

2. 

142.6 

142.8        141.1 

141.2 

An  inspection  of  the  values  of  c  in  Tables  15  to  27,  will 
show  the  slight  difference  in  the  value  of  c  up  to  a  slope 
of  1  in  5000. 

In  Kutter's  formula  the  value  of  c  is  found  from  an 
equation  involving  the  values  of  r,  n  and  s}  so  that  any 
change  in  the  value  of  s  would  cause  a  change  in  the 
value  of  c,  but  as  the  influence  of  s  on  the  value  of  c,  as 
shown  above,  is  not  very  marked  in  such  slopes  as  are 
usually  adopted  for  pipes,  sewers  and  conduits,  the 
value  of  the  co-efficient  c  has  been  computed  for  one 
slope,  that  is  1  in  1000,  or  s  =  .001.  The  value  of  the 


OPEN    AND    CLOSED    CHANNELS.  205 

co-efficient  for  all  channels,  open  and  closed,  is  practically 
constant  for  all  values  of  s  with  a  steeper  slope  than  1  in 
1000.  For  natter  slopes  than  1  in  1000,  up  to  even  2 
feet  per  mile,  or  1  in  2640,  the  tables  give  results  show- 
ing a  maximum  error  in  the  case  of  a  sewer  2  feet  in 
diameter,  and  n  —  .015,  of  less  than  two  per  cent.,  and 
in  the  case  of  a  sewer  8  feet  in  diameter,  less  than  one- 
half  per  cent.;  therefore,  for  all  practical  purposes,  the 
tables  are  sufficiently  accurate. 

Article  17.      Construction  of  Tables  for  Circular  Chan- 
nels. 

The  plan  on  which  these  tables  are  constructed  will  be 
briefly  stated  here,  and  their  use  will  be  fully  explained 
in  Article  26,  page  231. 

The  author  has  computed  the  value  of  c  for  different 
sizes  of  channels  and  different  values  of  n,  from  his  sim- 
plified form  of  Kutter's  formula  (73).  By  this  means 
the  complicated  form  of  Kutter's  formula  (40)  is  re- 
duced to  the  Chezy  form  of  formula: — 

v  =  c  \/r    X  v/8 

In  a  similar  way,  the  author  has  reduced  the  compli- 
cated formulae  of  D'Arcy  (51)  and  (53),  to  forms  better 
adapted  to  computations,  formulae  (52)  and  (54) — and 
by  the  latter  formulae,  the  values  of  c  have  been  com- 
puted. The  values  of  r  and  a  being  given,  and  the 

values  of  c  computed,  the  values  of  the  factors  c  yr  and 

ac\/r  are  computed  and  tabulated  from  Table  48  to 
Table  69,  inclusive.  These  tables  are  all  that  is  neces- 
sary for  the  rapid  solution  of  all  problems  relating  to 
pipes,  sewers  and  conduits,  by  the  formulae  of  Kutter 

and  D'Arcy.     The  author  was  the  first  to  use  the  v/s  as 


20G  FLOW    OF    WATER    IN 

a  separate  factor ,  and  its  use  has  simplified  the  application 
of  the  other  factors  very  much.     We  have: — 

v  —  c  \/r   X  v/6'  and,  therefore, 
Q  =  ac-\/r    X    i/s 

By  selecting  the  proper  factors  and  using  the  required 
formula  (41)  to  formula  (50),  any  problem  relating  to 
pipes,  sewers  and  conduits,  can  be  solved  rapidly. 

Article  18.     The  Tables  as  a  Labor  Saving  Machine. 

In  order  to  show  the  utility  of  these  tables  as  a  labor 
saving  machine,  and  also  their  correctness,  an  instance 
is  given  of  the  computation  of  discharge  from  sewers. 

A  few  years  since  a  report  was  published  on  the  sew- 
erage of  Washington,  D.  C.,  by  Captain  F.  V.  Greene, 
U.  S.  Engineers.  In  this  report  a  table  is  given  show- 
ing the  discharge  of  circular  and  egg-shaped  sewers 
with  n  =  .013,  computed  by  Kutter's  formula.  Table 
36  given  below  shows  about  half  of  the  table  given  in 
Captain  Greene's  report,  and  in  parallel  columns  is  also 
given  the  discharge  as  computed  by  the  tables  in  this 
work.  The  discrepancies  are  caused  by  Captain  Greene 
having  used  41.66  instead  of  41.6  on  the  right  hand 
side  of  formula  (40).  It  will  be  seen  that  the  results  by 
the  tables  in  this  book  are  practically  the  same  as  those 
obtained  by  the  use  of  Kutter's  formula  (40).  It  is  not 
an  exaggeration  to  assert,  that  in  the  computation  of 
similar  tables  to  these  in  Captain  Greene's  report,  as 
much  work  could  be  done  in  one  hour  by  the  use  of  the 
tables  in  this  book  as  could  be  done  in  twelve  or  more 
hours  by  the  use  of  Kutter's  formula  (40). 


OPEN    AND    CLOSED     CHANNELS. 


207 


TABLE  36.     Giving  discharge  in  cubic  feet  per  second  of  circular  and 
jgg-shaped  sewers,  based  on  Kutter's  formula,  with  n  =  .013. 


DISCHARGE  ix  CUBIC  FEET  PER  SECOND  

Dimensions 
of 

Slope  1  in  100 

Slope  1  in  200 

Slope  1  in  300 

- 

By  Kut- 
ter's form- 
ula. 

By  Flynn's 
Tables. 

By  Kut- 
ter's 
formula 

By 

Flynn  s 
Tables. 

By  Kut- 
ter's 
formula 

By 

Flynn's 
Tables. 

1'  0"  circular. 

3.39 

3.35 

2.40 

2.37 

1  96 

1.93 

V  3" 

6.25 

6.19 

4  42 

4.37 

3.61 

3.57 

1'  6" 

10.35 

10.21 

7.32 

7.22 

5.97 

5.9 

r  9" 

15.78 

15.57 

11.16 

11.01 

9.10 

8.99 

2/    0" 

22.68 

22.46 

16.04 

15.88 

13.08 

12.97 

10'  0" 

1673.7 

1670.9 

1183.3 

1181.5 

965.7 

964.7 

20'  0" 

10240. 

10256  . 

7240. 

7252. 

5909. 

5921. 

EGG-SHAPED. 

2/0"x3/  0"... 

36.69 

36.49 

25.94 

25.8 

21.17 

21.06 

2'  6"  x  3'  9".  .  . 

65  85 

66.8 

46.56 

47.23 

39.99 

38.57 

3'  0"  x  4'  6".  .  . 

109.84 

109.2 

77.66 

77.21 

63.38 

63.04 

3'  6"  x  5'  3".  .  . 

167.3 

165.4 

118.3 

117. 

96.5 

95.5 

4'  0"  x  6'  0"  ... 

240. 

236.6 

169.7 

167.4 

138.5 

136.8 

4'6"x6'  9"... 

325. 

324. 

229.8 

229.1 

187.5 

187.1 

5'0"x7/  6"... 

429.2 

429.1 

303.5 

303.4 

247.7 

247.7 

In  Table  37,  with  n  =  .011,  the  same  accordance  is 
shown  by  the  use  of  Kutter's  formula  (40)  and  Flynn's 
tables. 

TABLE  37,     Giving  the  velocity  in  feet  per  second  in  pipes,  sewers,  con- 
duits, by  Kutter's  formula,  with  n  =  .011. 


Diame- 
ter in 
feet 

Slope 
1   in 

Velocity 
by  Kut- 
ter's 
formula 
(40) 

Velocity 

by 

Flynn's 
Tables 

Diame- 
;    ter  in 
feet 

Slope 
1  in 

Velocity 
by  Kut- 
ter's 
formula 
(40) 

Velocity 

by 

Flynn's 
Tables. 

1 

66 

5.34 

5.25 

4 

66 

'    14.44 

14.34 

1 

2640 

.81 

.83 

4 

2640 

2.24 

2.27 

2 

66 

8.91 

8.8 

6 

66 

18.91 

18.82 

2 

2040 

1.36 

1.39 

6 

2640 

2.94 

2.98 

208  FLOW    OF    WATER    IN 

It  will  be  seen  that  the  results  as  given  by  the  rapid 
method  of  the  tables  may,  for  all  practicable  purposes, 
be  taken  as  identical  to  those  given  by  the  use  of  the 
troublesome  and  tedious  formula  (40). 

Should  the  engineer,  however,  prefer  to  use  the  for- 
mula (40),  even  then  the  tables  will  give  a  ready  means 
of  checking  the  computations. 

Article  19.     Discussion  on  Kutter 's  Formula. 

The  following  notes  by  the  Author  on  Kutter's  formula 
(40),  with  reference  to  Molesworth's  Kutter,  were  pub- 
lished in  the  Transactions  of  the  Technical  Society  of 
the  Pacific  Coast  of  January,  188G.  They  are  inserted 
here  as  they  contain  some  useful  information  on  Kut- 
ter's  formula  (40). 

In  that  admirable  and  useful  work,  "Moles worth's 
Pocket  Book  of  Engineering  Formulae,"  (21st  edition), 
a  modified  form  of  Kutter's  formula  for  pipe  discharge 
is  given,  in  which  the  value  of 

.00281 
18.1  -f  - 

.(70) 


c  z  /  .00281 

1  +  .026(41.6  +  -^— 

For  facility  of  reference  I  will  call  this  formula  Moles- 
worth's  Kutter  (70). 

No  mention  is  made  by  Molesworth  of  the  value  of  n, 
that  is,  as  to  whether  the  formula  is  intended  to  apply  to 
pipes  having  a  rough  or  a  smooth  inner  surface.  An  in- 
vestigation will,  however,  show  that  his  formula  is 
accurately  applicable  to  only  one  diameter,  that  is,  to  a 
diameter  of  one  foot  and  with  the  value  of  -M— .013. 

The  value  of  the  term  — ^  in   formula   (40),  is    given 

Vr 


OPEN    AND    CLOSED     CHANNELS.  209 

by  Molesworth  in.  formula  (70),  as  a  constant  quantity, 
and  =.026,  whereas,  in  fact,  it  is  a  variable  quantity, 
its  value — -with  the  same  value  of  n — changing  with 
every  change  in  the  hydraulic  mean  radius  or^ diameter 
of  pipe. 

Now,  assuming  the  value  of  n  taken  by  Molesworth  to 
be  =.013  and  substituting  this  value  for  n  in  Kutter's 
formula  (40),  we  have: — 

1.811       00281 

c  =  — 


181  + 


/ 

.00281 


but  by  Molesworth's  Kutter  (70) 


\/r 


?'=.25,    and    as    the    hydraulic 
mean  depth  of  a  pipe  is  one-fourth  of  the  diameter, 

If  we  substitute  in  formula  (71)  for  \/r  its  value  0.5, 
we  have: — 

181  +  _;.°.0281 

s 

°    1  +  .026(41 .6+^i1)  . 

which  is  Molesworth's  Kutter  (70). 

It  is  therefore  apparent  that,  no  matter  what  the  value 
of  n  may   be,  Molesworth's  Kutter  (70),  does  not  give 
14 


210  FLOW    OF    WATER    IN 

the  same  results  as  Kutter's  formula  (40),  as  it  gives  a 
constant  co-efficient  of  velocity,  c,  for  all  diameters  hav- 
ing the  same  slope  and  the  same  value  of  n. 

Kutter's  formula  (40),  has  certain  peculiarities  which 
are  wanting  in  Molesworth's  Kutter,  and  an  investiga- 
tion will  show  that  Molesworth's  Kutter  differs  materially 
from  Kutter's  formula  (40),  and  that  its  application,  ex- 
cept to  one  diameter,  is  sure  to  lead  to  serious  error.  I 
will  briefly  explain: 

1.  By  Kutter's  formula  (40),  the  value  of  c,  or  the 
velocity,  changes  with  every  change  in  the  value  of  r,  s, 
or  n,  and  with  the  same  slope  and  the  same  value  of  n, 
the  value  of  c  increases  with  the  increase  of  r,  that  is, 
with  the  increase  in  diameter.  It  is  on  this  variability 
of  its  co-efficient  to  suit  the  different  changes  of  slope, 
diameter  and  lining  of  channel,  that  the  accuracy  of 
Kutter's  formula  depends.  By  Molesworth's  Kutter  a 
change  in  the  diameter,  other  things  remaining  the 
same,  does  not  affect  the  value  of  c.  With  the  same 
slope  the  value  of  c  is  constant  for  all  diameters. 

As  an  instance,  with  a  slope  of  1  in  1000: — 


FORMULAE. 

6  inches  diameter. 

20  feet  diameter. 

c  = 

By  Kutter's  formula  (40)  
Molesworth's  Kutter  (70)  

69.5 
85.3 

146. 
85  3 

It  will  thus  be  seen  that  the  value  of  c  by  Kutter's 
formula  (40),  when  s  =  .001,  has  a  large  range,  from 
69.5  to  146.0,  showing  an  increase  of  111  per  cent,  from 
a  diameter  of  6  inches  to  a  diameter  of  20  feet. 

It  will  be  further  found  that  Molesworth's  formula 
gives  the  value  of  c,  and  therefore  the  value  of  the 
velocity  and  discharge,  too  high  for  diameters  less  than 


OPEN    AND    CLOSED    CHANNELS. 


211 


one  foot,  and  too  low  for  diameters  above  one  foot,  and 
the  more  the  diameter  differs  from  one  foot  the  greater 
is  the  error.  In  these  respects  it  follows  the  errors  of 
the  old  formulae. 

2.  According  to  Kutter's  formula  (40)  the  value  of  c 
increases  with  the  increase  of  slope  for  all  diameters 
whose  hydraulic  mean  depth  is  less  than  3.281  feet — 
one  metre — and  with  a  hydraulic  mean  depth  greater 
than  3.281  feet,  an  increase  of  slope  gives  a  diminution 
in  the  value  of  c. 

The  small  table,  herewith  given,  shows  this: — 

TABLE  38.     Giving  the  co-efficients  of  discharge,  c,  in  circular  pipes  of 
different  diameters  and  different  grades  with  n  =  .013. 


FORMULA. 

12  feet 

diameter. 

20  feet  diameter. 

1  in  1000 

.       1  in  40. 

i 

1  in  1000. 

Iin40. 

Molesworth's  Kutter  c  =..  . 
Kutter's  formula  c  —  . 

85.3 
137.7 

86.9 
137.9 

85.3 
146. 

86.9. 
145.7 

It  will  thus  be  seen  that  by  Kutter's  formula  (40), 
when  r  ~  3  feet,  that  is,  less  than  3.281  feet,  an  increase 
in  the  slope  from  1  to  1000  to  1  in  40,  causes  a  slight 
increase  in  the  co-efficient,  but  when  r  is  5  feet,  that  is, 
more  than  3.281  feet,  the  same  increase  in  the  slope 
causes  a  slight  diminution  in  the  value  of  c. 

By  Molesworth's  Kutter  formula  (70),  when  r  =  3 
feet,  an  increase  in  the  slope  from  1  in  1000  to  1  in  40 
causes  a  greater  proportional  increase  in  the  co-efficient 
than  Kutter  gives,  and  when  r  =  5  feet  the  value  of  the 
co-efficient  does  not  diminish  with  the  increase  of  slope, 
but,  011  the  contrary,  it  increases  with  the  increase  in 
slope,  and  its  value  is  the  same  as  when  r  =  3  feet. 


212  FLOW    OF    WATER    IN 

3.      By    Kutter's   formula  (40),   when    the    hydraulic 
mean  depth  is  equal  to  3.281  feet,  one  metre,  the  value 

1  811 

of  c  is  constant  for  all  slopes,  and  is   =  — ,  which  in 

n 

-j    o-i  i 

this  case  =  1'011  =  139.31 . 
.013 


Let  r  -=3.281  feet,  and,   therefore,   i/r  =  v/3.281  = 
1.811,  substitute  this  value  in  Kutter's  formula  (40),  and 
we  have 


c  = 


71.811 


1    Q1  1 

and  .  •.  c  =    '        ,  and  when  n  ==  .013,  c  =  139.31. 


This  is  the  only  instance,  I  believe,  where  Kutter's 
formula  (40)  gives  a  constant  co-efficient  with  a  change 
of  slope.  By  Molesworth's  Kutter  (70),  on  the  contrary, 
the  value  of  c  changes  with  every  change  of  slope  when 
r  =  3.281. 

It  is  evident  that  Molesworth's  Kutter  was  adopted  in 
order  to  simplify  the  application  of  Kutter's  formula 
(40),  but  its  simplification  is  of  no  practical  use,  as  it 
gives  very  inaccurate  results. 

As  shown  above,  with  the  exception  of  its  application 
to  one  diameter,  the  formula  is  not  Kutter's,  although 
in  appearance  bearing  a  resemblance  to  it. 

However,  a  modification  of  Kutter's  formula  can  be 
made  simpler  in  form  than  even  Molesworth's  Kutter 
(70),  and  giving  results  near  enough  for  all  practical 
purposes  to  those  obtained  by  the  use  of  the  more  com- 
plicated Kutter  formula  (40). 


OPEN    AND    CLOSED    CHANNELS. 


213 


The  value  of  c  in   Kutter's  formula  (40),  with  a  slope 
of  1  in  1000,  and  n  =.013  is  thus  expressed: — 


c  — 


.013   '     .001 

1    (4 

.00281\  .013 
i    r»   i                 \ 

- 

1-^4 

.001  Jyf 

183.72 

1        I 

/                 .013\  

1      1  A  A    A  1     \/ 

.(72) 


The  following  table  will  show  the  value  of  the  co- 
efficient c  for  several  slopes  and  diameters  according  to 
formula  (70),  (40)  and  (72). 

TABLE  39.     Giving  values  of  c,  the  co-efficient  of  discharge,  according 
to  different  modifications  of  Kutter's  formula  with  n  =  .013. 


Moles- 
worth's  Kut- 
ter  (70) 

Kutter's 
formula  (40) 
c  = 

Flynn's 
Kutter  (72) 
c  = 

c  = 

6  inch  diameter,  slope 

1  in  40.... 

86.9 

71.5 

69.5 

6  inch  diameter,  slope 

1  in  1000.. 

85.3 

69.5 

69.5 

4  feet  diameter,  slope 

1  in  400  ... 

87.2 

117. 

116.5 

4  feet  diameter,  slope 

1  in  1000... 

85.3 

116.5 

116.5 

8  feet  diameter,  slope 

1  in  700  ... 

85.8 

130.5 

130.5 

8  feet.diameter,  slope 

1  in  2600... 

82.9 

129.8 

130.5 

This  table  shows  the  close  agreement  of  formula  (72) 
with  Kutter's  formula  (40),  and  it  also  shows  the  inac- 
curate results  obtained  by  the  use  of  Molesworth's  Kut- 
ter. 

The  first  column  of  this  table  shows  that  a  formula 
with  a  constant  value  of  c  =  85,  that  is: — 

v  =  85  \/TS 


214 


FLOW    OP    WATER    IN 


will  give  results  differing  in  an  extreme  case  only  2J  per 
cent,  from  Molesworth's  Kutter,  and  in  the  greater  num- 
ber of  cases  differing  only  about  one  per  cent. 

The  second  column  of  the  table  shows  the  wide  range 
of  the  co-efficient  c  by  Kutter's  formula  (40)  from  69.5 
to  130.5,  to  suit  the  different  changes  in  the  hydraulic 
mean  depth  and  slope. 

The  objection  to  the  old  formulae  was  that  they  gave 
velocities  too  high  for  small  pipes  and  channels,  and  too 
low  for  large  pipes  and  channels.  The  following  table 
will  show  that  the  same  inaccurate  results  are  obtained 
by  the  use  of  Molesworth's  Kutter  (70). 

TABLE  40.     Giving  the  mean  velocity,   in  feet  per  second,   of   pipes  of 
different  diameters  and  grades,  with  n=  .013. 


Velocity  in  Feet  per  Second. 

Moles- 
worth  (70). 

Kutter 
(40). 

Flynn's  Kut- 
ter (72). 

6  inches  diameter,  slope  1 

in  40.. 

4.86 

4. 

3.89 

6  inches  diameter,  slope  1 

in  1000 

.95 

.78 

.78 

4  feet  diameter,  slope  1  in 

400.  .  . 

4.36 

5.85 

5.83 

4  feet  diameter,  slope  1  in 

1000.. 

2.70 

3.68 

3.68 

8  feet  diameter,  slope  1  in 

700... 

4.59 

6.97 

6.97 

8  feet  diameter,  slope  1  in 

2600.  . 

2.30 

3.60 

3.62 

This  table  shows  that  there  is  a  wide  difference  be- 
tween the  velocities  obtained  by  Molesworth's  Kutter 
(70)  and  Kutter's  formula  (40),  and  it  further  shows 
that  for  the  slopes  usually  adopted  in  practice  for  pipes, 
sewers,  conduits,  etc.,  that  is,  for  slopes  not  natter 
than  2  feet  per  mile,  or  1  in  2640,  formula  (72)  will  give 
velocities  that,  for  all  practical  purposes,  may  be  consid- 


OPEN    AND    CLOSED     CHANNELS 


215 


ered  as.  almost  identical  with  the  velocities   obtained  by 
Kutter's  formula  (40). 

In  Vau  Nostraud's  Engineering  Magazine  for  September,  1886,  is  a  let- 
ter on  this  subject  from  Mr.  Guildford  Molesworth,  the  author  ~uf  the 
Pocket  Book,  of  which  the  following  is  a  copy: 

To  the  Editor  of  Van  NostraiuVs  Magazine: 

Mr.  Flynn's  criticism  of  my  modification  of  Kutter's  formula  for  pipes 
has  just  reached  me.  Mr.  Flynii  is  quite  correct.  The  formula  as  it  stands 
in  page  25  of  the  twenty-first  edition  of  my  pocket  book  has  an  omission 

of  «^/d.     As  I  originally  framed  it,  it  stood  thus: 


181  + 


Unfortunately,  the  omission  of  ^/d  escaped  my  observation  in  correcting 
the  proofs  of  this  twenty-first  edition. 

Taking  the  side  cases  which  Mr.  Flynn  has  worked  out,  a  comparison  of 
Kutter's  formula  and  my  modification  of  it  for  pipes,  as  corrected,  stands 
thus : 


Diameter  of  Pipe. 

Slope  1  in 

Kutter. 

1 

Molesworth. 

6  inches 

40 

71.50 

71.48 

6  inches 

1000 

69.50 

69.79 

4  feet 

400 

117. 

117. 

4  feet 

1000 

116.5 

116.55 

8  feet 

700 

130.5 

130.68 

8  feet 

2600 

129  8 

129.93 

The  two  formulae  are  thus  far  substantially  identical  in  results,  though 
differing  slightly  in  form.  GUILDFORD  MOLESWORTH. 

Simla.  India,  May  17,  1886. 

Article  20.     Flynn's  Modification  of  Kutter's  Formula. 

The  author  has  reduced  Kutter's  formula  for  slopes 
up  to  1  in  2640,  into  the  simplified  form  given  in  for- 
mula (73). 

Referring  to  the  simplified  form  of  Kutter's  formula 


216 


FLOW    OF    WATER    IN 


(72),  if  we  call  the  numerator  on  the  right  hand  side  of 
the  equation  K,  for  any  value  of  n  we  have: — 

K 


and  v  =  -{  i 


(44.41  X^- 


.(73) 


In  the  following  table  the  value  of  K  is  given  for  the 
several  values  of  n. 

TABLE  41.     Giving  the  value  of  K  for  use  in  Flynn's   modification  of 
Kutter's  formula: 


n 

R 

| 
n 

K 

N 

K 

I 
|    n 

K 

n 

K 

.009 

245.63 

.012 

195.33 

.015 

165.14 

Lois 

145.03 

.021 

130.65 

.010 

225.51 

.013 

183.72 

.01G 

157.6 

.019 

139.73 

.022 

126.73 

.011 

209.05 

j.014 

137.77 

1.017 

150.94 

.020 

134.96 

.0225 

124.9 

To  further  simplify  formula  (73),  the  value  of  y/V  for 
a  large  range  of  diameters  will  be  found  in  Table  (42). 

If,  therefore,  in  the  application  of  formula  (73),  with- 
in the  limits  of  n  as  given  in  the  table,  we  substitute 
for  n,  K,  and  \/r,  their  values,  we  have  a  simplified 
form  of  Kutter's  formula  (40). 

For  instance,  when  ?i  =  .011,  and  d  =  3  feet,  we 
have:  — 


209.05 


44.41  X  - 


.011 


.866 


\ 


x 


Ol'EN    AND    CLOSED    CHANNELS. 


217 


TABLE  42.     Giving  values  of  \/r  for  circular  pipes,  sewers  and  conduits 
of  different  diameters: — 


Diamet'r 
Ft.    Ins. 

Vr 
in  Feet 

Diamet'r 
Ft.    Ins. 

x/V 
in  Feet. 

Diamet'r 
Ft.    Ins. 

! 

Vr 
in  Feet 

Diamet'r 

Ft.    Ins. 

-v*- 

in  Feet 

5 

.323 

2         9 

.829 

5         1 

1.127 

10 

1.581 

6 

.354 

2       10 

.842 

5         2 

1.137 

10       3 

1.601 

7 

.382 

2       11 

.854 

5         3 

.146 

10       6 

1.620 

8 

.408 

3 

.866 

5         4 

.155 

10       9 

1.639 

9 

.433 

3         1 

.878 

5         5 

.164 

11 

1.658 

10 

.456 

3         2 

.890 

5         6 

.173 

11       3 

1.677 

11 

.479 

3         3 

.901 

5        7 

.181 

11       6 

1.696 

1 

.500 

3         4 

.913 

5         8 

.190 

11       9 

1.714 

1           1 

.520 

3         5 

.924 

5         9 

.199 

12 

.732 

1           2 

.540 

3         6 

.935 

5       10 

.208 

12       3 

.750 

1           3 

.559 

3         7 

.946 

5       11 

.216 

12       6 

.768 

1           4 

.577 

3         8 

.957 

6 

.225 

12       9 

.785 

1           5 

.595 

3         9 

.968 

6         3 

.250 

13 

.803 

1           6 

.612 

3       10 

.979 

6         6 

.275 

13       3 

.820 

1          7 

.629 

3       11 

.990 

6         9 

.299 

13       6 

.837 

1           8 

.646 

4 

. 

7 

.323 

13       9 

.854 

1           9 

.661 

4         1 

.010 

7        3 

.346 

14 

1.871 

1          10 

.677 

4         2 

.021 

7        6 

.369 

14       6 

1.904 

1         11 

.692 

4         3 

.031 

7        9 

.392 

15 

1.936 

2 

.707 

4         4 

.041 

8 

.414 

15       6 

1.968 

2           1 

.722 

4         5 

.051 

8         3 

.436 

16 

2 

2           2 

.736 

4         6 

.061 

8        6 

.458 

16       6 

2^031 

2           3 

.750 

4         7 

.070 

8         9 

.479 

17 

2.061  • 

2           4 

.764 

4         8 

.080 

9 

.500 

17       6 

2.091 

2           5 

.777 

4         9 

.089 

9         3 

.521 

18 

2.121 

2           6 

.790 

4       10 

1.099 

9         6 

1.541 

19 

2.180 

2           7 

.804 

4       11 

1.109 

9         9 

1.561 

20 

2.236 

2           8 

.817 

5 

1.118 

Article  21.     D'Arcy's  Formulae. 

M.  H.  D'Arcy's  experiments  on  the  flow  of  water  in 
new  and  old  cast-iron  pipes  are  the  most  thorough  and 
elaborate  investigations  of  the  kind  which  have  ever 
been  carried  out.  He  demonstrated  that  the  degree  of 
roughness  of  the  wetted  surface  has  an  important  effect 
on  the  discharge  of  the  pipe. 

M.  D'Arcy  had  observed,  in  the  course  of  his  ex- 
perience on  waterworks,  that  in  proportion  to  the 
smoothness  of  the  inner  surface  of  the  pipe,  so  was  its 


218 


FLOW    OF    WATER    IN 


discharge  increased.  He  had  at  his  disposal  ample 
means  to  carry  out  experiments  to  prove  this.  He  was 
an  engineer  eminently  fitted  to  carry  out  such  experi- 
ments, on  account  of  his  great  scientific  attainments, 
and  his  practical  experience  gained  whilst  in  charge  of 
City  Waterworks,  and  the  results  of  his  observations 
fully  justified  the  confidence  placed  in  his  ability. 

It  is  to  be  regretted  that  his  experiments  did  not  ex- 
tend to  large  pipes.  He  made  experiments  with  22  pipes 
of  cast  and  wrought  iron,  sheet  iron  covered  with  bitu- 
men, and  lead  and  glass,  but  none  of  them  were  of  large 
dimensions.  His  experiments  on  pipes  fully  justified 
his  former  experience,  and  Bazin's  observations  on 
small  open  channels  gave  further  testimony  to  the  same 
effect. 

The  experiments  of  D'Arcy  and  Bazin.  *  were  after- 
wards of  great  value  to  Kutter  in  his  hydraulic  investi- 
gations. 

After  the  publication  of  the  results  of  D'Arcy's  ob- 
servations in  the  French,  Mr.  J.  B.  Francis,  M.  Am. 
Soc.  C.  E.f  presented  his  formula)  in  a  form  suitable  to 
feet  measures. 

Mr.  J.  W.  Adams,  M.  Am.  Soc.  C.  E.,  in  Engineering 
News  of  March  10th,  1883,  writes: — 

"When  the  Loch  Katrine  Water  Works  for  Glasgow 
were  being  extended  some  years  since,  a  portion  of  the 
distance  was  carried  over  low  grounds  by  a  cast-iron 
trough  6|  feet  deep  and  8  feet  in  width,  supported  on 
masonry  piers,  and  giving  good  opportunity  to  deter- 
mine the  daily  flow.  By  this  and  other  means  it  was 
found  that  the  cast-iron  pipes,  4  feet  in  diameter,  which 
with  a  fall  of  1  in  1056  on  the  rest  of  the  line,  had  been 
computed  to  carry  21,000,000  gallons,  were  really  dis- 

*  Recherches  Hydrauliques. 

t  Transactions  American  Society  of  Civil  Engineers.     Vol.  II. 


OPEN    AND    CLOSED    CHANNELS.  219 

charging  daily  23,430,000  gallons.  The  engineer,  Mr. 
Gale,  brought  the  matter  to  Professor  Rankine's  atten- 
tion; who,  in  a  paper  and  subsequent  discussion  before 
the  Institution  of  Engineers  of  Scotland,  Marcli~17th, 
1869,  uses  this  language:  '  It  might  be  interesting  to 
the  Institution  to  know  that  there  was  a  formula  which 
agreed  exactly  with  the  results  of  Mr.  Gale's  experi- 
ments. Suppose  that  before  these  four-feet  pipes  were 
laid,  the  probable  discharge  had  been  calculated  by 
D'Arcy's  formula,  the  result  would  have  differed  by  one 
jxirt  in  a  thousand,  from  the  actual  discharge,  which  was 
23,430,000  gallons  daily.  This  went  to  show  that  they 
now  possessed  a  general  formula  for  the  flow  of  water  in 
pipes,  and  the  resistance  to  that  flow,  which  applied  to 
large  as  well  as  small  pipes  (it  applied  to  pipes  of  an 
inch  in  diameter),  and  from  Mr.  Gale's  experiments  they 
would  see  that  it  also  applied  to  pipes  four  feet  in 
diameter.'  The  Glasgow  pipes  had  been  coated  with 
Dr.  Smith's  process,  and  were  treated  as  clean  pipes 
and  calculated  by  the  formula  (for  clean  pipes).  I  think 
that  D'Arcy's  experiments  conducted  as  they  were  under 
circumstances  which  contributed  in  every  way  to  inspire 
confidence.  Mr.  Francis'  labors  in  presenting  this 
formula  to  us  in  English  dress,  with  the  prestige  grow- 
ing out  of  his  well-known  capacity  for  careful  investiga- 
tion and  computation,  and  Professor  Rankine's  indorse- 
ment of  its  applicability  to  all  conditions  of  pipe  discharge 
up  to  four  feet  diameter,  must  be  considered  as  estab- 
lishing the  practical  value  of  this  special  formula  for  the 
flow  through  iron  pipes." 

Mr.  W.  Humber,  C.  E.,  in  his  work  on  "Water  Sup- 
ply/' states: — 

"  That  which  is  known  as  D'Arcy's  formula,  in  pipes 
of  large  diameter,  appears  to  approach  in  its  results 
nearer  to  the  actual  discharge  than  any  other,  and  it  was 


220  FLOW    OF    WATER    IN 

the  opinion  of  Professor  Rankine,  that  the  resistance 
decreases  to  a  greater  extent  in  pipes  of  larger  diameter 
than  has  been  previously  supposed.  The  experiments 
were  made  with,  and  the  formula  of  D'Arcy  deduced 
from,  pipes  which  had  been  long  in  use  without  offering 
any  impediment  from  incrustation." 

Example  23  is  an  illustration  of  the  accuracy  of 
D'Arcy's  formula,  where  the  actual  discharge  from  a  48- 
inch  pipe  was  found  to  be  the  same  as  that  given  by 
computing  by  D'Arcy's  formula. 

It  was  found,  however,  that  after  some  time  the  dis- 
charge gradually  fell  off,  and,  though  in  the  first  instance, 
the  amount  was  50  per  cent,  larger  than  that  given  by 
the  old  formula,  still  it  gradually  diminished,  though 
the  pipes  still  continued  to  discharge  more  than  the 
amount  gained  by  the  old  formula.  The  degree  of 
roughness  of  the  pipe  was  a  measure  of  its  discharging 
capacity. 

In  a  paper  presented  to  the  Technical  Society  of  the 
Pacific  Coast,  on  February  6,  1885,  the  author  simplified 
D'Arcy's  formula  (51),  into  the  form  of  formula  (52):  — 

/1  55256  d\J 


12 

This  was  done  in  order  to  obtain  a  formula  adapted  to 
the  preparation  of  a  table  facilitating  the  use  of  D'Arcy's 
formula.  In  a  similar  way  the  author  has  simplified 
D'Arcy's  formula  (53),  for  old  cast-iron  pipe  lined  with 
deposit,  into  the  form  given  in  formula  (54). 

Table  48  is  for  clean  cast-iron  pipe,  and  table  49,  for 
old  cast-iron  pipe  lined  with  deposit. 

D'  Arcy's  formula  for  finding  the    mean  velocity  in  clean 
cast-iron  pipes. 

For  feet  measures  D'Arcy's  formula  for  mean  velocity 
in  clean  cast-iron  pipes  is:  — 


OPEN    AND    CLOSED    CHANNELS.  221 


.000001B2 
I  .00007726  +  -  — — 

and  from  this  we  have: — 

.  00000162  \v2 


-I  .00007726  + 


r     )  r 

In  order  to  simplify,  substitute  for  r  in  feet  the  diameter 
d  in  inches,  arid  we  have 

/  .00000162  X  48\48  v2 

8  =  (    00007726  +  —j-  J  —j- 

.-.  s  =  f. 00370848  d+. 00373248  \-^- 


As  the  change  will  riot  materially  affect  the  result, 
Mr.  J.  B.  Francis,  C.  E.,  simplifies  this  into  the  form 

8  =  .00371  (d+  1  \-£- (A) 

\  /   d 

v—  (  Sc1*  V 

\  .00371  (d+~l)  ) 

In  order,  however,  to  further  simplify  the  equation 
into  the  Chezy  form  of  formula,  which  is  the  form  re- 
quired for  the  preparation  and  use  of  the  tables  adopted 
by  the  writer,  and  given  in  this  book,  let  equation  (A) 
be  transformed  into  one  with  the  diameter  d  in  feet,  and 
it  becomes: — 

(\      *,2 
12  d  +  1 

Therefore,  for  clean  iron  pipes 
f  144c?2s 

I  700371  (12  d  +  1) 
but  d2  =  16  r2  =  16  r  X  r  =  4d  X  r  substitute  this  value 
for  d2  in  the  last  equation,  and 


v  __  /  144  X  4d  X  r  X  s\ 
{  .00371(12^  +  1)  J 


222  FLOW    OF    WATER    IN 

Therefore,  for  feet  measures,  D'Arcy's  formula   for  ve- 
locity is  simplified  into 

/ 155256 


- 


^    /" 
X  \/rs 


and  putting  the  first  factor  on.  the  right-hand  side  of  the 
equation  =  c,  we  have 

v  ==  c\/rs  —  c\/r   X  ]/* 

1)'  Arcy'  s  formula  for  finding  the  mean  velocity  in  old  cast- 
iron  pipes. 

Mr.  J.  B.  Francis,  M.  Am.  Soc.  C.  E.,  has  given 
D'Arcy's  formula  for  the  Flow  of  Water  through  old  cast- 
iron  pipes  lined  with  deposit  as:— 

.......................  (B) 


where  s  and  v  have  the  same  values  as  given  at  pages  6 
and  7,  and  d  =  diameter  in  inches. 

In  order,  however,  to  further  simplify  the  equation 
into  the  Chezy  form  of  formula,  which  is  the  form  re- 
quired for  the  preparation  and  use  of  the  tables,  as 
already  stated,  let  formula  (B),  be  transformed  into  one 
with  the  diameter  d  in  feet,  and  it  becomes:  — 

«  --=.0082    l2d 


/  144  d2 

.  .  /         144  d2  s  __  U 

V0082   12  4-  1/ 


0082  (12  44-  1) 

but  d  =  4r,  and  d2  =  d  X  4  r,  substitute  these  values  in 
formula  (C)  for  c/2,  and:  — 

_  /      144  d  X  4rs      \* 

~\.0082(12cM-l)/ 
and  therefore,   for  feet  measures    D'Arcy's  formula  for 


OPEN    AND    CLOSED    CHANNELS.  223 

the  mean  velocity  in  old  cast-iron    pipes  lined  with  de- 
posit is  simplified  into  the  form: — 

/70243.9r/V 

•Viixrr)    (1/™ 

and  putting  the  first   factor  in  parenthesis  on  the  right 
hand  side  of  the  equation  =  c,  we  have: — 

V  —  C\/TS 

Article  22.  Comparison  of  the  Co-efficients  for  Small 
Diameters  of  the  Formulae  of  D'Arcy,  Kutter,  Jack- 
son and  Fanning. 

v  =  c\/r  X  \/s 

In  tables  48  to  57  inclusive,  the  values  of  the  factors 
of  Kutter's  formula  are  not  given  for  diameters  less  than 
5  inches.  Mr.  L.  D'A.  Jackson,  C.  E.,  in  his  Hydraulic 
Manual,  states:  — 

"  For  the  present,  and  until  further  experiments  have 
thrown  more  light  on  the  subject,  it  may  be  assumed 
that  the  co-efficient  of  discharge  for  all  full  cylindrical 
pipes,  having  a  diameter  less  than  0.4  feet,  will  be  the 
same  as  those  of  that  diameter." 

Although  Mr.  Jackson's  opinion  is  entitled  to  great 
weight,  still  the  facts  all  tend  to  prove  that  the  co- 
efficients of  diameters  below  5  inches  should  diminish 
with  the  diminution  of  diameter.  The  smaller  the 
diameter  the  more  effect  will  the  roughness  of  the  sur- 
face have  in  diminishing  the  discharge.  Table  43  shows 
that  Kutter's  co-efficient  for  5  inches  diameter  with 
??,— .011  is  82.9,  and  therefore,  according  to  Mr.  Jack- 
son, all  the  diameters  from  5  inches  to  |  inch  should 
have  a  co-efficient  of  82.9.  This  is  contrary  to  the 
principle  of  Kutter's  formula,  the  accuracy  of  which  is 
due  to  the-  fact  that,  other  things  being  equal,  its  co- 


224 


FLOW    OF    WATER    IN 


efficients  vary  with  the  diameter.  The  following  proofs 
are  given  in  support  of  the  opinion  that  co-efficients  of 
diameters  belowr  5  inches  should  diminish  according  to 
the  diminution  of  diameter. 

TABLE    43.     Of  co-efficieiits   (c)  from    the  formulae    of  D'Arcy,  Kutter, 
Jackson  and  Fanning,  for  small  pipes  below  5  inches  in  diameter, 

v  =  c\/rs 


(c) 

(c) 

(c) 

(c) 

Kutter's  co-em-  jKutter's  co-effi- 

Fanning's co- 

Diameter in 

D'Arcy's    co- 

cient from  for- 

cient  recom- 

efficient for 

inches. 

efficient  for 

mula 

mended   by  L. 

clean  iron 

clean  pipes. 

™  =  .on 

D'A.  Jackson. 

pipes. 

8  =  .001 

1 

59  4 

32. 

82.9 

1 

65.7 

36.1 

82.9 

1 

74.5 

42.6 

82  9 

I 

80.4 

47.4                     82.9 

80.4 

u 

84.8 

51.9 

82.9 

11 

88.1 

55.4 

82.9 

88. 

If 

90.7 

58  8 

82.9 

92.5 

2 

92.9 

61.5 

82.9 

94.8 

2J 

96.1 

66. 

82.9 

3 

91.5 

70.1 

82.9 

96.6 

4 

101.7 

77.4 

82.9 

103.4 

5 

103.8 

82.9 

82.9 

1.  In   Table  43  the  co-efficients  of  Darcy's  formula 
are  seen  to  diminish   with   the  diminution  of  diameter. 
At  5  inches  diameter  the  co-efficient   is   103.8,  and  at  f 
inch  diameter  59.4. 

2.  In  Table  43  the  co-efficients  of  Farming's  formula 
diminish  from  4  inches  diameter  with  a  co-efficient  of 
103.4,  to  1  inch  diameter  with  a  co-efficient  of  80.4. 

These  co-efficients  are  derived  from  the  mean  velo- 
cities in  clean  pipes  with  a  slope  of  1  in  125  given  in 
Fanning's  tables. 

3.  In  Table  43  the  co-efficients,  as  found  by  Kutter's 
formula  with    a  slope    of  1  in   1000,  and  n  =  .011,  are 
for  5  inches  diameter,  82.9,  and  for  f   inch   diameter, 
32.0. 


OPEN    AND    CLOSED    CHANNELS.  225 

The  facts,  therefore,  show  that  the  co-efficients  dimin- 
ish from  a  diameter  of  5  inches  to  smaller  diameters, 
and  it  is  a  safer  plan  to  adopt  co-efficients  varying  with 
the  diameter  than  a  constant  co-efficient.  No-  opinion 
is  advanced  as  to  what  co-efficients  should  be  used  with 
Kutter's  formula  for  small  diameters.  The  facts  are 
simply  stated,  giving  the  results  of  well-known  authors. 

As   the   co-efficients  of    D'Arcy's  formula   vary   only 

with   the   diameter,   the   values  of  the   factors  c\/r  and 

ac\/r  given  in  Tables  48  and  49  for  D'Arcy's  formula, 
are  practically  the  exact  values  for  all  diameters  and 
slopes  given,  and  the  results  found  by  the  use  of  the 
tables  will  be  the  same  as  the  results  found  by  using 
the  formula. 

In  Tables  50  to  67,  the  values  of  c\/r  and  ac\/r  for 
Kutter's  formula  sometimes  differ,  when  the  slope  is 
natter  than  1  in  1000,  by  a  small  quantity  from  the 
actual  values  as  found  by  the  use  of  formula  (40). 
These  values  by  Kutter's  formula  depend  not  only  on 
r,  but  also  on  n  and  s,  so  that  a  change  in  any  of 
these  three  quantities  causes  a  change  in  the  values  of 

c\/r  and  ac\/r.  It  is  found,  however,  that  the  slope 
of  1  in.  1000  will  give  co-efficients  which  practically 
differ  very  little  from  the  co-efficients  derived  from  the 
slopes  usually  given  to  lines  of  pipes,  sewers  and  con- 
duits. 

The  values  of  the  factors  c\/r  and  ac\/r,  from  Kutter's 
formula  given  in  the  tables  50  to  67,  have  been  computed 

for  a  slope  of  1  in.  1000,  and  they  give  values  of  c\/r  and 

ac\/r  near  enough  for  practical  work. 
15 


226  FLOW    OF    WATER    IN 

Article  23.     Pipes,  Sewers,  Conduits,  etc.,  Having  the 
Same  Velocity. 

The  columns  c\/r  in  Tables  48  to  57,  inclusive,  for 
circular  channels,  and  Tables  59  to  67,  inclusive,  for 
egg-shaped  sewers,  can  be  used  to  compare  velocities,  as, 
other  things  being  equal,  the  velocities  are  proportional 

to  c\/r.     The  formula: — 

v  —  c^/r    X  \/.s,  is  proof  of  this-. 

For  example,  a  circular  pipe  or  sewer  4  feet  in  diame- 
ter flowing  full,  with  a  value  of  n  ==  .013,  and  a  slope  of 
1  in  1500,  has  a  mean  velocity  of  2.988  feet,  that  is,  prac- 
tically, 3  feet  per  second.  In  Table  54  we  find  that  this 

channel  has  c\/r  —  116.5.  Now  all  pipes,  under 
different  values  of  n,  of  different  diameters,  having  the 

same  grade  and  the  same  value  of  c\/r,  will  have  the 
same  velocity. 

Again,  the  slope  being  equal,  we  can  find,  merely  by 
inspection,  the  dimensions  of  an  egg-shaped  sewer,  of  a 
different  value  of  n,  flowing  full,  two-thirds  full,  or  one- 
third  full,  that  will  have  the  same  velocity  as  a  circular 
sewer  with  a  different  value  of  n  flowing  full. 

Thus,  taking  the  circular  sewer  mentioned  above  of  4 
feet  in  diameter  and  n  =  .013,  and  we  want  to  find  the 
dimensions  of  an  egg-shaped  sewer  flowing  two-thirds 
full,  that,  with  n  —  .015,  and  the  same  grade,  will  have 
the  same  velocity.  In  Table  66  of  egg-shaped  sewers 
flowing  two-thirds  full  and  with  n  =.015,  we  find  opposite 

a  sewer  having  the  dimensions  of  4'x6',   that  c\/r  = 
116.5,  therefore  a  circular  sewer  4  feet  in  diameter  with 
n  =  .013,  will,    with    the    same    slope,    have    the    same 
velocity  as  an  egg-shaped  sewer  4'x6'  with  n  =  .015,  and 
flowing  two-thirds  full. 

Table  47,   giving  the  values  of  the   hydraulic  mean 


OPEN    AND    CLOSED    CHANNELS. 


227 


depth,  r,  of  circular  pipes,  etc.,  and  Table  58,  giving 
the  values  of  r  for  egg-shaped  sewers,  can  be  used  with 
great  advantage  in  a  variety  of  problems  in.  comparing 
the  velocities  in  pipes,  sewers  and  conduits. 

In  the  following  table,  given  to  illustrate   what  has 

been  just  stated,  the  nearest  values  of  c\/r  given  in  the 
working  tables  are  inserted: — 

TABLE  44.  Circular  Pipes,  Sewers  and  Conduits  having  the  same  mean 
velocity  and  the  same  grade,  but  with  different  diameters  and  different 
values  of  n,  based  on  Kutter's  formula: — 


No.  of 
Table 

Value  of 

n 

Diameter, 
Ft.      Ins. 

cVr 

Slope  1  in 
1500 

%A 

Velocity  in 
feet  per 
second. 

Remarks. 

50 

.009 

2             2 

117. 

.02582 

3.021 

Circular. 

51 

.01 

2            7 

116.8 

.02582 

3.016 

Circular. 

52 

.011 

3            1 

117.9 

.02582 

3.044 

Circular. 

53 

.012 

3            6 

116.3 

.02582 

3.003 

Circular. 

54 

.013 

4 

116.5 

.02582 

2.988 

Circular.  . 

55 

.015 

5            1 

117.1 

.  02582 

3.023 

Circular. 

56 

.017 

6            3 

117.6 

.02582 

3.036 

Circular. 

57 

.020 

8 

117.2 

.02582 

3.026 

Circular. 

The  mean  velocity  of  egg-shaped  sewers  can  be  com- 
pared in  the  same  way,  or  can  be  compared  with  circular 
sewers.  Thus,  let  us  find  the  dimensions  of  egg-shaped 
sewers  having  the  same  velocity  and  the  same  grade  as 
the  circular  sewers  in  Table  44,  but  with  different  values 
of  n. 


228 


FLOW    OF    WATER    IN 


TABLE  45.     Egg-shaped  sewers  having  the  same  velocity  and  the  same 
grade,  but  with  different  dimensions  and  different  values  of  n  : — 


No.  of 
Table 

Value  of 
n 

Dimen- 
sions 

cV 

Slope  1  in 
1500 

vT 

Velocity 
in  feet 
per  sec- 
ond. 

Kemarks. 

59 

.011 

2'  8"  x  4'  0" 

118. 

.02582 

3.047 

Full  depth. 

60 

.011 

2'  6"  x  3'  9" 

119.9 

.02582 

3.096 

f  full  depth. 

61 

.011 

3'  8"  x  5'  6" 

116.4 

.02582 

3.005 

i  full  depth. 

62 
63 

.013 
.013 

3'  6"  x  5'  3" 

3'  2"  x  4'  9" 

117.6 
116.5 

.02582 

.02582 

3.036 
3.008 

Full  depth, 
f  full  depth. 

64 
65 

.013 
.015 

4'  10"  x  7'3" 

4'  4"  x  6'  6" 

116.5 
116. 

.02582 
.02582 

3.008 
2.995 

I  full  depth. 
Full  depth. 

66 

.015 

4'  0"  x  6'  0" 

116.5 

.02582 

3.008 

f  full  depth. 

67 

.015 

6'  2"  x  9'  3" 

117.3 

.02582 

3.028 

I  full  depth. 

Article  24.     Pipes,    Sewers   and   Conduits   Having   the 
Same  Discharge. 

By   an   exactly   similar  method    to   that   adopted   for 
velocities    in    Article    23,  we    can    use   the   columns  of 

ac\/r  for  finding  equivalent  discharging  pipes,  sewers 
and  conduits.  We  can  also  find  the  dimensions  of  a 
single  sewer  having  a  discharge  equivalent  to  that  of 
several  other  sewers.  For  example,  three  circular  sewers 
have,  at  different  times,  been  constructed  to  an  outfall 
on  a  river.  The  sewers  are,  respectively,  10,  12  and  18 
inches  in  diameter.  The  grade  is  1  in  300,  and  their 
value  of  n  =  .013.  What  must  be  the  dimensions  of  an 
egg-shaped  sewer  that,  flowing  two-thirds  full  depth, 
with  the  same  value  of  n  and  the  same  grade,  will  have 
a  discharge  double  that  of  the  three  circular  sewers 
mentioned? 


OPEN    AND    CLOSED    CHANNELS. 


229 


In  Table  54,  of  circular  sewers  with  n  =  .013,  we 
find  a 

10  inch  sewer  has  ac\/r  =  20.095 
12  inch  sewer  has  ac\/r  =  33.497 
18  inch  sewer  has  ac\/r  =  102.140 

Therefore,  the  three  circular  sewers  ac\/r  =  155.732 
Now  155.732  X  2  =  311.464,   which    is    the   value    of 

ac\/r  of  the  water  section  of  the  new  sewer. 

In  Table  63  of  egg-shaped  sewers  flowing  two-thirds 
full  depth  with  n  =  .013,  we  find  opposite  a  sewer 

2'  2"  X  3'  3"  that  aci/r  =  317.19,  therefore  the  required 
sewer  is  2'  2"  X.3'  3". 

In  order  to  further  illustrate  this  subject,  Table  46  is 
given.  This  table  further  shows  the  effect  of  the  value 
of  n ;  for  a  pipe  2  feet  2  inches  diameter  with  a  value  of 
n  =  .009,  has  practically  the  same  discharge  as  a  2  foot 
9  inch  pipe  with  a  value  of  n  =  .015. 

TABLE  46.  Pipes,  Sewers  and  Conduits,  having  the  same  grade  and  the 
same  or  nearly  the  same  discharge,  but  with  different  diameters  and  differ- 
ent values  of  n. 


No.  of 
Table. 

Value 
of  n. 

DIAMETER. 

ac^/r 

Slope   1  in 
1500 

v^ 

Discharge 
in  cubic  ft. 
per  second 

Kemarks. 

Feet.  Inches. 

50 

.009 

2           2 

431.5 

.02582 

11.14 

Circular. 

51 

.01 

2           3 

421.9 

.02582 

10.89 

Circular. 

52 

.011 

2            5 

457.1 

.  02582 

11.8 

Circular. 

53 

.012 

2           6 

452.1 

.02582 

11.67 

Circular. 

54 

.013 

2           7 

450.5 

.02582 

11.63 

Circular. 

55 

.015 

2           9 

451.2 

.02582 

11.65 

Circular. 

230 


FLOW    OF    WATER    IN 


In  the  same  manner  the  discharge  of  egg-shaped 
sewers  can  be  compared. 

The  discharge  is  not  exactly  the  same  for  each  pipe, 

for  the  reason  that  the  exact  value  of  ac\/r  =  431.5 
could  not  be  found  opposite  the  diameters  in  tables,  and, 
therefore,  the  nearest  value  to  431.5  was  taken. 

What  has  been  shown  in  this  and  the  foregoing  articles 
is  sufficient  to  demonstrate  to  the  practical  engineer  the 
rapidity  with  which  problems  relating  to  pipes,  sewers 
and  conduits  can  be  solved  by  the  tables  in  this  work. 

Article   25.     Egg-Shaped  Sewers. 

Where  the  volume  of  sewage  fluctuates,  the  oval  form 
of  sewer  is  the  best  adapted  with  a  small  discharge,  to 
give  a  velocity  sufficient  to  prevent  the  deposit  of  silt,  as 
its  hydraulic  mean  depth  is  greater  for  small  volumes  of 
flow  than  the  circular  sewer. 


Fig.  4.    Egg-shaped  Sewer. 

The  egg-shaped  sewer  treated  of  in  this  work  has  its 
depth,  or  vertical  diameter,  equal  to  3.5  times  its  greatest 


OPEN    AND    CLOSED    CHANNELS.  231 

transverse  diameter,  that  is,  the  diameter  of  top  or  arch. 
This  form  of  cross-section  of  sewer  is  illustrated  in 
Figure  4. 

D  ==  AB  —  greatest  transverse  diameter,   that  is,— the 

2  // 

diameter  of  top  or  arch  =  — - — 

o 

H  =  CD  =  depth  of  sewer  or  vertical  diameter  =  1.5 D. 

TT 

B  =  ED  =  radius  of  bottom  or  invert  = 

6 

R  —  AF  =  radius  of  sides  =  H. 

By  reference  to  Table  69,  it  will  be  seen  that  the  value 
of  the  velocity  of  an  egg-shaped  sewer  flowing  two-thirds 
full  depth,  is  always  greater  than  that  of  the  mean  ve- 
locity of  the  same  sewer  flowing  full  depth.  The  dis- 
charge, however,  is  always  greater  in  the  sewer  flowing 
full  depth. 

Article  26.     Explanation  and  Use  of  the  Tables. 

Pipes,  Sewers  and  Conduits. 

EXAMPLE  21.  Given  the  diameter,  length,  fall  and  value 
of  n  of  a  pipe,  to  find  its  mean  velocity  and  discharge. 

An  inverted  syphon,  B,  G,  D,  E,  F,  measured  along 
the  line  of  pipe,  is  five  miles  in  length,  and  its  outlet  at 
F  is  40  feet  below  the  surface  of  the  reservoir  at  A.  The 


Fig.  5.    Inverted  Syphon. 

pipe  is  2  feet  in  diameter.       It  is  made  of  sheet-iron, 
double  riveted,    dipped   in   hot   asphaltum.        This  dip 


232  FLOW    OF    WATER    IN 

gives  a  very  smooth  surface  at  first,  but  to  allow 
for  the  deterioration  of  that  surface  the  value  of  n  is 
taken  =.013.  What  is  its  mean  velocity  in  feet  per 
second,  and  the  discharge  in  cubic  feet  per  second?  It 
is  well  to  remember  that  at  no  part  of  its  length  should 
the  pipe  rise  above  the  hydraulic  grade  line  A  F. 

A  fall  of  40  feet  in  five  miles  is  equivalent  to  8  feet 
per  mile,  or  1  in  660.  In  Table  33,  opposite  a  slope  of 

1  in  660,  we  find  i/s  =  .038925. 

In  Table  54,  for  circular  pipes  with  n  =.013,  we  find 

a  =  3.142,  cv/r  =  71.49  and  ac^/r  =  224.  63.     Now,  to 

find  mean  velocity,  substitute  the  values  of  C]/T  and  \/s 
in  formula  (41),  and  we  have: — 

v  =  71.49  X  .038925  =  2.783  feet  per  second. 
Again,  to  find  the  discharge,  substitute  the  values  of 

ac\/r  and  \/s  in  formula  (45),  and  we  have: — 

Q  =  224.63  X  .038925  =  8.744  cubic  feet  per  second. 
As  a  check  on  the  above  we  have  by  formula  (45): — 
Q  =  av  substitute  the  values  of  a  and  v  above  found 

and  we  have: — 

Q  =  3.142  X  2.783  =  8.744    cubic    feet    per    second, 

which  is  the  same  as  the  discharge  before  found. 

EXAMPLE  22.  Given  the  discharge  and  cross-sectional 
dimensions  of  a  rectangular,  masonry,  Inverted  Syphon, 
to  find  its  grade  or  fall  from  surface  of  water  at  inlet  to  its 
outlet. 

At  page  177  of  Irrigation  Canals  and  other  Irrigation 
Works,  there  is  a  description  of  an  inverted  syphon  un- 
der the  Agra  Canal,  India.  The  syphon  is  capable  of 
discharging  2,000  cubic  feet  per  second.  It  has  seven 
culverts  each  6  feet  wide  and  4  feet  deep.  The  syphon 
is  provided  with  a  floor  of  massive  rough  ashlar,  the 
entrance  and  egress  for  the  torrent  being  also  built  of 


OPEN    AND    CLOSED    CHANNELS.  233 

large  stone.  The  culverts  are  covered  with  large  stones 
bolted  down  to  the  piers.  The  length  of  the  syphon  is 
assumed  at  200  feet.  From  the  description  given  of  the 
surface  of  the  syphon  exposed  to  the  flow  of  water,  we 
may  assume  its  value  of  n  —  .017  (see  page  19). 

The  total  discharge  being  2,000  cubic  feet  per  second, 
therefore,  each  of  the  seven  syphons  has  to  discharge 
286  cubic  feet  per  second.  The  area  of  one  culvert 
=  6'  X  4'  ==  24  square  feet. 

Q          286       1  0  . 
v  =  -       =  —  —  =  12  feet  per  second  nearly. 

CL  LtQ. 

r  =  =  1.2  .-.^  =  1/0=  1.1  nearly. 

Under  a  slope  of  1  in  1000  and  opposite  \/r  =  1.1  in 
Table  21,  page  132,  we  find  c\/r  =  98.4. 

Now  substitute  this  value  of  CI/T  and  also  the  value  of 
v  in  formula  (43),  and  we  have:  — 


The  nearest  value  to  this,  in  Table  33,  is  .122169 
opposite  a  slope  of  1  in  67,  but  as  the  total  length  is  200 

feet  .*.  _—  =  3  feet  nearly,  being  the  head  required  to 

generate  a  velocity  of  12  feet  per  second. 

This  head  of  three  feet  can  be  given  to  the  culvert  in 
three  ways:  — 

1st.  The  culvert  having  a  level  floor,  the  water  will 
head  up  three  feet  on  the  upper  side,  the  pipe  being 
under  pressure. 

2d.  A  fall  of  three  feet  is  given  to  the  floor  of  the 
culvert  in  its  length  of  200  feet. 

3d.  A  less  fall  than  three  feet  is  given  to  the  floor  in 
its  length  of  200  feet,  and,  in  addition  to  this,  sufficient 
heading  takes  place  on  the  upper  side  to  give  the  re- 
quired velocity. 


234  FLOW    OF    WATER    IN 

In  so  short  a  channel,  an  addition  should  be  made  to 
the  head  to  generate  such  a  high  velocity  as  twelve  feet 
per  second,  but  as  the  flood  water  of  the  torrent  arrives 
at  the  inlet  of  the  syphon  with  a  high  velocity,  a  few 
inches  additional  to  the  head  will  suffice  for  this. 

There  is  even  a  quicker  method  than  that  given  above 
for  finding  the  head  approximately.  For  the  same  area 
of  channel,  a  circle  has  the  greatest  hydraulic  mean 
depth,  and,  therefore,  requires  the  least  head  to  give  the 
same  velocity.  The  culvert  6'x4'  has  a  cross-sectional 
area  of  twenty-four  square  feet,  and  a  circular  channel 
of  the  same  area,  will  require  less  head  to  produce  the 
same  velocity. 

We  will  use  Table  56  for  circular  channels,  with 
n  =.017,  to  find  the  required  head.  In  Table  56  the 
nearest  area  to  twenty-four  square  feet  is  23.758  square 
feet,  having  a  diameter  of  five  feet  six  inches.  In  the 

same  line  we  find  c\/r  =  107.6. 

Let  us  now  substitute  the  value  of  c\/r  and  v  in  for- 
mula (43). 

,/»=*=      12  .111524 

c\/r        107 . 6 

Now,  n  Table  33  the  nearest  value  of  \/s  to  this  is 
.111803  opposite  a  slope  of  1  in  80.  As  the  length  of  the 
culvert  is  200  feet,  the  head  required  for  a  circular  chan- 
nel is  2.5  feet,  while  that  required  for  the  rectangular 
channel  6'x4'  already  found,  is  three  feet. 

EXAMPLE  23.  Given  the  diameter  and  grade  of  a  Pipe 
to  find  the  mean  velocity  and  discharge  by  D' Arcy' s  formula 
(51),  for  clean  cast-iron  pipes. 

Humber,  in  his  work  on  Water  Supply,  states: — 
11  With  a  48-inch  cast-iron  pipe  in  the   Lock  Katrine 
Water  Works,  having  an  inclination  of  1  in  1056,  or  five 


OPEN    AND    CLOSED    CHANNELS.  235 

feet  per  mile,  the  actual  velocity  was  found  to  be  3.46 
feet  per  second,  and  D'Arcy's  formula  gives  practically 
the  same  results."  Compute  the  velocity  by  the  tables. 
In  Table  48,  computed  by  D'Arcy's  formula  for  clean 
pipes,  we  find  opposite  4  feet  diameter,  that  a  =  12.566, 

cv/r  =  H2.6,  and  ac^/r  =  1414.7. 

We  also  find  in  Table  33  that  opposite  a  grade  of  five 

feet  per  mile  \/s  =  .030773. 

Let  us  now  substitute  value  of  c\/r  and  \/s  in  formula 
(41),  and  we  have:  — 

v  ==  112.6X-  030773  =  3.46  feet  per  second,  being  the 
same  as  the  actual  velocity,  and  also  the  same  as  the 
velocity  obtained  by  computing  by  the  longer  method 
of  D'Arcy's  formula  (51). 

Now  Q  =  av  =  12.566X3.46  =  43.478  cubic  feet  per 
second. 

As  a  check  on  this,  let  us  substitute  the  value  of  ac\/r 

and  \/s  in  formula  (45)  and  we  have:  — 

Q=  1414.7  X.  030773  =43.535  cubic  feet  per  second-, 
being  practically  the  same  as  that  found  before. 

EXAMPLE  24.  Given  the  grade,  mean  velocity  and  value 
of  n,  of  a  Circular  Sewer  to  find  its  diameter. 

The  grade  of  a  circular  sewer  is  to  be  1  in  480,  its 
mean  velocity  4  feet  per  second,  and  its  value  of  n  =  .015. 
What  is  the  required  diameter? 

In  Table  33  we  find  opposite  a  slope  of  1  in   480  that 

V/«  =  .045644  —  substitute  this  and  the  value  of  v,  already 
given  in  formula  (42). 

and  we  have 


Vs 

cyr  =  _  —  -  =  87  .  63 
.045644 


236  FLOW    OF    WATER    IN 

Now  look  out  in  Table  55  for  the  nearest  value  of  c\/r 
to  this,  which  we  find  to  be  87.15  opposite  three  feet  four 
inches  in  diameter,  which  is  the  diameter  required. 

EXAMPLE  25.  Given  the  discharge,  grade  and  value  of 
n  of  a  Circular  Sewer  to  find  its  diameter. 

A  circular  brick  sewer,  with  a  value  of  n  =  .015,  is  to 
discharge  9  cubic  feet  per  second  and  to  have  a  grade  of 
1  in  200.  What  must  its  internal  diameter  be? 

In  Table  33,   opposite   a  slope  of    1   in   200,   we  find 

\/s  =  .07071.      Now  substitute  this  value  and  also  the 
value  of  Q  already  given  in  formula  (47):  — 

ac^/r  =  —  ^L.-  and  we  have 

Vs 

=  127.28 


.07071 
In  Table  55,   with  a  value  of  n  =  .015,  the  value  of 

ac\/r,  nearest  to  this  we  find  to  be  130.58  opposite  to 
which  is  the  diameter  of  1  foot  and  9  inches  which  is  the 
diameter  required. 

EXAMPLE  26.  Given  the  diameter,  the  value  of  n  and 
the  mean  velocity  in  a  Pipe,  to  find  its  inclination  or  grade. 

A  sheet-iron,  double  riveted  pipe,  18  inches  diameter, 
with  a  very  smooth  interior,  and  laid  in  an  almost 
straight  line,  is  to  have  a  velocity  of  3  feet  per  second. 
Under  the  above  favorable  conditions  its  value  of  n  is 
assumed  equal  to  .011.  What  should  its  slope  or  grade 
be  by  Kutter's  formula? 

In  Table  52,  with  a  value  of  n  =  .011   the   value  of 

c\/r  opposite  a  diameter  of  1  foot  6  inches  is  71.08. 
Substitute  this  value,  and  also  the  value  of  v  already 
given,  in  formula  (43):  — 


OPEN    AND    CLOSED    CHANNELS.  237 

V/s  =  -        =.  and  we  have 
cv/r 

^=  -708-  =   -042206 

Look  out  the  nearest  value  of  \/s  to  this  in  Table  33, 
and  we  find  it  to  be  .042258  opposite  a  slope  of  1  in  560. 
This  is  near  enough  for  all  practical  purposes.  If,  how- 
ever, a  greater  degree  of  accuracy  is  required,  we  have: — 

l/s  =  .042206  squaring  each  side 

s  ===  .001781346436, 
and          =561.      Therefore  the  slope  is  1  in  561. 

S 

EXAMPLE  27.  Given  the  diameter,  discharge  and  value 
of  n  of  a  Circular  Conduit  flowing  full  to  jind  the  slope  or 
grade. 

A  circular  conduit  flowing  full  is  to  have  a  diameter 
of  6  feet,  and  its  value  of  n  is  assumed  as  equal  to  .017. 
What  must  be  its  slope  or  grade  in  order  that  its  dis- 
charge may  be  180  cubic  feet  per  second? 

In  Table  56,  with  n  —  .017,  we  find  opposite  6  feet  in 

diameter   that   ac\/r  ==  3232.5.       Substitute  this   value 
and  also  the  value  of  Q  in  formula  (48),  and  wTe  have: — 

V"7=       Q      =      18Q     =   .055684 
ac]/T         3232.5 

In  Table  33  the  nearest  value  of  \/s  to  this  is  .055470 
opposite  a  slope  of  1  in  325.  The  required  slope  is, 
therefore,  1  in  325. 

EXAMPLE  28.  To  Jind  the  diameter  in  three  sections  of 
an  Intercepting  Seicer,  with  increasing  discharget  the 
grade  or  inclination  being  the  same  throughout,  and  the 
value  of  n  being  given. 

A  circular  brick  sewer  has,  for  500  feet  of  its  length  to 


238 


FLOW    OF    WATER    IN 


discharge,  flowing  full,  10  cubic  feet  per  second,  then 
for  600  feet  more  it  has  to  discharge  12  cubic  feet  per 
second,  and  again,  for  700  feet  further,  it  has  to  discharge 
15  cubic  feet  per  second.  The  total  fall  available  is  5 
feet.  Its  value  of  n  =  .015.  What  is  the  required  di- 
ameter and  fall  of  each  section? 

In  the  total  length  of  1,800  feet  there  is  a  fall  of  5  feet, 
that  is  at  the  rate  of  1  in  360.      In  Table  33,  opposite  a 

fall  of  1  in  360,  we  find  •  /«  ==  .052705. 

V  8 

In  this  equation  substitute  the  values  of  Q  and  s  for 
each  section  and  compute   the   corresponding   values  of 

ac\/r.       Now,    in   the  first    column  of    Table   55,   with 

n  =  .015,  and  opposite  these  values  of  ac\/r  we  shall  find 
the  diameters  required.  For  example:  — 

10 


By  formula  (47):  —   ac\/^  =  —  — 


acy  r  = 


.052705 

12 
.052705 

JL5 
7052705 


=  189.7 


=  227.7 


1  8 

o> 

1 

a 
O 


diam.  2'  0" 


diam.  2'  2" 


diam.  2'  4" 


Now  s  =  ---.'.  h  =  si,  therefore,  the 

Fall  of  first  section  =  d  =  .002777  X  500.  .  .  .  =  1.39  ft. 
Fall  of  second  section  =  si  =  .002777  X  600. .  .  =  1.67  ft. 
Fall  of  third  section  =  ttl  —  .002777  X  700  .'.  .=  1.95  ft, 

Total  fall 5.00  ft. 

We  have,  therefore, 

1st  section,  diameter  2'  0",  fall  1.39  ft. 
2d  section,  diameter  2'  2",  fall  1.67  ft. 
3d  section,  diameter  2'  4",  fall  1.94  ft. 


OPEN    AND    CLOSED    CHANNELS.  239 

EXAMPLE  29.     To  find  the  value  of  c  and  n  of  a  Pipe. 

A  tuber  culated  pipe  originally  twenty-four  inches  in 
diameter,  but  reduced  by  tuberculation  to  a  mean  diam- 
eter in  the  clear  of  twenty-three  inches,  and  ha\dng_a^ 
slope  of  1  in  1000,  is  found  to  discharge  4.5  cubic  feet 
per  second.     What  is  its  value  of  c  and  n? 

4'5      =  1.56  feet  per  second. 


a          2.885 
In  Table  33  it  will  be  found  that  a  slope  of  1  in  1000 

has  \/s  =  .031623,  and  in  Table  47  opposite,  a  diameter 
of  twenty-three  inches  the  value  of  r=  .479,  therefore 

j/V  =  .69.  Substitute  values  of  v,  \/H  and  \/r  in  for- 
mula (50). 

c  =  —/==        -----   and  we  have 
Vr    X  Vs 

c  =  -         -L56-  =  71.5 

.69  X    .031623 

Now  let  us  look  in  the  tables  of  the   values   of  c  and 

c\/r,  and  under  a  slope  of  1  in  1000,  and  opposite  \/r  =.7 
(which  is  the  nearest  given  to  .69),  until  we  find,  in 
Table  21,  under  a  value  of  n  =  .017  that  c  =  72.6,  but 
by  the  column  of  difference  it  should  be  .51  less,  there- 
fore, the  value  of  c  =  72.09  and  n  —  .017. 

Now,  as  a  check  on  this,  let  us  find  in  Table   56   with 
n=  .017,  and  opposite  a  diameter  1  foot  11  inches,  that 

ac\/r  ==  144.     Substitute  this  value  and  also  the  value  of 
\/s  given  above,  in  formula  (45),  and  we  have:  — 
Q  =  ac\/r  X  \/s 

=  144X  .031623 

=  4.55   cubic   feet  per  second,  being  near 
enough  for  all  practical  purposes. 


240  FLOW    OF    WATER    IN 

EXAMPLE  30.  Given  the  diameter  of  an  old  pipe  to  find 
the  diameter  of  a  neiu  pipe  to  discharge  double  that  of  the 
old  pipe. 

An  old  cast-iron  pipe  3  feet  6  inches  in  diameter, 
whose  natural  co-efficient  is  assumed  =  .013,  is  to  be  re- 
placed by  a  new  sheet-iron  pipe  capable  of  discharging 
double  that  of  the  old  pipe,  the  slope  remaining  un- 
changed. What  is  the  diameter  by  Kutter's  formula  of 
the  new  pipe?  It  is  to  bo  dipped  in  hot  asphalt,  and  its 
natural  co-efficient  is  assumed  —  .011 

Find  by  inspection   in   Table   54,  with  n  =  .013,  the 

value  of  ac]/i'  opposite  3  feet  6  inches  diameter,  and  it 
is  found  to  be  1021.1.  Then  1021.1  X  2=  2042.2.  As 
the  value  of  n  for  the  new  pipe  =  011,  look  out  in  Table 

52  the  value  of  ac\/r  nearest  to  2042.2  and  it  is  found 
to  be  2072.7  opposite  a  diameter  of  4  feet  3  inches,  which 
is  the  diameter  required. 

EXAMPLE  31.  Given  the  discharges  and  grades  of  a 
System  of  Pipes  to  find  the  diameters. 

A  system  of  pipes  consisting  of  one  main  and  two 
branches,  is  required  to  discharge  by  one  branch  15,  and 
by  another  24  cubic  feet  of  water  per  minute,  and,  there- 
fore, the  main  is  to  discharge  39  cubic  feet  of  water  per 
minute.  The  levels  show  the  main  pipe  to  have  an  in- 
clination of  4  feet  in  1000  feet,  the  first  branch  3  feet  in 
600  feet,  and  the  second  branch  1  foot  in  200  feet.  What 
should  be  the  diameters  of  the  pipe? 

The  pipe  being  clean  cast-iron  pipe,  Table  48,  derived 
from  D'Arcy's  formula  (51),  will  be  used  in  the  solution 
of  the  problem. 

The  main  is  to  discharge  39  cubic  feet  per  minute, 
equivalent  to  0.65  cubic  feet  per  second,  with  a  grade  of 
1  in  250.  One  branch  is  to  discharge  15  cubic  feet  per 


OPEN    AND    CLOSED    CHANNELS.  241 

minute,  equivalent  to  0.25  cubic  feet  per  second,  with  a 
grade  of  1  in  200,  and  the  other  branch  24  cubic  feet  per 
minute,  equivalent  to  0.4  cubic  feet  per  second,  with  a 
grade  of  1  in  200. 

By  inspection,  we  find  in  Table  33,  that  with  a  grade 

of  1  in  250  the  \/s  ==  .063246  and  a   slope  of  1  in   200 

has  ^/s  =.07071. 

Now,  by  formula  (47):— 

/-          Q 
acyr  =  —7=.  •'  -  for  main  pipe 

Vs 


nearest  value   of   ac\/r  to  this,  in  Table  48,  is  10.852, 
opposite  to  which  is  the  diameter,  7  inches. 
In  the  same  way  for  the  first  branch 

0  25 
ac\/r  =  —  -  -  =  3.535,  and  the  nearest  value 

f 

of  ac\/r  to  this  is  4.561,  corresponding  to  diameter  of 
5  inches. 

For  the  second  branch:  — 

0  4 

ac\/V  =  --   =  5.657,  and  the 
.07071 

nearest  value  of  acj/r  to  this,  in  Table  48,  is  7.3  opposite 
a  diameter  of  6  inches.  The  required  diameters  are, 
therefore,  for  the  main  pipe  7  inches,  for  the  first  branch 
5  inches,  and  for  the  second  branch  6  inches. 

Although  the  explanation  of  this  example  in  the  use 
of  the  tables  may  appear  somewhat  long,  still  the  actual 
work  can  be  done  very  rapidly  and  with  little  trouble. 
If  a  comparison  is  made  of  the  work  required  for  the 
solution  of  this  example,  as  given  above,  with  the  work 
required  for  its  solution  by  the  method  of  approximation 
as  given  in  Weisbach's  Mechanics  of  Engineering,  from 
16 


242  FLOW    OF    WATER    IN 

which  the  example  is  extracted,  it  will  be  seen  that 
there  is  a  great  saving  of  labor  effected  by  the  use  of  the 
tables. 

EXAMPLE  32.  To  find  the  dimensions  of  an  Egg-shaped 
Sewer  to  replace  a  Circular  Sewer. 

A  circular  sewer  5  feet  in  diameter  and  4,800  feet  in 
length  has  a  fall  of  16  feet.  It  is  to  be  removed  and  re- 
placed by  an  egg-shaped  sewer  with  a  fall  of  8  feet,  whose 
discharge  flowing  full  shall  equal  that  of  the  circular 
sewer  flowing  full,  the  value  of  n  in  each  sewer  being 
assumed  =  .015. 

A  grade  of  16  in.  4800  ==  1  in  300,  and  in  Table  33  the 

\/8  corresponding  to  this  is,  .057735.  In  Table  55, 
opposite  5  feet  diameter,  the  value  of  ac\/r  =  2272.7. 

Substitute  this  value  and  also  the  value  of  ]/s  in  formula 
(45),  and  we  have: — 

Q  =  2272.7  X  .057735  =  131.21  cubic  feet  per  second, 
the  discharge  of  the  circular  sewer.  The  egg-shaped 
sewer  is  to  have  a  grade  of  8  in  4800  =  1  in  600,  and  in. 

Table  33  the  \/H  corresponding  to  this  =.040825.  Sub- 
stitute this  value  and  also  the  value  of  \/ A  just  found  in 
formula  (47),  and  we  have: — 

/-  Q  131.21 

acyr  =  —3*-.    =    . —          .    =  3213.9 
1/7          .040825 

In  Table  65  the  nearest  value  of  ac\/r  to  this  is  3353, 
opposite  an  egg-shaped  sewer  having  the  dimensions  of 
4'  10"  X  7'  3",  therefore,  with  a  value  of  n  =  .015  for 
both  sewers. 

A  circular  sewer  of  5  feet  in  diameter,  and  having  a 
grade  of  1  in  300,  has  the  same  discharging  capacity  as 
an  egg-shaped  sewer  4'  10"  X  7'  3",  having  a  grade  of 
1  in  600. 


OPEN    AND    CLOSED    CHANNELS.  243 

EXAMPLE  33.  To  find  the  diameter  of  a  Circular  Seiuer 
whose  discharge  flowing  full  depth  shall  equal  that  of  an 
Egg-shaped  Sewer  flowing  one-third  full  depth. 

Find  the  diameter  of  a  circular  sewer,  with  ~n  -=^7013, 
whose  discharge  flowing  full  shall  equal  that  of  the  egg- 
shaped  sewer  in.  last  example,  flowing  one-third  full 
with  n  =  .015,  the  slope  being  the  same  in  each. 

In  Table  67  with  n  =  .015  and  ^  full  depth  and  oppo- 
site the  size  4'  10"  X  7'  3"  we  find  acy/r  =  657.53.  Also 

in  Table  54  circular  n  =  .013,  the  nearest  value  of  ac\/r 
to  this  is  found  to  be  674.09  opposite  a  diameter  of  3  feet, 
which  is  the  diameter  of  the  circular  sewer  required. 

EXAMPLE  34.  In  the  same  way  as  in  Example  33 ,  we 
can  find  the  diameter  of  a  Circular  Sewer  whose  velocity 
flowing  full  shall  equal  the  velocity  of  an  Egg-shaped  Sewer 
flowing  one-third  full  depth. 

EXAMPLE  35.  To  find  the  dimensions  and  grade  of  an 
Egg-shaped  Sewer  flowing  full,  the  mean  velocity  and  disr 
charge  being  given. 

An  egg-shaped  sewer  flowing  full  is  to  have  a  mean 
velocity  not  greater  than  five  feet  per  second,  and  is  to 
discharge  108  cubic  feet  per  second.  Its  value  of  n  is 
.015.  What  are  its  dimensions  and  grade? 

By  formula  (46). 

a  =  J?_  =  -.—  =  21.6  square  feet. 
v  5 

In  column  two  of  Table  65,  the  nearest  area  to  this  is 
21.566  square  feet  opposite  the  dimensions  4'  4"  X  6'  6". 

In  the  same  line  we  find  the  value  of  c\/r=  116.0,  and 

ac\/r  =  2501.4.  Substitute  this  latter  value  and  the 
value  of  Q  in  formula  48,  and  we  have: — 

1/s  =  —^=  •=      *°,8  ,  -   .043176,  and  in  table  33. 
acv/>         2501.4 


244  FLOW    OF    WATER    IN 

the  nearest  to  this,  is  .043234  opposite  a  slope  of  1  in 
535.  The  sewer  required  is  therefore  4'  4"  X  6'  6",  and 
has  a  slope  of  1  in  535. 

As  a  check  on  this  work  by  formula  45,  and  by  substi- 
tuting the  values  of  a,  c\/r  and  \/s  already  found,  we 
have : — 

Q  =  a  X  c]/r  X  i/s 
=  21.6X  116  X  .043234 
=  108.3  cubic  feet  per  second,  being  near 
enough  for  all  practical  purposes. 

EXAMPLE  36.  The  diameter  and  grade  of  a  Circular 
Seiver  being  given,  to  find  the  dimensions  and  grade  of  an 
Egg-shaped  Sewer,  whose  discharge  floiuing  tico-thirds  full 
depth  shall  equal  that  of  the  Circular  Sewer  flowing  full 
depth,  and  ivhose  mean  velocity  at  the  same  depth  shall  not 
exceed  a  certain  rate. 

A  circular  sewer  6  feet  in  diameter  and  with  a  slope  of 
1  in  600  is  to  be  removed  and  to  be  replaced  by  an  egg- 
shaped  sewer  whose  discharge  flowing  at  two-thirds  of 
its  full  depth,  shall  be  equal  to  that  of  the  circular  sewer 
flowing  full  depth,  and  whose  mean  velocity  at  the  same 
two-thirds  depth  shall  not  exceed  five  feet  per  second, 
the  value  n  in  each  being  =  .015.  Give  the  dimensions 
and  slope  of  the  egg-shaped  sewer. 

In  Table  55  for  circular  channels  with  n  —  .015  and 
6  feet  in  diameter,  the  value  of  ac\/r  =  37 02 .3 ,  and  in 

Table  33  opposite  1  in  600,  the  value  of  v/s  =  .040825. 
Substitute  these  values  in  formula  (45). 

C]  —  ac\/r  X  1/8  and  we  get 
Q  =  3702 . 3  X  .040825  =  151.15  cubic  feet  per 
second    as  the    discharge  of  the    circular   sewer.     Now 


OPEN    AND    CLOSED    CHANNELS.  245 

substitute  this  discharge  and  the  velocity  given,  five  feet 
per  second,  in  formula  (46). 

a  =  —  and  we  get 

a  = —  =  30 . 23  square  feet,  the 

5 

area  at  two-thirds  full  depth  of  the  egg-shaped  sewer. 

In  Table  66,  of  egg-shaped  sewers  flowing  two-thirds 
full  depth  with  n  =  .015,  we  find  the  nearest  value  of 
a  to  this  is  30.317  square  feet  opposite  a  sewer  having 
the  dimensions  of  6  feet  4  inches  by  9  feet  6  inches. 

At  the  same  time  take  out  the  value  of  aci/r  in  the  same 
line  and  we  find  it  equal  to  4811.9.     Substitute  this  value 

of  ac\/r,  and  also  the  value  of  Q,  already  found  in    for- 
mula (48), 

\/s  =  — Su-  and  we  get 


ac 

=          -  -031412- 


Look  out  in  Table  33,  and  by  interpolation  we  find 
the  nearest  slope  to  this  is  1  in  1015.  The  egg-shaped 
sewer  required  is,  therefore,  Q'  4"  X  9'  6"  and  the  grade 
1  in  1015. 

EXAMPLE  37.  To  find  the  dimensions  and  grade  of  an 
Egg-shaped  Sewer  to  have  a  certain  discharge  when  flowing 
full,  and  whose  mean  velocity  shall  not  exceed  a  certain  rate 
when  flowing  two-thirds  full  depth. 

An  egg-shaped  sewer  is  to  discharge  110  cubic  feet  per 
second  flowing  full,  and  its  mean  velocity  flowing  two- 
thirds  full  depth  is  not  to  exceed  5  feet  per  second. 
Find  its  dimensions  and  slope,  the  value  of  n  being 
taken  =  .015. 


246  FLOW    OF    WATER    IN 

In  an  egg-shaped  sewer  the  velocity  flowing  full  is 
always  less  than  the  velocity  flowing  two-thirds  full, 
therefore,  as  a  first  approximation  let  us  assume  the  ve- 
locity flowing  full  at  5  feet  per  second. 

a  =     ^     =  -   ~  =  22  square  feet,  the  area  of  the 
v  5 

assumed  egg-shaped  sewer  flowing  full,  and  in  Table  65 
the  nearest  size  sewer  to  this  is  4'  4"  X  6'  6".  Now  with 

these  dimensions  the  value  of  c\/r  full  depth  =  116.0  and 

Table  66  the  value  of  c\/r  two-thirds  full  depth  ==  123.1; 
therefore,  we  may  assume  that  the  velocity  of  the  sewer 
of  the  given  dimensions  flowing  full  is  about  six  per 
cent,  less  than  when  flowing  two-thirds  full  depth,  that 
is,  assuming  the  velocity  at  two-thirds  full  depth  =  5  feet 
per  second  the  velocity  at  full  depth  will  be  about  4.7 
feet  per  second.  Substituting  this  velocity  and  also  the 
given  discharge  in  formula  (46), 

a  =  =  23.4  square  feet,  the  area  of 

egg-shaped  sewer  flowing  full.  In  Table  65,  the  near- 
est size  opposite  to  this  area  is  4'  6"  X  6'  9"  which  is  the 
diameter  required  for  the  egg-shaped  sewer.  At  the 
same  time  that  this  size  of  sewer  is  found,  its  value  of 

ae\/r  will  be  found  on  the  same  line  ==  2770.  Substi- 
tute this  value  and  also  the  value  of  Q  in  formula  (48), 
and  we  have:  — 


=  .039711. 
2770 

Look  out  in  Table  33  and  the  nearest  \/s  to  this  is 
.039684  opposite  a  slope  of  1  in  635.  Therefore,  the 
size  of  the  sewer  is  4'  6"  X  6'  9",  and  its  grade  1  in  635. 
As  a  check  on  the  above  work  by  substituting  the  factors 
already  found,  we  can  find  the  discharge  of  the  sewer 


OPEN    AND    CLOSED    CHANNELS.  247 

flowing  full  depth,  and  also  find  the   mean  velocity  of 
the  same  sewer  flowing  two-thirds  full  depth. 

Q  =  ac^/r  X  v/s  =  2770  X  .039684  ==  109.9  cubic  feet 
per  second,  that  is,  practically,  110  cubic  feet  peiLsecond 
which  was  required,  and 

v  =  c\/r  X  v/s  =  126-3  X  .039684  —  5.01  feet  per  sec- 
ond, that  is,  practically  5  feet  per  second,  which  was  re- 
quired. 


248 


FLOW    OF    WATER    IN 


TABLE  47. 

Giving  the  value  of  the  hydraulic  mean  depth  r,  for  Circular  Pipes,  Con- 
duits and  Sewers.  The  hydraulic  mean  depth  is  equal  to  one-fourth  the 
diameter  of  a  circular  channel. 


Diam- 
eter, 
ft.       in. 

r 
in  feet. 

Diam- 
eter, 
ft.      in. 

r 
in  feet. 

Diam- 
eter, 
ft.      in. 

r 

in  feet. 

Diam- 
eter, 
ft.        in. 

r 
in  feet. 

I 

.0078 

2         1 

.521 

4         7 

.146 

9         3 

2.312 

.0104 

2         2 

.542 

4         8 

.167 

9         6 

2.375 

1 

.0156 

2         3 

.562 

4         9 

.187 

9         9 

2.437 

1 

.0208 

2         4 

.583 

4       10 

.208 

10 

2.5 

li 

.0260 

2         5 

.604 

4       11 

.229 

10         3 

2.562 

H 

.0312 

2        6 

.625 

5 

.25 

10         6 

2.625 

It 

.0364 

2        7 

.646 

5         1 

.271 

10         9 

2.687 

2 

.0417 

2         8 

.667 

5         2 

.292 

11 

2.750 

2* 

.052 

2         9 

.687 

5         3 

1.312 

11         3 

2.812 

3 

.063 

2       10 

.708     ! 

5         4 

1.333 

11         6 

2.875 

4 

.084 

2       11 

.729 

5         5 

1.354 

11         9 

2.937 

5 

.104 

3 

.75 

5         6 

1.375 

12 

3. 

6 

.125 

3         1 

.771 

5        7 

1  .  396 

12         3 

3.062 

7 

.146 

3         2 

.792 

5         8 

1.417 

12         6 

3.125 

8 

.167 

3         3 

.812 

5         9 

1.437 

12         9 

3.187 

9 

.187 

3         4 

.833 

5       10 

1.558 

13 

3.25 

10 

.208 

3        5 

.854 

5       11 

1.479 

13         3 

3.312 

11 

.229 

3         6 

.875 

6 

1.5 

13         6 

3.375 

.250 

3         7 

.896 

6         3 

1.562 

13         9 

3.437 

1 

.271 

3         8 

.917 

6         6 

1.625 

14 

3.5 

2 

.292 

3         9 

.937 

6         9 

1.687 

14         6 

3.625 

3 

.313 

3       10 

.958 

7 

1.75 

15 

3.75 

4 

.333 

3       11 

.979 

7        3 

1.812 

15         6 

3.875 

5 

.354 

4 

1. 

7        6 

1.879 

16 

4. 

6 

.375 

4         1 

1.021 

7        9 

1.937 

16         6 

4.125 

7 

.396 

|  4         2 

1.042 

8 

2. 

17 

4.250 

8 

.417 

4         3 

1.062 

8         3 

2.062 

17        6 

4.375 

9 

.437 

4         4 

1.083 

8         6 

2.125 

18 

4.5 

10 

.458 

4         5 

1.104 

8         9 

2.187 

19 

4.75 

11 

.479 

4         6 

1  .  125 

9 

2.25 

20 

5. 

2 

.5 

1 

OPEN    AND    CLOSED    CHANNELS. 


249 


TABLE  48. 

Circular  Pipes,  Conduits,  etc.,  flowing  under  pressure.  Based  011 
D'Arcy's  formula  for  the  flow  of  water  through  clean  cast-iron  pipes. 

Table  giving  the  value  of  a,  and  also  the  values  of  the  factors  c\/r  and 
ac-s/77  for  use  in  the  formulas; — 

v  =-.  c\/r   X  -\A~  aud  Q  —  ac\/r   X  \/s 

These  factors  are  to  be  used  only  for  clean  cast-iron  pipes,  flowing  under 
pressure,  and  also  for  other  pipes  or  conduits  having  surfaces  of  other 
material  equally  rough. 


d  =  di- 
ameter 
in 
ft.     in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 
cVr 

For  dis- 
charge 

ac\/r 

d  =  di- 
ameter 
in 
ft.    in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 
cv/r 

For  dis- 
charge 
ac\/r 

§ 

.00077 

5.251 

.00403 

1     10 

2  640 

75.32 

198.83 

| 

.00136 

6.702 

.00914 

1     11 

2.885 

77.05 

222.30 

1 

.00307 

9.309 

.02855 

j  2 

3.142 

78.80 

247.57 

1 

.  00545 

11.61 

.06334 

2       1 

3.409 

80.53 

274.53 

li 

.00852 

13.68 

.11659 

i  2       2 

3.687 

82.15 

302.90 

H 

.01227 

15.58 

.19115 

2       3 

3.976 

83.77 

333.07 

if 

.01670 

17.32 

.28936 

|  2       4 

4.276 

85.39 

365.14 

2 

.02182 

18.96 

.41357 

2       5 

4.587 

86.89 

398.57 

2i 

.0341 

21.94 

.74786 

2       6 

4.909 

88.39 

433.92 

3 

.0491 

24.63 

1.2089 

2      7 

5.241 

90.01 

471.73 

4 

.0873 

29.37 

2.5630 

2       8 

5.585 

91.51 

511.10 

5 

.136 

33.54 

4.5610 

2       9 

5.939 

92.90 

551/72 

6 

.196 

37.28 

7.3068 

2     10 

6.305 

94.40 

595.17 

7 

.267 

40.65 

10.852 

2     11 

6.681 

95.78     639.88 

8 

.349 

43.75 

15.270 

3 

7.068 

97.17     686.76 

9 

.442 

46.73 

20.652 

3       1 

7.466 

98.55     735.75 

10 

.545 

49.45 

26.952 

3       2 

7.875 

99.93 

786.94 

11 

.660 

52.16 

34.428 

3       3 

8.295 

101  2 

839.38 

1 

.785 

54.65 

42.918 

3      4 

8.726 

102.6 

895.07 

1       1 

.922 

57. 

52.551 

3       5 

9.169 

103.8 

952.10 

1       2 

1.069 

59.34 

63.435 

3      6 

9.621 

105.1 

1011.2 

1       3 

1.227 

61  56 

75.537 

3      7 

10.084 

106.4 

1072.6 

1       4 

1.396 

63.67 

88.886 

3      8 

10.559 

107.6 

1136.5 

1       5 

1.576 

65.77 

103.66 

3      9 

11.044 

108.9 

1202.7 

1       6 

1.767 

67.75 

119.72 

3     10 

11.541 

110.2 

1271.4 

1       7 

1.969 

69.74 

137.31 

3     11 

12.048 

111.4 

1342.4 

1       8 

2.182 

71.71 

156.46 

4 

12.566 

112  6 

1414.7 

1       9     !  2.405 

73.46 

176.66 

4       1 

13.096 

113.7 

1489.4 

250 


FLOW    OF    WATER    IN 


TABLE  48. 

Circular  Pipes,  Conduits,  etc.,  flowing  under  pressure.  Based  on 
D'Arcy's  formula  for  the  flow  of  water  through  clean  cast-iron  pipes,  for 
use  in  the  formulae: — 

V»  and  Q  =  ac^/r  X  \A 


d  =  di- 
ameter 
in 
ft.       in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 

Cv/f 

For  dis- 
charge 
ac\/r 

d  =  di- 
ameter 
in 
ft.        in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 
cVr 

For  dis- 
charge 
ac\/r 

4           2 

13.635 

115. 

1567.8 

8         6 

56.745 

165. 

9364.7 

3 

14.186 

116.1 

1647.6 

8         9 

60.132 

167.4 

10068. 

4 

14  748 

117.3 

1729.8 

9 

63.617 

169.8 

10804. 

5 

15.321 

118.4 

1814.6 

9         3 

67.201 

172  2 

11575. 

6 

15.904 

119.6 

1901.9 

9         6 

70.882 

174.5 

12370. 

7 

16.499 

120.6 

1990.1 

9         9 

74.662 

176.8 

13200. 

8 

17  104 

121.8 

2082.6 

10 

78.540 

179.1 

14066. 

9 

17.721 

122.8 

2176.1 

10         3 

82.516 

181.4 

14967  . 

4         10 

18.348 

124. 

2274.1 

10         6 

86.590 

183.6 

15893. 

4         11 

18.986 

125.1 

2374.8 

10         9 

90.763 

185.7 

16856. 

5 

19.635 

126.1 

2476.4 

11 

95.033 

187.9 

17855. 

5           1 

20.295 

127.2 

2580.5 

11         3 

99.402 

190.1 

18892. 

5           2 

20.966 

128.3 

2689.9 

11         6 

103.869 

192.2 

19966. 

5           3 

21.648 

129.3 

2799.7 

11         9 

108.434 

194.3 

21065. 

5           4 

22.340 

130.4 

2912.4 

12 

113.098 

196.3 

22204. 

5          5 

23.044 

131.4 

3027.8 

12         3 

117.859 

198.4 

23379. 

5           6 

23.758 

132.4 

3146.3 

12         6 

122.719 

200.4 

24598  . 

5           7 

24.484 

133.4 

3264.9 

12         9 

127.677 

202.4 

25840. 

5           8 

25  .  220 

134.4 

3388.9 

13 

132.733 

204.4 

27134. 

5           9 

25.967 

135.4 

3516. 

13         3 

137.887 

206.4 

28456. 

5         10 

26.725 

136.4 

3646.1 

13         6 

143.139 

208.3 

29818. 

5         11 

27.494 

137.4 

3776.2 

13         9 

148.490 

210.2 

31219. 

6 

28.274 

138.4 

3912.8 

14 

153.938 

212.2 

32664. 

6           3 

30.680 

141.3 

4333.6 

14         6 

165.130 

216. 

35660. 

6           6 

33.183 

144.1 

4782.1 

15 

176.715 

219.6 

38807. 

6           9 

35.785 

146.9 

5255.1 

15         6 

188.692 

223.3 

42125. 

7 

38.485 

149.6 

5757.5 

16 

201.062 

226.9 

45621. 

7          3 

41.283 

152  .  2 

6284.6 

16         6 

213.825 

230.4 

49273. 

7          6 

44.179 

154.9 

6841.6 

17 

226.981 

233.9 

53082. 

7          9 

47.173 

157.5 

7429.3 

17        6 

240.529 

237  .  3 

57074. 

8 

50.266 

160. 

8043. 

18 

254.470 

240.7 

61249. 

8           3 

53.456 

162.5 

8688. 

19 

283.529 

247.4 

70154. 

20 

314.159 

253.8 

79736. 

OPEN    AND    CLOSED    CHANNELS. 


251 


TABLE  49. 

Circular  Pipes,  Conduits,  etc.,  flowing  under  pressure.  Based  on 
D  Arcy's  formula  for  the  flow  of  water  through  old  cast-iron  pipes  lined 
with  deposit. 

Table  giving  the  value  of  a,  and  also  the  values  of  the  factors-rj-v^"  and 
ac\/r  for  use  in  the  formulae: — 

v  =  c\/r  X  -s/^aiid  Q  =  ac\/r   X  \/s 

These  factors  are  to  be  used  only  for  old  cast-iron  pipes  flowing  under 
pressure,  and  also  for  other  pipes  or  conduits  having  surfaces  of  other 
material  equally  rough. 


Diam- 
eter in 
ft.   in. 

a  =  area 
in  square 
feet. 

For  ve- 
locity 
c^r 

For 

discharge 
ac\/r 

Diam- 
eter in 
ft.    in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 
cVr 

For 

dis- 
charge 

ac\/r 

1 

.  00077 

3.532 

.00272 

1       9 

2.405 

49.410 

118.83 

1 

.00136 

4.507 

.00613 

1     10 

2.640 

50.658 

133.74 

4 

.00307 

6.261 

.01922 

1     11 

2.885 

51.829 

149.53 

1 

.  00545 

7.811 

.04257 

2 

3.142 

52.961 

166.41 

11 

.00852 

9  255 

.07885 

2       1 

3.409 

54.166 

184.65 

H 

.01227 

10.48 

.  12855 

2       2 

3.687 

55.258 

203.74 

if 

.01670 

11.65 

.  19462 

2       3 

3.976 

56  .  348 

224.04 

2 

.02182 

12.75 

.27824 

2       4 

4.276 

57.436 

245  .  60 

2i 

.0341 

14.76 

.50321 

2       5 

4.587 

58.448 

268.10 

3 

.0491 

16.56 

.81333 

2       6 

4.909 

59.455 

291.87 

4 

.0873 

19.75 

1.7246 

2       7 

5.241 

60.544 

317.31 

5 

.136 

22  56 

3.0681 

2       8 

5  .  585 

61.55 

343.8 

6 

.196 

25.07 

4.9147 

2       9 

5.939 

62.49 

371.1 

7 

.267 

27.34 

7  .  2995 

2     10 

6.305 

63.49 

400.3 

8 

.349 

29.43 

10.271 

2     11 

6.681 

64.42 

430.4 

9 

.442 

31.42 

13.891 

3 

7.068 

65.35 

461.9 

10 

.545 

33.26 

18.129 

3       1 

7.466 

66.29 

494.9 

11 

.660 

35.09 

23  .  158 

3       2 

7.875 

67.21 

529.3 

1 

.785 

36.75 

28.867 

3       3 

8.295 

68.09 

564.6 

1     1 

.922 

38.33 

35.345 

3       4 

8.726 

69. 

602. 

2 

1.069 

39.91 

42.668 

3       5 

9.169 

69.85 

640.4 

3 

1.227 

41.41 

50.811 

3       6 

9.621 

70.70 

680.2 

4 

1  .  396 

42.83 

59.788 

3       7 

10.084 

71.55 

721.5 

5 

1.576 

44.24 

69.723 

3       8 

10.559 

72.40 

764.5 

6 

1.767 

45.57 

80.531 

3       9 

11.044 

73.25 

809. 

7 

1  .  969 

46.90 

93.357 

3     10 

11.541 

74.10 

855.2 

8 

2.182 

48.34 

105.25 

3     11 

12.048 

74.95 

903. 

252 


FLOW    OF    \YATER    IN 


TABLE  49. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  under  pressure.  Based 
on  D'Arcy's  formula  for  the  flow  of  water  through  old  cast-iron  pipes 
lined  with  deposit,  for  use  in  the  formulae— 

v  =  c*/r  X  \A~  and  Q  =  ac\/r  X  Vs 


Diam- 
eter in 
ft.       in 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 
c\/r 

For  dis- 
charge 
ac^/'T 

Diam- 
eter in 
ft.      in. 

a  =  area 
in  square 
feet. 

For  ve- 
locity 
c\/r 

For  dis- 
charge 
ac\/r 

4 

12.566 

75.73 

951.6 

8       6 

56.745 

111. 

6299.1 

4           1 

13.096 

76.50 

1000.8 

8       9 

60.  132 

112.6 

6772.2 

4           2 

13.635 

77.35 

1054.6 

9 

63.617 

114.2 

7267.3 

4           3 

14.186 

78.12 

1108.2 

9      3 

67  .  201 

115.8 

7785.2 

4           4 

14.748 

78.89 

1163.5 

9      6 

70.882 

117.4 

8320.6 

4           5 

15.321 

79.66 

1220.5 

9      9 

74.6G2 

118.9 

8879. 

4           6 

15.904 

80.43 

1279.2 

10 

78.540 

120.4 

9460  9 

4          7 

16.499 

81.13 

1338.6 

10      3 

82.516 

122. 

10CC7. 

4          8 

17.104 

81.90 

1400.8 

10      6 

86.590 

123.4 

10GCO. 

4          9 

17.721 

82.20 

1456.8 

10      9 

90.763 

124.9 

11338. 

4         10 

18.348 

83.37 

1529.6 

11 

95.033 

126.3 

12010. 

4         11 

18.986 

84.14 

1597.5 

11       3 

99.402 

127.8 

127C7. 

5 

19.635 

84.83 

1665.7 

11       6 

103.869 

129.3 

13429. 

5           1 

20.295 

85.54 

1735.8 

11'      9 

108.434 

130.6 

141G9. 

5           2 

20  .  966 

86.30 

1809.3 

12 

113.098 

132. 

14935  . 

5           3 

21.648 

86.99 

1883.2 

12       3 

117.859 

133.4 

15727. 

5           4 

22.340 

87.69 

1958.9 

12      6 

122.719 

134.8 

16545. 

5           5 

23.044 

88.38 

2036.6 

12       9 

127.677 

136.1 

17380. 

5           6 

23.758 

89.07 

2116.2 

13 

132.733 

137.5 

1825-2. 

5          7 

24.484 

89.69 

2191.5 

13      3 

137.887 

138.8 

19140. 

5          8 

25  .  220 

90.38 

2279.5 

13      6 

143.139 

140.1 

2005G. 

5          9 

25  967 

91.08 

2365. 

13       9 

148.490 

141.4 

20999. 

5         10 

26.725 

91.77 

2452.9 

14 

153.938 

142.7 

21971 

5         11 

27.494 

92.39 

2540.1 

14      6 

165.130 

145.2 

23986. 

6 

28.274 

93.08 

2631.7 

15 

176.715 

147.7 

26103. 

6          3 

30.680 

95. 

2914.8 

15      6 

188.692 

150.1 

28335. 

6          6 

33.183 

96.93 

3216.4 

16 

201.062 

152.6 

30686. 

6          9 

35.785 

98.78 

3534.7 

16      6 

213.825 

155. 

33144. 

7 

38.485 

100.61 

3872.5 

17 

226.981 

157.3 

35704. 

7          3 

41.283 

102.41 

4227.1 

17      6 

240.529 

159.6 

38389. 

7          6 

44.179 

104.11 

4601.9 

18 

254.470 

161.9 

41199 

7          9  |  47.173 

105.91 

4997.2 

19 

283.529 

166.4 

47186. 

8 

50.266      107.61 

5409.9 

20 

314.159 

170.7 

53633. 

8           3 

53.456 

109.31 

5843.6 

1 

OPEN    AND    CLOSED     CHANNELS. 


253 


TABLE  50. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  full.  Based  on  Kutter's 
formula,  with  n  —  .009. 

Table  giving  the  values  of  a,  and  also  the  values  of  the  factors  c\/r  and 
ac\/v"  for  use  in  the  formulae: — 

v  =  c\/r   X  Vs  and  Q  =  ac\/r   X  -^/s 

These  factors  are  to  be  used  only  when  the  value  of  n,  that  is  the  co- 
efficient of  roughness  of  lining  of  channel  =  .09,  as  for  well-planed  tim- 
ber in  perfect  order  and  alignment;  otherwise,  perhaps  .01  would  be  suit- 
able. It  is  also  suitable  for  other  channels  having  surfaces  equally  rough. 


Diam- 
eter in 
ft.       in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 
c\/r 

For  dis- 
charge 
ac^r 

Diam- 
eter in 
ft.      in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 

CV/F 

For  dis- 
charge 
acv/V" 

5 

.136 

35.31 

4.803 

2         6 

4.909 

128.8 

622.3 

6 

.196 

40.62 

7.962 

2        7 

5.241 

131.9 

691.3 

7 

.267 

45.70 

12.20 

2        8 

5.585 

134.7 

752.2 

8 

.349 

50.55 

17.64 

2         9 

5.939 

137.3 

815.3 

9 

.442 

55.13 

24.37 

2       10 

6.305 

140  1 

883.4 

10 

.545 

59.49 

32.42 

2       11 

6.681 

142.7 

953.7 

11 

.660 

64. 

42.24 

3 

7.068 

145.4 

1027.6 

1 

.785 

68.25 

53.60 

3         1 

7.466 

148.1 

1105.5 

1           1 

.922 

72.11 

66.49 

3         2 

7.875 

150.7 

1187.1 

1           2 

.069 

76.06 

81.31 

3         3 

8.295 

153.2 

1270.9 

1           3 

.227 

79.90 

98.03 

3         4 

8.726 

155.8 

1359.9 

1           4 

.396 

83.60 

116:7 

3         5 

9.169 

158.3 

1451  3 

1           5 

.576 

87.38 

137.7 

3         6 

9.621 

160.7 

1546.3 

1           6 

.767 

90.86 

J60.5 

3         7 

10.084 

163.2 

1645.4 

1           7 

.969 

94.34 

185.7 

3         8 

10.559 

165.6 

1749. 

1           8 

2.182 

97.86 

213.5 

!  3         9 

11.044 

168.1 

1856.6 

1           9 

2.405 

101. 

242.9 

1  3       10 

11.541 

170.6 

1969. 

1         10 

2.640 

104.4 

275.7 

1  3       11 

12.048 

173.1 

2085.6 

1         11 

2.885 

107.7 

310.6 

4 

12.566 

175.4 

2204.1 

2 

3.142 

110.9 

348.4 

4         1 

13.096 

177.6 

2326.2 

2           1 

3.409 

U4. 

388.7 

4         2 

13.635 

180.1 

2455.6 

2           2 

3.687 

117. 

431.5 

4         3 

14.186 

182.3 

2586.7 

2           3 

3.976 

120. 

477.3 

4         4 

14.748 

184.6 

2722.5 

2           4 

4.276 

123.1 

526.3 

4         5 

15.321 

186.9 

2863. 

2           5 

4.587 

125.9 

577.7 

4         6 

15.904 

189.1 

3008.2 

254 


FLOW    OF    WATER    IN 


TABLE  50. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  full. 
formula,  with  n  =  .009,  for  use  in  the  formulae:  — 

X  V~s  and  Q  =  ac^/r  X 


Based  on  Kutter's 


Diam- 
eter in 
ft.       in. 

a  =  area 
in 
square 
feet. 

For  re- 
locity 
cv> 

For  dis- 
charge 
ac\/r 

Diam- 
eter in 
ft.      in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 
cVr 

For  dis- 
charge 
ac^/r 

4           7 

16.499 

191.2 

3154.6 

9       3 

67.201 

295.7 

19875 

4           8 

17.104 

193.5 

3309.5 

9       6 

70.882 

300.4 

21296 

4           9 

17.721 

195.5 

3465.6 

9       9 

74.562 

305.1 

22784 

4         10 

18.348 

197.9 

3630.6 

10 

78.540 

309.9 

24339 

4         11 

18.986 

200.1 

3799.9 

10       3 

82.516 

314.6 

25962 

5 

19.635 

202.2 

3969.8 

10       6 

86.590 

319.1 

27630 

5           1 

20.295 

204.2 

4144.7 

10       9 

90.763 

323.5 

29365 

5           2 

20.966 

206.5 

4329.5 

11 

95.033 

328. 

31171 

5          3 

21.648 

208.5 

4514.9 

11       3 

99.402 

332.5 

33051 

5           4 

22.340 

210.6 

4705  4 

11       6 

103.869 

337. 

35005 

5           5 

23.044 

212.7 

4901  .  1 

11       9 

108.434 

341.3 

37006 

5           6 

23.758 

214.7 

5102.4 

12 

113.098 

345.5 

39079 

5           7 

24.484 

216.6 

5303.7 

12       3 

117.859 

349.8 

41230 

5           8 

25.220 

218.7 

5515.9 

12       6 

122.719 

354.1 

43459 

5           9 

25.967 

220.8 

5733.7 

12       9 

127.677 

358.2 

45733 

5         10 

26.725 

222.8 

5956. 

13 

132.733 

362.5 

48117 

5         11 

27.494 

224.7 

6177.7 

13      3 

137.887 

366.5 

50537 

6 

28.274 

226.7 

6411.1 

13      6 

143.139 

370.5 

53036 

6           3 

30.680 

232.5 

7133.1 

13      9 

148.490 

374.5 

55619 

6           6 

33.183 

238.3 

790.7 

14 

153.938 

378.6 

58280 

6           9 

35.785 

243.9 

8728. 

14      6 

165.130 

386.4 

63805 

7 

38.485 

249.4 

9599.6 

15 

176.715 

394.1 

69639 

7          3 

41.283 

254.7 

10517. 

15       6 

188.692 

401.7 

75799 

7          6 

44.179 

260.1 

11492. 

16 

201.062 

409.4 

82315 

7          9 

47.173 

265.5 

12525. 

16       6 

213.825 

416.7 

89114 

8 

50.266  i     270.6 

13605. 

17 

226.981 

423.9 

96219 

8          3 

53.456        275.8 

14741. 

17       6 

240.529 

431  .  1 

103687 

8          ,6 

56.745  i     280.9 

15941. 

18 

254.470 

438.2 

111519 

8          9 

60.132 

285.9 

17190. 

19 

283.529 

452.3 

128254 

9 

63.617 

290.8 

18503. 

20 

314.159 

465.7 

146322 

OPEN    AND    CLOSED    CHANNELS. 


255 


TABLE  51. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  full.  Based  on  Kutter  s 
formula,  with  n  =  .010. 

Table  giving  the  values  of  a,  and  also  the  values  of  the  factors  c\/r  and 
acv/J7  for  use  in  the  formulas: — 

v  =  c\/r   X  \/s  and  Q  =  ac-^/r  X  \/s~ 

These  factors  are  to  be  used  only  where  the  value  of  n,  that  is  the  co- 
efficient of  roughness  of  lining  of  channel  =  .010,  as  for  plaster  in  pure 
cement;  planed  timber;  glazed,  coated  or  enamelled  stoneware  and  iron 
pipes;  glazed  surfaces  of  every  sort  in  perfect  order,  and  also  surfaces  of 
other  material  equally  rough. 


Diam- 
eter in 
ft.       in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 
cVr 

For  dis- 
charge 
ac^/r 

Diameter 
in 
ft.        in. 

a  —  area 
in 
square 
feet. 

For  ve- 
locity 
cVr 

For  dis- 
charge 
ac^/r 

5 

.136 

30.54 

4.154 

2           6 

4.909 

114. 

559.6 

6 

.196 

35.23 

6.906 

2          7 

5.241 

116.8 

612. 

7 

.267 

39.73 

10.61 

2          8 

5.585 

119.3 

668.3 

8 

.349 

44.02 

15.36 

2           9 

5.939 

121.6 

722.4 

9 

.442 

48.09 

21.25 

2         10 

6.305 

124.2 

783.1 

10 

.545 

51.96 

28.32 

2         11 

6.681 

126.6 

845.8 

11           .660 

55.97 

36.94 

3 

7.068 

129. 

911.8 

1                      .785 

59.75 

46.93 

3           1 

7.4(36 

131.4 

981.2 

1           1          .922 

63.19 

58.26 

3          2 

7.875 

133.8 

1054.1 

1           2        1.069 

66.71 

71.31 

3          3 

8.295 

136.1 

1128.9 

1          3        1.227 

70.13 

86.05 

3          4 

8.726 

138.5 

1208.4 

1           4 

1.396 

73.44 

102.5 

3          5 

9.169 

140.7 

1289.9 

1           5        1.576 

76.81 

121. 

3          6 

9.621 

142.9 

1374.7 

1          6        1.767 

79.93 

141.2 

3          7 

10.084 

145.1 

1463.3 

1           7        1  969 

83.05 

163.5 

3          8 

10.559 

147.3 

1555.8 

1          8       2.182 

86.21 

188.1 

3          9 

11.044 

149.6 

1652.1 

1           9 

2.405 

89.05 

214.1 

3         10 

11.541 

151.8 

1752.5 

1         10 

2.640 

92.19 

243.3 

3         11 

12.048 

154  1 

1856.9 

1         11 

2.885 

95.03 

274.2 

4 

12.566 

156.2 

1962.8 

2 

3.142 

97.91 

307.6 

4           1 

13.096 

158.2 

2072. 

2           1 

3.409 

100.7 

343.4 

4           2 

13.635 

160.4 

2187.7 

2           2 

3.687 

103.4 

381.3 

4           3 

14.186 

162.5 

2305. 

2           3 

3.976 

106.1 

421.9 

4           4 

14.748 

164.5 

2426.5 

2           4 

4  276 

108.8 

465.4 

4           5 

15.321 

166.6 

2552  .  2 

2           5 

4.587 

111.41 

511. 

4           6 

15  .  904 

168.6 

2682.1 

256 


FLOW    OF    WATER    IN 


TABLE  51. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  full.     Based  on  Kutter  s 
formula,  with  n  =  .010,  for  use  in  the  formulae: — 

v  —  c^/r  X  \/«~  and  Q  ==  ac^/r  X  \A~ 


Diam- 
eter in 
ft.        in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 
<Vr 

Fo'r  dis- 
charge 
ac\/r 

Diam- 
eter in 
ft.      in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 
c^/r 

For  dis- 
charge 
acv/F 

4           7 

16.499 

170.5 

2813.2 

9       3 

67.201 

265.4 

1783.9 

4          8 

17.104 

172.6 

2951.9 

9      6 

70.882 

269.7 

19118. 

4           9 

17.721 

174.5 

3091  .  8 

9       9 

74.662 

274. 

20157. 

4         10 

18.348 

176.6 

3238.7 

10 

78.540 

278.3 

21858. 

4         11 

18.986 

178.6 

3391  . 

10       3 

82.516 

282.6 

23320. 

5 

19.635 

180.4 

3543. 

10      6 

86.590 

286.7 

24823. 

5           1 

20.295 

182.3 

3699.6 

10      9 

90.763 

290.7 

26390. 

5           2 

20.966 

184.3 

3865.1 

11 

95.033 

294.8 

28020. 

5           3 

21.648 

186.2 

4031  .  1 

11       3 

99.402 

298.9 

29717. 

5           4 

22.340 

188.1 

4202. 

11       6 

103.87 

303.1 

31482 

5          5 

23.044 

189.9 

4377.5 

11       9 

108.43 

306.9 

33285. 

5           6 

23  758 

191.8 

4557.8 

12 

113.10 

310.8 

35156. 

5          7 

24.484 

193.5 

4738.1 

12       3 

117.86 

314.7 

37095. 

5           8 

25  .  220 

195  4 

4928.2 

12       6 

122.72 

318.6 

39104. 

5           9 

25.967 

197.3 

5123.5 

12       9 

127.68 

322.3 

41157. 

5         10 

26.725 

199.2 

5323. 

13 

132.73 

326.3 

43307. 

5         11 

27.494 

200.8 

5521.7 

13      3 

137.88 

329.9 

45493. 

6 

28.274 

202.7 

5731.5 

13      6 

143.14 

333.6 

47751. 

0           3 

30.680 

207.9 

6379.5 

13      9 

148.49 

337.3 

50085. 

6           6 

33.183 

213.2 

7075.2 

14 

153.94 

341. 

52491. 

G           9 

35.785 

218.3 

7812.7 

14      6 

165.13 

348  2 

57496. 

7 

38.485 

223  3 

8595.1 

15 

176.72 

355.1 

62748. 

7          3 

41.283 

228.2 

9420.3 

15      6 

188.69 

362. 

68313. 

7          6 

44.179 

233. 

10296. 

16 

201.06 

369. 

74191. 

7          9 

47.173 

237.9 

11225. 

16      6 

213.83 

375.7 

80342. 

8 

50.266 

242.6 

12196. 

17 

226.98 

382.3 

86769. 

8           3 

53.456 

247.3 

13219. 

17      6 

240.53 

388.8 

93528. 

8           6 

56.745 

252. 

14298. 

18 

254.47 

395.4 

100617. 

8           9 

60.132 

256.5 

15422. 

19 

283.53 

408.3 

115769. 

9 

63.617 

261. 

16604. 

20 

314.16 

420.6 

132133. 

OPEN    AND    CLOSED    CHANNELS. 


257 


TABLE  52. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  full.  Based  on  Kutter's 
formula,  with  n  •=  .011. 

Table  giving  the  value  of  a,  and  also  the  values  of  the  factors  c\/r  and 
ac\/r  for  use  in  the  formulae: — 

v  —  c\/r  X  \/s  and  Q  =  ac\/r  X  \/s 

These  factors  are  to  be  used  only  where  the  value  of  n,  that  is  the  co- 
efficient of  roughness  of  lining  of  channel  =.011,  as  for  surfaces  care- 
fully plastered  with  cement  with  one-third  sand,  in  good  condition;  also 
for  iron,  cement  and  terra-cotta  pipes,  well  jointed  and  in  best  order,  and 
also  surfaces  of  other  material  equally  rough. 


d  =--  di- 
ameter 
in 
ft.        in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 
cVr 

For 
discharge 
ac^/r 

d  =  di- 
ameter 
in 
ft.      in. 

a  =  area 
in 
square 
feet. 

For  ve-  For  dis- 
locity     charge 
c^/r        ac\/r 

5 

.136 

26.76 

3.6398 

2       11 

6.681      113.5 

758.16 

6 

.196 

30.93 

6.0627 

3 

7  068      115  7 

817.50 

7 

.267 

34.94 

9.3294 

3         1 

7.466 

117.9 

880.03 

8 

.349 

38.77 

13  531 

3         2 

7.875 

120.1 

945.69 

9 

.442 

42.40 

18  742 

3         3 

8.295      122.1 

1013.1 

10 

.545 

45.83 

24.976 

3        4 

8  726 

124.3 

1084.6 

11 

.660 

49.46 

32.644 

3         5 

9.169 

126.3 

1158.     . 

I 

.785 

52.85 

41.487 

3         6 

9.621 

128.3 

1234  4 

I      .    1 

.922 

55.95 

51.588 

3        7 

10  .  084 

130.3 

1314.1 

I           2 

1.069 

59.13 

63.210 

3         8 

10.559 

132.3 

1397.4 

1           3 

1.227 

62.22 

76.347 

3         9 

11  044 

134.4 

1484.2 

I           4 

1  .  396 

65.21 

91.037 

3       10 

11.541 

136  4 

1574.7 

I           5 

1.576 

68.26 

107.58 

3       11 

12.048 

138.3 

1666.5 

I           6 

1.767 

71.08 

125.60 

4 

12.566 

140.4 

1764.3 

1           7 

1.969 

73  90 

145  51 

4         1 

13  .  096 

142.2 

1862  7 

I          8 

2.182 

76.76 

167  50 

4         2 

13  635 

144.3 

1967.1 

I           9 

2.405 

79.33 

190.79 

4         3 

14.186      146  1 

2072.7 

1         10 

2.640 

82.11 

216.76 

4         4 

14.748      148. 

2182.5 

I         11 

2.885 

84.75 

244.50 

4         5 

15.321 

149  9 

2296. 

2 

3.142 

87.36 

274.50 

4         6 

15.904 

151.7 

2413  3 

2           1 

3  409 

89  94 

306.60 

4        7 

16.499 

153.4 

2531.7 

2           2 

3.687 

92.38 

340.59 

4        8 

17.104 

155.3 

2657  .  1 

2           3 

3.976 

94  84 

377.07 

4        9 

17.721 

157  .  1 

2783.4 

2           4 

4.276 

97  .  33 

416.16 

4       10 

18.348 

159. 

2917 

2           5 

4.587 

99.66 

457.13 

4       11 

18.986 

160  9 

3054.1 

2           6 

4.909 

102. 

500.78 

5 

19.635 

162.6 

3191  8 

2           7 

5.241 

104  5 

547  .  92 

5         1 

20  295 

164  5 

3337.5 

2           8 

5.585 

106.8 

596.70 

5         2. 

20.966 

166. 

3480.8 

2           9 

5  939 

109. 

647.18 

5         3 

21.648 

167.9 

3634.2 

2         10 

6.305 

111.3 

701.77 

5        4 

22.340 

169.6 

3789. 

17 


258 


FLOW    OF    WATER    IN 


TABLE  52. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  full.     Based  on  Kutter's 
formula  with  n  =  .011  for  use  in  the  formulae: — 

v  —  cv/r   X  Vs  and  Q  =  ac\/r~  X  \A~ 


d  =  di- 

a =  area 

For  ve- 

For 

d  =  di- 

a —  area 

For  ve- 

For dis- 

ameter 

in 

locity 

discharge 

ameter 

in 

locity 

charge 

in 

square 

c^/r 

ac\/r 

in 

square 

cVr 

ac\/r 

ft.       in. 

feet. 

ft.      in. 

feet. 

5         5 

23.044 

171.3 

3944.4 

10       9 

90.763 

264 

23951 

5         6 

23.758 

173.1 

4111.9 

11 

95.033 

567.7 

25444 

5        7 

24.484 

174  6 

4275.4 

11       3 

99.402 

271.5 

26987 

5         8 

25.220 

176.4 

4448. 

11       6 

103.869 

275.3 

28593 

5         9 

25.967 

178  1  i     4625.2 

11       9 

108.434 

278.8 

30235 

5       10 

26.725 

179.8 

4806.1 

12 

113.098 

282.4 

31937 

5       11 

27.494 

181.4 

4986.1 

12       3 

117.359 

286. 

33702 

6 

28.274 

183.1 

5176.3 

12       6 

122.719 

289.5 

35529 

6         3 

30.680 

187.9 

5764. 

12       9 

127.677 

292.9 

37399 

6         6 

33.183 

192.7 

6394  9 

13 

132.733 

296.5 

39358 

6         9 

35.785 

197.2 

7057.1 

13      3 

137.887 

299.9 

41352 

7 

38  485 

202. 

7774.3 

13       6 

143  139 

303.3 

43412 

7        3 

41.283 

206.5 

8522.9 

13       9 

148.490 

306.7 

45543 

7        6 

44.179 

210.9 

9318.3 

14 

153.938 

310.1 

47739 

7        9 

47.173 

215.4 

10162. 

14      6 

165.130 

316.8 

52308 

8 

50.266 

219.7 

11044 

15 

176.715 

323.1 

57103 

8         3 

53.456 

224. 

11978. 

15       6 

188.692 

329.6 

62186 

8         6 

56.745 

228.3 

12954. 

16 

201.062 

336. 

67557 

8         9 

60.132 

232.4 

13974. 

16       6 

213.825 

342  2 

73176 

9 

63  617 

236.6 

15049. 

17 

226.981 

348.3 

79050 

9        3 

67.201 

240.7 

16173. 

17       6 

240.529 

354.3 

85229 

9        6 

70.882 

244.6 

17338 

18 

254.470 

360  4 

91711 

9         9 

74.662 

248.6 

18558. 

19 

283.529 

372.3 

105570 

10 

78  540 

252.5 

19834. 

20 

314.159 

383.8 

120570 

10         3 

82.516 

256.5 

21166 

10        6 

86.590 

260.2 

22534 

- 

OPEN    AND    CLOSED    CHANNELS. 


250 


TABLE  53. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  full.  Based  on  Kutter's 
formula  with  n  =  .012. 

Table  giving  the  value  of  a,  and  also  the  values  of  the  factors^Cy/F  and 
ac\/Ffor  use  in  the  formulae: — 

v  —  cx/r"  X  \/s  and  Q  =  ac^/r  X  v^*" 

These  factors  are  to  be  used  only  where  the  value  of  n,  that  is  the  co- 
efficient of  roughness  of  lining  of  channel  =  .012  as  for  unplaned  timber 
when  perfectly  continuous  on  the  inside  and  also  flumes,  and  the  surfaces 
of  other  material  equally  rough. 


d  =  di- 
ameter 
in 
ft.        in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 
cv/F 

For 

discharge 
ac\/r 

1 

d  =  di- 
ameter 
in 
ft.      in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 
cv/r 

For  dis- 
charge 
ac\/r 

5 

.136 

23.70 

3.2234 

2         4 

4.276 

87.81 

375.46 

6 

.196 

27.45 

5.3800 

2         5 

4.587 

89.94 

412.54 

7 

.267 

31.05 

8.2911 

2         6 

4.909 

92.09 

452.07 

8 

.349 

34  51 

12.042 

2        7 

5.241 

94.41 

494.78 

9 

.442 

37.80 

16.708 

2         8 

5.585 

96.52 

539.07 

10 

.545 

40  95 

22.317 

2         9 

5  939 

98.49 

584.90 

11 

.666 

44.22 

29.183 

2       10 

6.305 

100.6 

634.46 

1 

.785 

47.30 

37.149 

2       11 

6.681 

102.6 

685.64 

1           1 

.922 

50.11 

46.19 

3 

7.068 

104.6 

739.59 

1           2 

1.069 

52.99 

56.64 

3         1 

7.466 

106.7 

796.38 

1           3 

1.227 

55.78 

68.44 

3         2 

7.875 

108.7 

856.12 

1           4 

1  .  396 

58  50 

81.66 

3         3 

8  295 

110.6 

917.41 

1           5 

J.576 

61.26 

96.54 

3         4 

8.726 

112.6 

982.39 

1           6 

1.767 

63.83 

112.79 

3         5 

9.169 

114.4 

1049.1 

1           7 

1.969 

66.41 

130.76 

3         6 

9.621 

116.3 

1118.6 

1          8 

2.182 

69.03 

150.61 

3         7 

10.084 

118.1 

1191.1 

1           9 

2.405 

71.38 

171.66 

3         8 

10.559 

120. 

1267. 

1         10 

2.640 

73.92 

195  14 

3         9 

11.044 

121  9 

1345.9 

1         11 

2.885 

76.33 

220.21 

3       10 

11.541 

123.8 

1428.3 

2 

3.142 

78.72 

247.33 

3       11 

12.048 

125.7 

1514. 

2           1 

3.409 

81.07 

276.38 

4 

12.566 

127.4 

1600.9 

2           2 

3.687 

83.29 

307  .  10 

4         1 

13.096 

129.1 

1690.7 

2           3 

3.976 

85.54 

340.10 

4         2 

13  635 

131. 

1785.8 

260 


FLOW    OF    WATER    IN 


TABLE   53. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  full.     Based  on  Kutter's 
formula  with  n  =  .012  for  use  in  the  formulae: — 

v  =  c\/r   X  \A  and  Q  = 


d  =  di- 

a —  area  For  ve- 

For 

d  =  di- 

a =  area 

For  ve- 

For   dis- 

ameter 

in 

locity 

discharge 

ameter 

in 

locity 

charge 

in 

square 

cVr 

ac\/r 

in 

square 

cVr 

ac\/r 

ft.        in. 

feet. 

ft.      in. 

feet. 

4           3 

14.186 

132.7 

1882  3 

8       9 

60.132 

212.3 

12766. 

4           4 

14.748 

134.4 

1982.3 

9 

63  617 

216.2 

13751. 

4           5 

15.321 

136.2 

2085.9 

9       3 

67.201 

219.9 

14780. 

4           6 

15.904 

137.9 

2193. 

9       6 

70.882 

223.6 

15847  . 

4          7 

16.499 

139.5 

2301. 

9       9 

74.662 

227.2 

16965. 

4          8 

17.104 

141.2 

2415.4 

10 

78  .  540 

230.9 

18134. 

4           9 

17.721 

142  8 

2530.8 

10       3 

82  516 

234.6 

19356. 

4         10 

18.348 

144.6 

2652.8 

10       6 

86.590 

238. 

20612. 

4         11 

18.986 

146.3 

2777.8 

10       9 

90.763 

241.5 

21921. 

5 

19.635 

147.9 

2903.6 

11 

95.033 

245. 

23285. 

5           1 

20.295 

149.4 

3032.9 

11       3 

99  402 

248.5 

24703. 

5           2 

20.966 

151.2 

3169.8 

11       6 

103  869 

252. 

26179. 

5           3 

21.648 

152  8 

3307. 

11       9 

108.434 

255.4 

27689. 

5           4 

22.340 

154.4 

3448  3 

12 

113.098 

258.7 

29254  . 

5           5 

23.044 

155.9 

3593.5 

12       3 

117.859 

262. 

30876. 

5           6 

23.758 

157.5 

3742.7 

12       6 

122.719 

265.3 

32558. 

5           7 

24.484 

159. 

3892. 

12       9 

127.677 

268.5 

34277. 

5           8 

25.220 

160.6 

4049.5 

13 

132  733 

271.8 

36077  . 

5           9 

25.967 

162.2 

4211.2 

13       3 

137.887 

274.9 

37909. 

5         10 

26.729 

163.8 

4376.4 

13       6 

143.139 

278.1 

39802. 

5         11 

27.494 

165.1 

4540  5 

13       9 

148.490 

281  2 

41755. 

6 

28.274 

166.7 

4713.9 

14 

153.938 

284.4 

43773. 

G           3 

30.680 

171.1 

5250.1 

14       6 

165.130 

290.5 

47969. 

6           6 

33.183 

175.6 

5825.9 

15 

176.715 

296.4 

52382. 

6           9 

35.785 

179.9 

6436.7 

15       6 

188.692 

302.4 

57061. 

7 

38.485 

184.2 

7087. 

16 

201.062 

308  .  4 

62008  . 

7          3 

41.283 

188.3 

7772.7 

16       6 

213.825 

314.2 

67183. 

7          6 

44.179 

192  4 

8501.8 

17 

226.981 

319.8 

72594. 

7          9 

47.173 

196.6 

9275.8 

17       6 

240.529 

325.5 

78289. 

6 

50.266 

200.6 

10083. 

18 

254.470 

331  .  1 

84247  . 

8           3 

53  456 

204.5 

10934. 

19 

282.529 

342.1 

96991  . 

8          6 

56.745 

208.5 

11832. 

20 

314.149 

352.6 

110905. 

OPEN    AND    CLOSED    CHANNELS. 


261 


TABLE  54. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  full.  Based  on  Kutter's 
formula  with  n  —  .013. 

Table  giving  the  value  of  a,  and  also  the  values  of  the  factors  c\/r  and 
ae-v/^for  use  in  the  formulae: — 

v  =  c^/7  X  \/s~ an(l  Q  =  acVr   X  \/*" 

These  factors  are  to  be  used  only  where  the  value  of  n,  that  is  the  co- 
efficient of  roughness  of  lining  of  channel  —  .013,  as  in  ashlar  and  well  laid 
brickwork,  ordinary  metal,  earthenware  and  stoneware  pipe,  in  good  con- 
dition, but  not  new,  cement  and  terra  cotta  pipe  not  well  jointed  nor  in 
perfect  order,  plaster  and  planed  wood  in  imperfect  or  inferior  condition, 
and  also  surfaces  of  other  materials  equally  rough. 


d  =  di- 
ameter 
in 
ft.        in. 

a  =  area 
in 
square 
feet 

For  ve- 
locity 
c-s/r 

For 
discharge 
ac\/r 

d  =  di- 
ameter 
in 
ft.      in. 

a  =  area 
in 
square 
feet 

For 
velocity 
cVr 

For  dis- 
charge 
ac\/r 

5 

.136        21.20 

2.8839 

2       11 

6.681 

93.52 

624.82 

6 

.196 

24.60 

4.8216 

3 

7.068 

95.37 

674.09 

7 

.267 

27.87 

7.4425 

3         1 

7.466 

97.25 

726.05 

8 

.349 

31. 

10.822 

3         2 

7.875 

99.13 

780.63 

9 

.442 

34. 

15.029 

3         3 

8.295 

100.9 

836.69 

10 

.545 

36.87 

20.095 

3         4 

8.726 

102.8 

896.27 

11 

.660 

39.84 

26.296 

3         5 

9.169 

104.4 

957  .  35 

1 

.785 

42.65 

33.497 

3         6 

9.621 

106.1 

1021  .  1 

1 

.922 

45.22 

41.692 

3         7 

10.084 

107.9 

1087.7 

2 

1.069 

47.85 

51.157 

3         8 

10.559 

109.6 

1157.2 

3 

1.227 

50.42 

61.867 

3         9 

11.044 

111.3 

1229.7 

4 

1.396 

52.90 

73.855 

3       10 

11.541 

113.1 

1305.3 

5 

1.576 

55.44 

87.376 

3       11 

12.048 

114.9 

1384.1 

6 

1.767 

57.80 

102.14 

4 

12.566 

116.5 

1463.9 

7 

1.969 

60.17 

118.47 

4         1 

13.096 

118.1 

1546.9 

8 

2.182 

62.58 

136.54 

4         2 

13.635 

119.8 

1633.5 

9 

2.405 

64.73 

155.68 

4         3 

14.186 

121.4 

1722. 

10 

2.640 

67.07 

177.07 

4         4 

14.748 

123. 

1813.8 

1         11 

2.885 

69.29 

199.90 

4         5 

15.321 

124.6 

1908. 

2 

3.142 

71.49 

224.63 

4         6 

15.904 

126.2 

2007. 

2      i 

3.409 

73.66 

251.10 

4         7 

16.499 

127.7 

2206.1 

2           2 

3.687 

75.70 

279.12 

4         8 

17.104 

129.3 

2211.1 

2           3 

3.976 

77.77 

309.23 

4         9 

17.721 

130.7 

2316.9 

2           4 

4.276 

79.87 

341.52 

4       10 

18.348 

132.4 

2429.1 

2           5 

4.587 

81.83 

375.37 

4       11 

18.986 

134. 

2543.9 

2           6 

4.909 

83.82 

411.27 

5 

19.635 

135.4 

2659. 

2          7 

5.241 

85.95 

450.49 

5         1 

20.205 

136.9 

2778.7 

2           8 

5.585 

87.89 

490.88 

5         2 

20.966 

138.5 

2903.5 

2           9 

5.939 

89.71 

532.76 

5         3 

21.648 

139.9 

3029.4 

2         10 

6.305 

91.68 

578.02 

5         4 

22.340 

141.4 

3159. 

1             ! 

262 


FLOW    OF    WATER    IN 


TABLE  54. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  full.     Based  on  Kutter's 
formula  with  n  =  .013  for  use  in  the  formulae:— 


v  -—  c\/r  X 


Q  =  ac\/r   X  \A 


d  =  di- 

a =  area 

For 

For  dis- 

d =  di- 

a =  area 

For 

For   dis- 

ameter 

in 

velocity 

charge 

ameter 

in 

velocity 

charge 

in 

square 

cVr 

ac\/r    \ 

in 

square 

cV 

ac<)/r 

ft.        in. 

feet 

ft.        in. 

feet 

5         5 

23.044 

142.9 

3292 

10       6 

86  590 

219.4 

18996. 

5         6 

23.758 

144.3 

3429. 

10       9 

90.763 

222.6 

20205  . 

5        7 

24.484 

145.6 

3566. 

11 

95.033 

225.9 

21464. 

5         8 

25.220 

147.1 

3710. 

11       3 

99.402 

229.1 

22774. 

5         9 

25.967 

148.6 

3859. 

11       6 

103.869 

232.4 

24139. 

5       10 

26.729 

150.1 

4012. 

11       9 

108.434 

235.4 

25533. 

5       11 

27.494 

151.4 

4162. 

12 

113.098 

238.6 

26981. 

6 

28.274 

152.9 

4322. 

12       3 

117.859 

241.7 

28484. 

6         3 

30.680 

157. 

4816. 

12       6 

122.719 

244  8 

30041. 

6         6 

33.183 

161.2 

5339. 

12       9 

127.677 

247  8 

31633. 

6         9 

35.785 

165.2 

5911. 

13 

132.733 

250.9 

33301. 

7 

38.485 

169.2 

6510. 

13       3 

137.887 

253.8 

34998. 

7        3 

41.283 

173. 

7142. 

13       6 

143  139 

256.8 

36752. 

7        6 

44.179 

176.9 

7814. 

13       9 

148.490 

259.7 

38561. 

7        9 

47.173 

180.8 

8527. 

14 

153.938 

262.6 

40432 

8 

50.266 

184.5 

9272. 

14       6 

165.130 

268.4 

44322. 

8         3 

53.456 

188.2 

10059. 

15 

176.715 

274. 

48413. 

8         6 

56.745 

19.1.9 

10889. 

15       6 

188.692 

279.6 

52753. 

8         9 

60.132 

195.4 

11753. 

16 

201.062 

285.2 

57343. 

9 

63.617 

199.1 

12663. 

16       6 

213.825 

290.6 

62132. 

9         3 

67.201 

202.6 

13613. 

17 

226.981 

295.8 

67140. 

9         6 

70.882 

205.9 

14597. 

17       6 

240.529 

301 

72409. 

9         9 

74.662 

209.3 

15629. 

18 

254.470 

306.3 

77932. 

10 

78.540 

212.8 

16709. 

19 

282.529 

316.6 

89759. 

10        3 

82.516 

216.2 

17837. 

20 

314.159 

326.5 

102559 

OPEN    AND    CLOSED    CHANNELS. 


263 


TABLE  55. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  full. 
formula  with  n  =  .015. 


Based  on  Kutter's 


Tables  giving  the  value  of  a,  and  also  the  values  of  the  factors  c\/r  and 
or  use  in  the  formulae:  — 


X  \/8  and  Q  =  ac^/r 
These  factors  are  to  be  used  only  where  the  value  of  n,  that  is  the  co- 
efficient of  roughness  of  lining  of  channel  =  .015,  as  in  second  class  or 
rough  faced  brickwork;  well  dressed  stonework;  foul  and  slightly  tuber  - 
culated  iron;  cement  and  terra  cotta  pipes  with  imperfect  joints  and  in 
bad  order;  canvas  lining  on  wooden  frames,  and  also  the  surfaces  of  other 
channels  equally  rough. 


d  =  di- 

a =  area 

For  ve- 

For 

d  =  di- 

a =  area 

For 

For  dis- 

ameter 

in 

locity 

discharge 

ameter 

in 

velocity 

charge 

in 
ft.       in. 

square 
feet. 

cV~r 

ac\/r 

in 
ft.     in. 

square 
feet. 

cVr 

ac\/r 

5 

.136 

17.36 

2.3615 

2     10 

6.305 

77.56 

488.99 

G 

.196 

20.21 

3.9604 

2     11 

6.681 

79.16 

528.85 

7 

.267 

22.95 

6.1268 

Q 

7.068 

80.77 

570.90 

8 

.349 

25.56 

8.9194 

3       1 

7.4G6 

82.39 

615.14 

9 

.442 

28.10 

12.421 

3       2 

7.875 

84.03 

661.77 

10 

.545 

30.52 

16.633 

3      3 

8.295 

85.54 

709.56 

11 

.660 

33.03 

21.798 

3       4 

8.726 

87  .  15 

760.44 

.785 

35.40 

27.803 

3       5 

9.169 

88.61 

812.38 

1 

.922 

37.60 

34.664 

3       6 

9.621 

90.11 

866.91' 

2 

!069 

39.85 

42.602 

3      7 

10  084 

91.60 

923.70 

3 

.227 

42.05 

51.600 

3       8 

10.559 

93.11 

983.11 

4 

.396 

44.19 

61.685 

3       9 

11.044 

94.62 

1045. 

5 

.576 

46.36 

73.066 

3     10 

11.541 

96.15 

1109.6 

6 

.767 

48.38 

85  .  496 

3     11 

12.048 

97.55 

1175.2 

7 

.969 

50.40 

99.242 

4 

12.566 

99.10 

1245.3 

8 

2  182 

52.45 

114.46 

4       1 

13.096 

100.5 

1315.8 

1           9 

2.405 

54.29 

130.58 

4       2 

13.635 

102. 

1390.8 

1           0 

2.640 

56.29 

148.61 

4       3 

14.186 

103.4 

1466.7 

1     -    11        2.885 

58.20 

167.90 

4       4 

14.748 

104.8 

1545.7 

2 

3.142 

60.08 

188.77 

4       5 

15.321 

106.2 

1627. 

2           1 

3.409 

61.95 

211.20 

4       6 

15.904 

107.6 

1711.4 

2           2 

3.687 

63.72 

234.94 

4       7 

16.499 

108.9 

1796.5 

2           3 

3.976 

65.51 

260.47 

4       8 

17.104 

110.3 

1886.8 

2           4 

4.276 

67.32 

287.87 

4       9 

17.721 

111.6 

1977.7 

2           5 

4.587 

69.02 

316.59 

4     10 

18.348 

113. 

2074.1 

2           6 

4.909 

70.74 

347.28 

4     11 

18.986 

114.4 

2172.9 

2          7 

5.241 

72.59 

380.46 

5 

19.635 

115.7 

2272.7 

2           8 

5.585 

74.27 

414.81 

5       1 

20.295 

117.1 

2376.7 

2           9 

5.939 

75.98 

451.23 

5       2 

20.966 

118.4 

2482. 

264 


FLOW    OF    WATER    IN 


TABLE  55. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  full.     Based  on  Kutter's 
formula  with  n  =  .015  for  use  in  the  formulae: — 

v  =  c^/r  X  -\A~and  Q  =  ac^/r  X  •>/* 


d  =  di- 
ameter 
in 
ft.       in. 

a  =  area 
in  square 
feet. 

For  ve- 
locity 
cVr 

For  dis- 
charge 
ac\/r 

d  =  di- 
ameter in 
ft.      in. 

a  =  area 
in 
square 
feet 

For  ve- 
locity 
cx/r 

For  dis- 
charge 

ac\/r 

5         3 

21.648 

119.7 

2590.5 

12 

113.10 

206.5 

23352. 

5        4 

22.340 

121. 

2702.1 

12         3 

117.86 

209.2 

24658 

5         5 

23.044 

122.2        2816.7 

i   12         6 

122.72 

212. 

26012. 

5         6 

23.758 

123.5 

2934.8 

12         9 

127.68 

214.6 

27399. 

5         7 

24.484 

124.8 

3056.4 

13 

132.73 

217.4 

28850. 

5         8 

25.220 

126. 

3177.3 

13         3 

137.88 

220. 

30330. 

5         9 

25.967 

127.3 

3305.6 

13         6 

143.14 

222.6 

31860. 

5       10 

26.725 

128.6 

3436.3 

13         9 

148.49 

225.2 

33441  . 

5       11 

27.494 

129.7 

3566.6 

14 

153.94 

227.8 

35073. 

6 

28.274 

131. 

3702  .  3 

14         3 

159.48 

230. 

36736. 

6         3 

30.680 

134.6 

4130.3 

14         6 

165.13 

232.9 

38454. 

6         6 

33.183 

138.3 

4588  .  3 

14         9 

170.87 

235.4 

40221  . 

6         9 

35.785 

141.8 

5074.7 

15 

176.72 

237.9 

42040. 

7 

38.485 

145.3 

5591.6 

15         3 

182.65 

240.5 

43931  . 

7        3 

41.283 

148.7 

6136.8    |   15         6 

188.69 

242.8 

45820. 

7        6 

44.179 

152. 

6717. 

|   15         9 

194.83 

245.3 

47792. 

7        9 

47.173 

155.5 

7333.5 

16 

201.06 

247.8 

49823. 

8 

50.266 

158.7 

7978.3 

1   16         3 

207.40 

250.3 

51904. 

8         3 

53.456 

162. 

8658.8 

16         6 

213.83 

252.7 

54056  . 

8         6 

56.745 

165.3 

9377.9 

16         9 

220.35 

254.9 

56171. 

8         9 

60.132 

168.4 

10128. 

17 

226.98 

257.2 

58387  . 

9 

63.617 

171.6 

10917. 

17         3 

233.71 

259.7 

60700. 

9         3 

67.201 

174.7 

11740. 

17        6 

240.53 

261.9 

62999. 

9         6 

70.882 

177.7 

12594. 

17         9 

247.45 

264.4 

65428. 

9         9 

74.662 

180.7 

13489. 

18 

254.47 

266.6 

67839. 

10 

78.540 

183.7 

14426.      ||   18         3 

261.59 

268.9 

70346  . 

10         3 

82.516 

186.7 

15406. 

18         6 

268  .  80 

271.3 

72916. 

10        6 

86.590 

189.5 

16412. 

18         9 

276.12 

273.5 

75507  . 

10         9 

90.763 

192.4 

17462. 

19 

283.53 

275.8 

78201  . 

11 

95.033 

195.2 

18555.          19         3 

291.04 

278. 

80216. 

11         3 

99.402 

198  1 

19694. 

19         6 

298.65 

280.2 

83686 

11         6 

103.87 

201. 

20879. 

19         9 

306.36 

282.4 

86526. 

11         9 

108.43        203.7 

22093. 

20 

314.16 

284.6  I  89423. 

OPEN    AND    CLOSED    CHANNELS., 


265 


TABLE  56. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  full.     Based  on  Kutter's 
formula  with  n  =  .017. 

Tables  giving  the  value  of  a,  and  also  the  values  of  the  factors  Cv/r  and 
use  in  the  formulae:  — 
X 


Q  =  acv/r  X  >/«" 

These  factors  are  to  be  used  only  where  the  value  of  n,  that  is  the  co- 
efficient of  roughness  of  lining  of  channel  =  .017,  as  for  brickwork,  ashlar 
and  stoneware  in  an  inferior  condition;  tuberculated  iron  pipes;  rubble  in 
cement  or  plaster  in  good  order;  fine  gravel,  well  rammed,  £  to  f  inches 
diameter;  and  generally  the  materials  mentioned  with  n  =  .013  when  in 
bad  order  and  condition,  and  the  surfaces  of  other  channels  equally  rough. 


Diameter 
in 
ft.       in. 

a  =  area 
in  sqiiare 
feet. 

For 
velocity 
q/r 

For          1 
discharge 
acj/r 

Diameter 
,in 
ft.    in. 

a  —  area 
in  square 
feet. 

For 
velocity 
cy7 

For 
discharge 
acf/r 

5 

.136 

14.55 

1.979 

6     6 

33.183 

120.8 

4010. 

6 

.196 

16.98 

3.329 

6     9 

35.785 

124. 

4437.9 

7 

.267 

19.33 

5.162 

7 

38.485 

127.1 

4893. 

8 

.349 

21.59 

7.535 

7     3 

41.283 

130.1 

5373.3 

9 

.442 

23.76 

10.50     j 

7     6 

44.179 

133.2 

5884.2 

10 

.545 

25.84 

14.08 

7     9 

47.173 

136.2 

6427  .  9 

11 

.660 

28. 

18.48 

8 

50.266 

139.2 

6995.3 

1 

.785 

30.05 

23.60 

8     3 

53  .  456 

142. 

7594.1 

1         1 

.922 

31.95 

29.46 

8     6 

56.745 

145. 

8226  .  3 

1         2 

1.069 

33.90 

36.24 

8     9 

60.132 

147.  S 

8886.4 

1         3 

1.227 

35.80 

43.93 

9 

63.617 

150.6 

9580  7 

1         4 

1.396 

37.65 

52.56 

9     3 

67.201 

153.4 

10307. 

1         5 

1.576 

39.55 

62.33 

9     6 

70.882 

156. 

11061.' 

6 

1.767 

41.31 

72.99 

9     9 

74.662 

158.7 

11851. 

7 

1.969 

43.07 

84.81 

10 

78.540 

161.4 

12678. 

8 

2.182 

44.88 

97.92 

10     3 

82.516 

164.1 

13544. 

9 

2.405 

46.49 

111.8 

10     6 

86.590 

166.7 

14434. 

10 

2.640 

48.25 

127.3 

10     9 

90.763 

169.3 

15364. 

1       11 

2.885 

49.92 

144. 

11 

95.033 

171.9 

16333 

2 

3.142 

51.57 

164. 

11     3 

99.402 

174.5 

17343. 

2         3 

3.976 

56.32 

223.9 

11     6 

103.869 

177   1 

18395 

2         G 

4.909 

60.98 

299.3 

11     9 

108.434 

179.5 

19468. 

2         9. 

5.939 

65.47 

388.8 

12 

113.098 

182. 

20584. 

3 

7.068 

69.80 

493.3 

12     6 

122.719 

186.9 

22938. 

3         3 

8.295 

74. 

613.9 

13 

132.733 

191.7 

25451. 

3         6 

9.621 

78.04 

750.8 

13     6 

143.139 

196.4 

28117. 

3         9 

11.044 

82.04 

906. 

14 

153.938 

201.1 

30965. 

4 

12.566 

86. 

1080.7 

14     6 

165.130 

205.7 

33975. 

4         3 

14.186 

89.79 

1273.8 

15 

176.715 

210  2 

37147. 

4         C 

15.904 

93.51 

1487.3 

15     6 

188.692 

214.7 

40510. 

4         9 

17.721 

97.05 

1719.9 

16 

201.062 

219.2 

44073. 

5 

19.635 

100.6 

1977. 

16     6 

213.825 

223.5 

47784. 

5         3 

21.648 

104.2 

2255  .  8 

17 

226.981 

227.6 

51669. 

5         6 

23.758 

107.6 

2557  .  2 

17     6 

240.529 

231.8 

55762. 

5         9 

25.967 

111. 

2882  1 

18 

254.470 

236. 

60067. 

6 

28.274 

114.3 

3232.5 

19 

282.529 

244.4 

69301 

6         3 

30.680 

117.5 

3606.8 

20 

314.159 

252  3 

79259. 

266 


FLOW    OF    WATER    IN 


TABLE  57. 

Circular  Pipes,  Conduits,  Sewers,  etc.,  flowing  full.  Based  on  Kutter's 
formula  with  n  =  .020. 

Table  giving  the  values   of   a   and  r,  and   also   the   values   of  factors 

c\/r  and  ac-^/r  for  use  in  the  formulae: — 

v  =  c\/r-   X  \/s~  and  Q  =  ac\/r   X  %/s" 

These  factors  are  to  be  used  only  where  the  value  of  n  =  .020,  as  in  rub- 
ble in  cement  in  an  inferior  condition;  coarse  rubble  rough  set  in  a  nor- 
mal condition;  coarse  rubble  set  dry;  ruined  brickwork  and  masonry; 
coarse  gravel  well  rammed,  from  1  to  1£  inch  diameter;  canals  with  beds 
and  banks  of  very  firm,  regular  gravel,  carefully  trimmed  and  rammed  in 
defective  places;  rough  rubble,  with  bed  partially  covered  with  silt  and 
mud;  rectangular  wooden  troughs,  with  battens  on  the  inside  two  inches 
apart;  trimmed  earth  in  perfect  order,  and  surfaces  of  other  materials 
equally  rough. 


diam- 

a =  area 

For  ve- 

For 

diam- 

a =  area 

For  ve- 

For  dis- 

eter 

in 

locity 

discharge 

eter 

in 

locity 

charge 

in 

square 

cVr 

acy/r 

in 

square 

cV'r 

ac\/r 

ft.        in. 

feet. 

ft.      in. 

feet. 

6 

.196 

13.56 

2.658 

6 

28.274 

95.85 

2710.2 

9 

.442 

19.10 

8.442 

6       6 

33.183 

101.4 

3365  .  6 

1 

.785 

24.30 

19.07 

7 

38.485 

106.8 

4111.4 

1           3 

1.227 

29.08 

35.68 

7      6 

44.179 

112.1 

4951. 

1           6 

1.767 

33  66 

59.49 

8 

50.266 

117.2  , 

5891.5 

1           9 

2.405 

38.01 

91.42 

9 

63  617 

127.2 

8092.1 

2 

3.142 

42.29 

132.9 

10 

78.540 

136.6 

10731. 

2           3 

3.976 

46.31 

184.1 

11 

95.033 

145.8 

13856. 

2           6 

4.909 

50.20 

246.4 

12 

113.098 

154.5 

17479. 

2           9 

5.939 

54.01 

320.8 

13 

132.733 

163. 

21639. 

3 

7.068 

57.71 

407.9 

14 

153.938 

171.3 

20365. 

3           3 

8.295 

61.23 

507.9 

15 

176.715 

179  1 

31660. 

3           6 

9.621 

64.72 

622  7 

16 

201.062 

186.9 

37583. 

3          9 

11.044 

68.13 

752.4 

17 

226.981 

194  4 

44119. 

4 

12.566 

71.50 

898.5 

18 

254.470 

201  .  6 

51312. 

4           6 

15  904 

77.93 

1239.4 

19 

283.529 

208.9 

59238. 

5 

19.635 

84.10 

1651.2 

20 

314.159 

215.9 

67837. 

5           6 

23.758 

90.12  |  2140.8 

OPEN    AND    CLOSED    CHANNELS. 


267 


TABLE  58. 

Giving  the  value  of  the  hydraulic  mean  depth  r,  for  egg-shaped  sewers 
flowing  full  depth,  two-thirds  full  depth  and  one-third  full  depth. 

Let  D  =  transverse  diameter,  that  is,  diameter  of  top  of  sewer,  then 
Hydraulic  mean  depth  of  sewer  flowing  full  depth  —  D  X  (L2897._ 
Hydraulic  mean  depth  of  sewer  flowing  f  full  depth  —  D  X  0.3157. 
Hydraulic  mean  depth  of  sewer  flowing  £  full  depth  =  D  X  0.2066. 


r  =  hydraulic  mean 

r  =  hydraulic  mean 

depth  in  feet 

depth  in  feet 

Size 

Size 

of  Sewer 

;                       i 

of  Sewer 

1 

Full     !  |  Full    %  Full 

Full 

f  Full  i  £  Full 

Depth  '  (jepth  ;  Depth 

Depth 

Depth  j  Depth 

ft.  in.   ft.  in. 

ft.    in.      ft.  in. 

.1 

1        XI  6 

.2897 

.316  |      .207 

5    2X  7  9 

1.497 

1.631 

.068 

1     2X1  9 

.3380 

.368  '      .241 

5    4X  8 

1  545 

1.684 

.102 

1     4X2 

.3864 

.421 

.276 

5     6X  8  3 

1.593 

1.736 

.136 

1     6X2  3 

.4345 

.474 

.310 

5     8X   8  6 

1.642  i  1.789 

.171 

I     8X2  6 

.4828 

.526 

.344 

5  10X  8  9 

1.690      1.842 

.205 

1  10X2  9 

.5311 

.579 

.379 

6       X  9 

1.738 

1.894 

.240 

2       X3 

.5794 

.631 

.413 

6    2X  9  3 

1.787 

1.947 

.274 

2     2X3  3 

.6277 

.684 

.448 

6    4X  9  6 

1.835 

1.999 

.309 

2     4X3  6 

.6760 

.737 

.482 

6    6X  9  9 

1.883 

2.052 

.343 

2     6X3  9 

.7242 

.789 

.517 

6     8X10 

1.931 

2.095 

.377 

2     8X4 

.7725 

.842 

.551 

6  10X10  3 

1.980 

2.157 

.412 

2  10X4  3 

.  8208 

.894 

.585 

7       X10  6 

2.028 

2.210 

.446 

3       X4  6 

.8691 

.947 

.620 

7     4X11         2.124 

2.315 

515- 

3    2X4  9 

.9174 

1.000 

.654 

7     8X11  6 

2.221 

2.420 

.584 

3     4X5 

.9657 

1.052 

.689 

8       X12 

2.318 

2  526 

.653 

3    6X5  3 

1.014 

1.105 

.723 

8     4X12  6 

2.414 

2.631 

.722 

3     8X5  6 

1  062 

1.158 

.758 

8     8X13 

2.511 

2.736 

.791 

3  10X5  9 

.111 

1.210 

.792 

9       X13  6     2.607 

2  841 

.859 

4       X6 

.159 

1  .  263 

.826 

9    4X14 

2.704 

2.947 

.928 

4     2X6  3 

.207        1.315 

.861 

9    8X14  6 

2.800 

3  052 

.997 

4     4X6  6        .255        1.368 

.895 

10       X15 

2.897 

3.157 

2.066 

4     6X6  9 

.304        1.421  !      .930 

10    6X15  9 

3.042 

3.315 

2.169 

4     8x7 

.352     !   1.473 

.964 

11       X16  6 

3.187 

3.473 

2.273 

4  10x7  3 

.400 

1.526 

.999 

12       XlS 

3.476 

3.788 

2.479 

5       X7  6        .449 

1.579      1.033 

268 


FLOW    OF    WATER    IN 


TABLE  59. 


Egg-shaped  Sewers  flowing  full  depth. 
=  .011. 


Based  on  Kutter's  formula  with 


Giving  the  value  of    a,   and  also  the  values    of  the  factors  c\/r   and 
ac\/'r  for  use  in  the  formulae:  — 


X 


Q 


These  factors  are  to  be  used  only  when  the  value  of  n  =  .011  as  in 
plaster  in  cement  with  one-third  sand  in  good  condition;  also  for  iron, 
cement,  and  terra  cotta  pipes,  well  jointed  and  in  best  order,  and  also  the 
surfaces  of  other  materials  equally  rough. 

The  egg-shaped  sewer  referred  to  has  a  vertical  diameter  equal  to  1.5 
times  the  greatest  transverse  diameter  D,  that  is,  the  diameter  of  the  top 
of  sewer. 

Area  of  egg-shaped  sewer  flowing  full  depth  =  D2  X  1.148525. 
Perimeter  of  egg-shaped  sewer  flowing  full  dep'th  =  D  X  3.9649. 
Hydraulic  mean  depth  of  egg-shaped  sewer  flowing  full  depth  =  D  X  0.2897. 


Size 
of  sewer 

ft.  in.   ft.  in. 

a  =  area 
in 
square 
feet 

For  ve- 
locity 
c^/r 

For  dis- 
charge 
ac\/r 

Size 
of  sewer 

ft.   in.     ft.  in 

a  =  area 
in 
square 
feet 

For  ve-  Fordis- 
locity  !  charge 
c\/r    i  ac-v/r 

1       XI  6 

1  .  1485 

58.8 

67.5 

5     2X   7  9 

30.660 

182.7 

5602  . 

1     2X1  9 

1.5632 

65.9 

102.9 

5    4X  8 

32.669 

186.5 

6093  5 

1     4X2 

2.0417 

72.7 

148.4 

5    6X  8  3 

34.743 

190.2 

6607.5 

1     6X2  3 

2.5841 

78.9 

204. 

5    8X  8  6 

36.880 

193.8 

7150.2 

1     8X2  6 

3.1903 

85.2 

272. 

5  10X   8  9 

39.081 

197.6 

7722.4 

1  10X2  9 

3.8602 

91.1 

351.7 

6       X   9 

41.347 

201. 

8312.7 

2       X3 

4.5941 

96.8 

444.7 

6    2X  9  3 

43.676 

204.7 

8940.8 

2     2X3  3 

5.3914 

102.3 

551.7 

6    4X   9  6 

46  .  068 

208. 

9582.1 

2    4x3  6 

6.2529!  107.7 

673.3 

6     6X  9  9 

48.525 

211.5 

10263. 

2    6X3  9 

7.1783 

112.9 

810.6 

6     8X10 

51.046 

215. 

10976. 

2    8X4 

8.1674 

118. 

964.1 

6  10X10  3 

53.629 

218.3 

11709. 

2  10X4  3 

9.2198 

123. 

1134.3 

7       X10  6 

56.278 

221.6 

12473. 

3       X4  6 

10.377 

127.7  J1325.1 

7     4x11 

61.764 

228.1 

14087. 

3    2X4  9 

11.517 

132.5  11526. 

7    8X11  6 

67.508 

234.6 

15835. 

3    4X5 

12.761 

137.1    1749.9 

8       X12 

73.506 

240.8 

17704. 

3    6X5  3 

14.069 

141.7 

1993.3 

8     4X12  6 

79.758 

247.1 

19713. 

3    8X5  6 

15.442 

146.1 

2255.9 

8     8x13 

86.268 

253.3 

21853. 

3  10X5  9 

16.877 

150.4 

2538.4 

9       X13  6 

93.031 

259.2 

24119 

4       X6 

18.376 

154.7 

2843.9 

9    4X14 

100.049 

264.9 

26509. 

4    2X6  3 

19.940 

159. 

3170.9 

9    8X14  6 

107.324 

270  7 

29051  . 

4    4X6  6 

21.566 

162.9 

3514.4 

10       X15 

114.853 

276.5 

31754. 

4    6x6  9 

23.258 

167. 

3885.8 

10    6x15  9 

126.625 

284.7 

36058. 

4    8x7 

25.013 

171. 

4279.1 

11       X16  6 

138.972 

292.9   40707. 

4  10x7  3 

26.830 

174.9   4694.3 

12       X18 

165.388 

308.7 

51051. 

5       X7  6 

28.713 

179. 

5140.6 

OFKN    AND    CLOSED    CHANNELS. 


269 


TABLE  60. 

Egg-shaped  Sewers  flowing  two-thirds  full  depth.     Based  on  Ktitter's 
formula  with  n  =  .011. 

• 

Giving  the  value  of  a,  and  also  the  values  of  the  factors  c\/r"  and  ac\/r 
for  use  iii  the  formulae: — 

v  =  c\/r   X    \A  and  Q  =  ac\/r   X  \S& 

The  egg-shaped  sewer  referred  to  has  a  vertical  diameter  1.5  times  the 
greatest  transverse  diameter,  Z>,  that  is,  the  diameter  of  the  top  of  sewer. 
A.rea  of  egg-shaped  sewer  flowing  two-thirds  full  depth  —  Z>2  X  0.755825. 
Perimeter  of  egg-shaped  sewer  flowing  two-thirds  full  depth  =  D  X  2.3941. 
Hydraulic  mean  depth  of  egg-shaped  sewer  flowing  two-thirds  full  depth 
=  D  X  0.3157. 


1               1 

a—  area  For  ve-  Fordis- 

a=area  For  ve- 

For dis- 

Size 

• 

Size 

of  Sewer 

m      1  locity  1  charge 

of  Sewer 

in 

locity 

charge 

square 

Cv/r    j  ac\/r 

square     ^- 

ac\/r 

ft.  in.   ft.  in. 

feet 

\        \ 

ft.  in.     ft.  in. 

feet 

1       Xl  6 

.7558 

62.71 

47.40!    5    2x  7  9 

20.176 

193.1 

3896.2 

1     2X1  9 

1.0287 

70.26 

72.27 

5     4X  8 

21.498 

197.2 

4239.5 

1     4X2 

1  .  3436 

77.27 

103.8 

5     6X  8  3 

22.864 

201. 

4596.7 

1     6X2  3 

1.7005 

84  04 

142.9 

5     SX   8  6 

24.269 

204.9 

4972.8 

1     8X2  6 

2.0994 

90.63 

190.3 

5  10X   8  9 

25.718 

208.6 

5364.3 

1  10X2  9 

2.5402 

96.79 

245.9 

6       X  9 

27.210 

212.3 

5776.3 

2       X3 

3.0232 

102.9 

311.2 

6     2X   9  3 

28.742 

216. 

6208.8 

2     2x3  3 

3.5480 

108.6 

385.4 

6     4X   9  6 

30.317 

219.7 

6660.6 

2     4x3  6 

4.1149 

114.2 

469.9 

6     6X   9  9 

31.933 

223.4 

7133.6 

2    6X3  9 

4.7237 

119.9 

566.6 

6     8X10 

33.592 

226.9 

7622.3 

2     8X4 

5.3746 

125.2 

672.9 

6  10X10  3 

35.292 

230.4 

8132.3 

2  10X4  3 

6.0674 

130.3 

790.6 

7       X10  6 

37.035 

234. 

8670.0 

3       X4  6 

6.8022 

135.3 

920.5 

I  7     4X11 

40  .  646 

240.8 

9789.8 

3    2X4  9 

7.5790 

140.4 

1064.1 

7     8X11  6 

44.426 

247.5 

10988. 

3    4X5 

8.3970 

145.2 

1219.3 

8       X12 

48.372 

254.1 

12293. 

3    6X5  3 

9.2585 

149.8 

1387.5 

8    4X12  6 

52.487 

260.6 

13679. 

3    8X5  6 

10.161 

154.6 

1570.8 

8     8X13 

56.771 

266.9 

15154. 

3  10X5  9 

11.106 

159.2 

1767.7 

9       X13  6 

61.222 

273.3 

16731. 

4       X6 

12.093 

163.7 

1979.6 

9    4X14 

65.840 

279.4 

18397. 

4    2X6  3 

13.122 

168.1 

2205.5 

9    8X14  6 

70.628 

285.3 

20154. 

4    4X6  6 

14.192 

172.5 

2448. 

10       X15 

75.582 

291.3 

22018. 

4    6X6  9 

15.305 

176.7 

2705.3 

10    6X15  9 

83.330 

300.1 

25007. 

4    8X7 

16.460 

181.1 

2981.6  ! 

11       X16  6 

91.455 

308.7 

28233. 

4  10X7  3 

17.656 

185. 

3266.2    |12       X18 

108.838 

325.1 

35387. 

5       X7  6 

18.895 

189. 

3571.8 

270 


FLOW    OF    WATER    IN 


TABLE    61. 

Egg-shaped  Sewers  flowing  one-third  full  depth.  Based  on  Kutter's 
formula  with  n  =  .011. 

Giving  the  value  of  a,  and  also  the  values  of  the  factors  c\/r  and  ac\/r 
for  use  in  the  formulae: — 

v  —  c\/r   X  %/«" and  Q  =  ac^/r   X  \/s~ 

The  egg-shaped  sewer  referred  to  has  a  vertical  diameter  1 .5  the  greatest 
transverse  diameter,  Z),  that  is,  the  diameter  of  the  top  of  the  sewer. 
Area  of  egg-shaped  sewer  flowing  one-third  full  depth  =  £>'2  X  0.284. 
Perimeter  of  egg  shaped  sewer  flowing  one-third  full  depth  =D  X  1 .3747. 
Hydraulic  mean  depth  of  egg-shaped   sewer  flowing  one-third  full  depth 
=  D  X  0.2066. 


Size 
of  Sewer 

ft.  in.    ft.  in. 

a  =  area 
in 
square 
feet 

For  ve- 
locity 
cVr 

i 
For  dis- 
charge 
ac\/r 

Size 
of  Sewer 

ft.  in.     ft.  in. 

a—  area 
in 
square 
feet. 

For  ve- 
locity 
C%/7 

For  dis- 
charge 
ac\/r 

XI  6 

.2840 

45.72 

12.98 

5    2X   7  9 

7.5812 

146.5 

1110.6 

2X1  9 

.3865 

51.39 

19.89 

5     4X   8 

8.0782 

149  7 

1209.1 

4X2 

.5049 

56.74 

28.65 

5     6X  8  3 

8.5910 

152.7 

1311.8 

6X2  3 

.6390 

61.89 

39.55 

5     Sx  8  6 

9.1196 

155.7 

1420.3 

8X2  6 

.7889 

66.90 

52.78 

5  10X  8  9 

9.6639 

158.8 

1534.4 

10X2  9 

.9545 

71.58 

68.36 

6       X   9 

10.224 

161.6 

1652.4 

2       X3 

1  .  1360 

76.26 

86.63 

62x9  3    10.800 

164.6 

1778.1 

2    2x3  3 

1.3332 

80.71 

107.6 

6     4X   9  G    11.391 

167.5 

1908.1 

2    4X3  6 

1.5462 

85.28 

131.8  ! 

6     6X   9  9 

1  1  .  999 

170.4 

2044.3 

2    6X3  9 

1.7750 

89.42 

158.7 

6     8X10 

12.622 

173.3 

2187. 

2    8X4 

2.0195 

93.42 

188.7 

6  10X10  3 

13.261 

176. 

2334.7 

2  10X4  3 

2.2799 

97.50 

222.3 

7       X10  6 

13  916 

178.9 

2489.4 

3       X4  G 

2.5560 

101.6 

259.8 

7     4x11 

15.273 

184.2 

2813.5 

3    2X4  9 

2.8479 

105.4 

300.2 

7     8X11  C> 

16.693 

189.4 

3161  9 

3    4X5 

3.1556 

109.1 

344.5 

8       X12 

18.176 

194.8 

3541.7 

3    6X5  3 

3.4790 

112.7 

392.3 

8     4X12  6 

l'J.722 

199.9 

3942.3 

3    8X5  6 

3.8182 

116.4 

444.4  | 

8     8X13 

21.331 

204.9 

4370.8 

3  10X5  9 

4.1732 

120.1 

501.1  ! 

9       X13  6 

23.004 

209.9 

4829.6 

4       X6 

4  .  5440 

123.6 

561  5  i 

9    4X14 

24.739 

214.8 

5314  8 

4    2X6  3 

4.9306 

127. 

626.3 

9    8X146 

26  538 

219.5 

5825  3 

4    4X6  6 

5.3329 

130.3 

694.9 

10       X15 

28.400 

224.2 

6366.4 

4    6X6  9 

5.7510 

133.6 

768.6       10    6x15  9 

31.311 

231.2 

7239.6 

4     8X7 

6.1849 

137. 

847.4    1   11       X16  6 

34.364 

237  .  9 

8176. 

4  10X7  3 

6.6346 

140.4 

931.5 

12       X1S 

40.892 

251.3 

10277. 

5       X7  6      7.100 

143  3 

1017.8 

OPEN    AND    CLOSED    CHANNELS. 


271 


TABLE  62. 

Egg-shaped  Sewers  flowing  full  depth.  Based  on  Kutter's  formula  with 
n  =  .013. 

Giving  the  value  of  a,  and  also  the  values  of  the  factors  c\/3"  and  ac\/r 
for  use  in  the  formulae: — 

v  =  c\/r  X  -N/S  and  Q  =  ac\/r  X  \A 

The  factors  are  to  be  used  only  where  the  value  of  n,  that  is  the  co-effi- 
cient of  roughness  of  lining  of  channel  =  .013  as  in  ashlar  and  well  laid 
brickwork;  ordinary  metal;  earthenware  and  stoneware  pipe,  in  good  con- 
dition but  not  new;  cement  and  terra  cotta  pipe  not  well  jointed  nor  in 
perfect  order,  and  also  plaster  and  planed  wood  in  imperfect  or  inferior 
condition  and  generally  the  materials  mentioned  with  n  =  .010  when  in 
imperfect  or  inferior  condition  and  also  the  surfaces  of  other  materials 
equally  rough. 

The  egg-shaped  sewer  referred  to  has  a  vertical  diameter  equal  to  1.5 
times  the  greatest  transverse  diameter,  D,  that  is,  the  diameter  of  the  top 
of  sewer. 

Area  of  egg-shaped  sewer  flowing  full  depth  =  7>aX  1.148525. 
Perimeter  of  egg-shaped  sewer  flowing  two-thirds  full  depth  =  D  x  3.9649. 
Hydraulic  mean  depth  of  egg-shaped  sewer  flowing  one-third  full  depth 
=  D  X  0.2897. 


a=area 

For  ve- 

For dis- 

a=area 

For 

For  dis- 

Size of 

Size  of 

Sewer. 

in 
square 

locity 
c^/r 

charge 
ac-^/r 

Sewer. 

in 
square 

ve- 
locity 

charge 
ac\/r 

ft.  in.  ft.  in. 

feet. 

ft.  in.    ft.    in 

feet. 

cVr 

1       XI  6 

1.148J  47.58 

54.653 

5     2X  7  9 

30.66 

152.5 

4677.4 

1     2X1  9 

1.563 

53.46 

83.585 

5    4x  8 

32.669 

155.8 

5091.4 

1     4x2 

2.041 

59.19 

120.83 

5     6X  8  3  I  34.743 

159. 

5523.7 

1     6X2  3 

2.584 

64.44 

166.53 

5     8X  8  6  i  36.88 

162.1 

5980.5 

1     8x2  6 

3.19 

69.74 

222  .48 

5  10X  8  9      39.081 

165.3 

64G2.4 

1   10X2  9 

3.86 

74.68 

288.27 

6X91  41.347 

168.3 

6960.1 

2       X3 

4.594 

79.42 

364.85 

6     2X   9  3 

43.676 

171.5 

7490.3 

2     2X3  3 

5.391 

84.12 

453.56 

6    4X  9  6 

46.068 

174.3 

8032.2 

2     4X3  6 

6.253 

88.64 

554.29 

6     6X  9  9      48.525 

177.4 

8607.6 

2     6X3  9 

7.178 

93.06 

667.99 

6    SxiO         51.046 

180.4 

9210.5 

2     8X4 

8.167 

97.40 

795.52 

6  10X10  3 

53.629 

183.3 

9830.4 

2  10X4  3 

9.22 

101  6 

937.06 

7       XlO  6 

56.278 

186.1 

10476. 

3       X4  6 

10.337 

105.6 

1092.2 

7     4X11 

61.764 

191.7 

11841. 

3    2X4  9 

11.517 

109.7 

1264.1 

7     8X11  6 

67.508 

197.3 

13322. 

3    4X5 

12.761 

113.7 

1451.6 

8       X12 

73.506 

202.7 

14903. 

3     6X5  3 

14.069 

117.6 

1654.5 

8     4X12  6 

79.758 

208.1 

16601. 

3    8X5  6 

15.442 

121  4 

1874.5 

8     8X13 

86.268 

213.4 

18413. 

3  10X5  9 

16.877 

125.1 

2110.8 

9       X13  6 

93.03 

218.5 

20331  . 

4       X6 

18.376 

128.8 

2366.6 

j  9    4X14 

100.049 

223.4 

22356. 

4     2X6  3 

19.94 

132.4 

2639.8 

9     8X14  6 

107.324 

228.4 

24514. 

4     4X6  6 

21.566 

135.7 

2927.5 

10       X15 

114.853 

223.4 

26808. 

4     6X6  9 

23  258 

139.3 

3239.6 

10     6X15  9 

126.625 

240.6 

30471. 

4    8X7 

25.013 

142.7 

3569.6 

11       X16  6 

138.972 

247.7 

34431. 

4  10X7  3 

26.83 

146. 

3917 

12       X18 

IG5.388 

261.4 

i3237. 

5       X7  6 

28.713 

149.4 

4291.2 

272 


FLOW    OF    WATER    IN 


TABLE  63. 

Egg-shaped  Sewers  flowing  two-thirds  full.     Based  ou  Kutter's  formula 
with  n  =  . 013. 

Giving  the  value  of  a,  and  also  the  values  of  the  factors  c\/r  and  ac\/r 
for  use  in  the  formulae: — 

v  =  c-v/r  X  •s/Fand  Q  =  ac^/r  X  \/s 

The  egg-shaped  sewer  referred  to  has  a  vertical  diameter  1.5  times  the 
greatest  transverse  diameter,  Z>,  that  is,  the  diameter  of  the  top  of  sewer. 
Area  of  egg-shaped  sewer  flowing,  two-thirds  full  depth  =  D2  X  0.755825. 
Perimeter  of  egg-shaped  sewer  flowing  two-thirds  full  depth  =  D  X2.3941. 
Hydraulic  mean  depth  of  egg-shaped  sewer  flowing  two-thirds  full  depth 
=  Z>  X  0.3157. 


Size  of 
sewer. 

ft.  in.    ft.  in. 

a=area 
in 
square 
feet. 

For  ve- 
locity 
cVr 

For  dis-  ! 
i 
charge 

ac-^/r 

Size  of 
sewer. 

ft.  in.     ft,   in. 

a=area 
in 
square 
feet. 

For 
ve- 
locity 

c\/r 

For  dis- 
charge 
ac\/r 

1       XI  6 

.756 

50.83       38.42 

5    2X  7  9 

20.177 

161  5 

3258.4 

1     2X1  9 

1.029 

57.12 

58.76 

5     4X   8 

21.498 

165. 

3547  .  8 

1     4X2 

1.344 

63. 

84.65 

5     6X   8  3 

22.863 

168.3 

3848.8 

1     6X2  3 

1.701 

68.7 

116.82 

5     8X  8  6 

24.270 

171.7 

4166.3 

1     8X2  6 

2.099 

74.24 

155.86 

5  10X  8  9 

25.718 

174.8 

4496  .  8 

1  10X2  9 

2.540 

79.42i     201.74 

6       X  9 

27.21 

178. 

4844  .  9 

2       X3 

3.023 

84.59 

255.73 

6    2X  9  3 

28.743 

181.3 

5210.9 

2    2X3  3 

3.548 

89.4 

317.19 

6    4X  9  6 

30.317 

184.5 

5603.7 

2    4X3  6 

4.115 

94.14     387.38 

6     6X  9  9 

31.933 

187.7 

5992.9 

2    6X3  9 

4.724 

98.97     467.52 

6     8X10 

33.592 

190.7 

6406.4 

2    8X4 

5.375 

103.5        556.2 

6  10X10  3 

35.292 

193.7 

6837.9 

2  10X4  3 

6.067 

107.8 

654.45 

7       X10  6 

37  .  035 

196.8 

7289.2 

3       X4  6 

6.802 

112.1 

762.85 

7    4X11 

40.646 

202.7 

8240.8 

3    2X4  9 

7.579 

116.5 

882.95 

7     8X11  6 

44.426 

208.5 

9262.3 

3    4X5 

8.398 

120.6 

1012  7 

8       X12 

48.373 

214.1 

10358. 

3    6X5  3 

9.259 

124  6 

1153.4 

8    4X12  6 

52.487 

219.7 

11532. 

3    8X5  6 

10.161 

128.6 

1307. 

8     8X13 

56.771 

225.1 

12783. 

3  10X5  9 

11.106 

132.5 

1472.1 

9       X13  6 

61  222 

230.6 

14122. 

4       X6 

12.093 

136.4 

1649.3 

9    4X14 

65.84 

236. 

15537. 

4    2X6  3 

13.123 

140.1 

1838.5 

9    8X14  6 

70.628 

241.1 

17032. 

4    4X6  6 

14.192 

143.8 

2041  5 

10       X15 

75.583    246.3 

18621  . 

4    6X6  9 

15  305 

147.5 

2257.1 

10     6X15  9 

83.33     254. 

21165. 

4    8X7 

16.46 

151.1 

2486.8 

11       X16  6 

91.455    261.4 

23909. 

4  10X7  3 

17.656 

154.5 

2728.3 

12       X18 

108.84 

275.730008. 

5       X7  6 

18.895 

158. 

2985.4 

OPEN    AND    CLOSED    CHANNELS. 


273 


TABLE  64. 

Egg-shaped  Sewers  flowing  one-third  full  depth.  Based  on  Kutter's 
formula  with  n  =  .013. 

Giving  the  value  of  a,  and  also  the  values  of  the  factors  c^/r  and  ac^/r 
for  use  in  the  formulae  :  — 


v  =  c-v/r"  X  •>/»  and  ac^/7  X  \A~ 

The  egg-shaped  sewer  referred  to  has  a  vertical  diameter  1.5  times  the 
greatest  transverse  diameter,  Z>,  that  is,  the  diameter  of  the  top  of  the 
sewer. 

Area  of  egg-shaped  sewer  flowing  one-third  full  depth  =  Z>2  X  .284. 
Perimeter  of  egg-shaped  sewer  flowing  one-third  full  depth  =D  X  1.3747. 
Hydraulic  mean  depth  of  egg-shaped  sewer  flowing  one-third  full  depth 
=  Z>  X  .2066. 


a  =  area 

For  ve- 

For dis- 

a —area 

For 

For  dis- 

Size of 

Size  of 

in 

locity 

charge 

in 

ve- 

charge 

sewer. 

square 

cVr 

ac\/r 

sewer. 

square 

locity 

acv'r 

ft.  in.   ft.  in. 

feet. 

ft.  in       ft.  in. 

feet. 

cV~r 

1       XI  6 

.284 

36.74 

10.436 

5    2X  7  9 

7.581 

121.7 

922.69 

1     2X1  9 

.387 

41.43 

16.015 

5     4X  8 

8.078 

124.4 

1005.1 

1     4X2 

.505 

45.87 

23.162 

5     6X  8  3 

8.591 

127. 

1091.1 

1     6X2  3 

.639 

50.14 

32.044 

5     8X  8  6 

9.120 

129.6 

1181.9 

1     8X2  6 

.789 

54.31 

42  .  845 

5  10X  8  9 

9.664 

132.2 

1277.8 

I  10X2  9 

.955 

58.22 

55  .  573 

6       X   9 

10.224 

134.6 

1376.4 

2       X3 

1.136 

62.14 

70.598 

6    2X   9  3 

10.8 

137.2 

1481.7 

2     2X3  3 

1  .  333 

65.89 

87  853 

6    4X  9  6 

11.391 

139.6 

1590.3 

2     4X3  6 

1.546 

69.74 

107.84 

6    6X  9  9      12.999 

142. 

1704.6 

2    6X3  9  !   1.776 

73.22 

129.97 

6     8X10 

12.622 

144.5 

1824. 

2     8X4       !  2.020 

76.59 

154.67 

6  10X10  3 

13.261 

147. 

1S49.2 

2  10X4  3 

2.280 

80.02 

182.44 

7       XlO  6      13.916 

149.3 

2077.6 

3       X4  6 

2.556 

83.51 

213.46 

7     4X11          15.273 

153.8 

2349.9 

3    2X4  9 

2.848 

86.70 

246.91 

7    8X11  6      16.693 

158.3 

2643. 

3     4X5 

3.156 

89.85 

283.55 

8       X12 

18.176 

163. 

2962.7 

3    6X5  3 

3.479 

92.90 

323.22 

8    4X12  6 

19  722 

167.3 

3300.4 

3    8X5  6 

3.818 

96. 

366.53 

8     8X13 

21.332 

171.7 

3662. 

3  10X5  9 

4.173 

99.13 

413.68 

9       X13  6 

23.004 

176. 

4049.6 

4       X6 

4.544 

102  1 

463.9 

9    4X14 

24.739 

180.2 

4459.6 

4    2X6  3 

4.931 

105. 

517.91 

9    8X14  6 

26.538 

184.3 

4891.3 

4    4X6  6 

5.333 

107.8 

575.22 

10       X15 

28.4 

188.3 

5348.7 

4    6X6  9 

5.751 

110.7 

636.6 

10    6X15  9 

31.311 

194.4 

6088. 

4    8X7 

6.189 

113.6 

702.5 

11       X16  6 

34.364 

200.2 

6880.4 

4  10X7  3 

6.635 

116.5 

772.9 

12       X18 

40.892 

211.7 

8658. 

5       X7  6 

7.100    119. 

845. 

18 


274 


FLOW    OF    WATER    IN 


TABLE  65. 

Egg-shaped  Sewer  flowing  full  depth.  Based  on  Kutter's  formula  with 
n  =  ,015. 

Giving  the  value  of  a,  and  also  the  values  of  the  factors  c\/r  and  ac^/r 
for  use  in  the  formulae: — 

v  —  c\/r  X  \A  and  Q  —  ac\/r  X  \A 

These  factors  are  to  be  used  only  where  the  -value  of  n,  that  is  the  co- 
efficient of  roughness  of  lining  of  channel  =  .015,  as  in  second-class  or 
rough  faced  brickwork;  well-dressed  stonework;  foul  and  slightly  tuber- 
culated  iron;  cement  and  terra  cotta  pipes,  with  imperfect  joints  and  in 
bad  order,  and  canvas  lining  on  wooden  frames,  and  also  the  surfaces  of 
other  materials  equally  rough. 

The  egg-shaped  sewer  referred  to  has  a  vertical  diameter  equal  to  1.5 
times  the  greatest  transverse  diameter,  D,  that  is,  the  diameter  of  the  top  of 
sewer. 

Area  of  egg-shaped  sewer  flowing  full  depth  =  Z>2  X  1.148525. 
Perimeter  of  egg-shaped  sewer  flowing  full  depth  —  D  X  3.9649. 
Hydraulic  mean  depth  of  egg-shaped  sewer  flowing  full  depth  =  D  X  0.2897. 


Size  of 
sewer, 
ft.  in.  ft.  in. 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 

cVr 

For  dis- 
charge 

ac\/r 

Size  of 
sewer, 
ft.  in.     ft.  in. 

a=area 
in 
square 
feet. 

For  ve- 
locity 

cVr 

For  dis- 
charge 

ac\/r 

1       XI  6 

1.148 

39.62 

45.528 

5     2X  7  9 

30.660 

130.7 

4007.9 

1     2X1  9 

1.563 

44.66 

69  804 

5     4X  8 

32.669 

133.6 

4364.9 

1     4X2 

2.041 

49.57 

101.17 

5    6X  8  3 

34.743 

136.4 

4738. 

1     6X2  3 

2.584 

54.08 

139.74 

5    8X  8  6 

36.880 

139.2 

5131.7 

1     8X2  6 

3.190 

58.64 

187.06 

5  10X  8  9 

39.081 

142. 

5548. 

1  10X2  9 

3.860 

62.83 

242  .  52 

6       X  9 

41.347 

144.6 

5980  3 

2       X3 

4.594 

66.93 

307.48 

62X93 

43.676 

147.3 

6435.1 

2    2X3  3 

5.391 

71.01 

382.81 

6    4x  9  6 

46.068 

149  8 

6902  6 

2    4X3  6 

6.253 

74.93 

468.54 

66X99 

48  .  525 

152.5 

7399  3 

2     6X3  9 

7.178 

78.76 

565.34 

6    8X10 

51.046 

155.2 

7920.6 

2    8X4 

8.167 

82.44 

673.29 

6  10X10  3 

53.629 

157.7 

8547.1 

2  10X4  3 

9.220 

86.21 

794.86 

7       X10  6 

56.278 

160.2 

9015.7 

3       X4  6 

10.337 

89.70 

927  23 

7     4X11 

61.764 

165. 

10192 

3    2X4  9 

11.517 

93.25 

1074. 

7     8X11  6 

67  .  508 

170.1 

11482. 

3    4X5 

12.761 

96.73 

1234.4 

8       X12 

73  506 

174.8 

12852. 

3    6X5  3 

14.069 

100.1 

1407  .  6 

8     4X12  6 

79.758 

179.6 

14327 

3    8X5  6 

15  442 

103.4 

1596.7 

8     8X13 

86.268 

184.3 

15898. 

3  10X5  9 

16.877 

106.6 

1799.1 

9       X136 

93.030 

188.8 

17563. 

4       X6 

18.376 

109.9 

2019.5 

9     4X14 

100.049 

193.1 

19323. 

4    2X6  3 

19.940 

113. 

2254. 

9    8X14  6 

107.324 

197.5 

21198. 

4    4X6  6 

21.566 

116. 

2501.4 

10       X15 

114.853 

201.9 

23191. 

4     6X6  9 

23  .  258 

119.1 

2770. 

10    6X15  9 

126.625 

208  .  3 

26376. 

4     8X7 

25.013 

122.1 

3053  8 

11        X16  6 

138.972 

214  6 

29822. 

4  10X7  3 

26.830 

125. 

3353. 

12       X18 

165.388 

226.8 

37502. 

5       X7  6 

28.713 

128. 

3675.6 

OPEN    AND    CLOSED    CHANNELS. 


275 


TABLE  66. 

Egg-shaped  Sewers   flowing  two-thirds  full  depth.     Based  on  Kutter's 
formula  with  n  =  .015. 

Giving  the  value  of  a,  and  also  the  values  of  the  factors  c\/r  and  ac\/r 
for  use  in  the  formulae: — 

v  =  c\/r  X  \A'  and  Q  =  ac^/r  X  \A 

The  egg-shaped  sewer  referred  to  has  a  vertical  diameter  1.5  times  the 
greatest  transverse  diameter,  7),  that  is,  the  diameter  of  the  top  of  sewer. 
Area  of  egg-shaped  sewer  flowing  two-thirds  full  depth  =  Dl  X  0.755825. 
Perimeter  of  egg-shaped  sewer  flowing  two-thirds  full  depth  =  D  X  2.3941. 
Hydraulic  mean  depth  of  egg-shaped  sewer  flowing  two-thirds  full  depth 
=  DX  .03157. 


Size    of 
sewer 
ft.  in.  ft.  in. 

a=area 
in 
square 
feet. 

For  ve- 
locity 

C-v/f 

For  dis- 
charge 

ac-^/r 

Size    of 
sewer 
ft.  in.   ft.  in 

\ 

a  =  area 
in 
square 
feet. 

For  ve- 
locity 

c\/r 

For  dis- 
charge 

ac\/r 

1       Xl  6 

.756 

42.40 

32.048 

5     2X    7  9 

20.177 

138.6 

2795.9 

1     2X1  9 

1.029 

47.80 

49.181 

5     4X   8 

21.498 

141.7 

3045.5 

1     4X2 

1  .  344 

52.82 

70.993 

5    6X  8  3 

22.863 

144.6 

3305  .  3 

1     6X2  3 

1.701 

57.68 

98.115 

5    8X  8  6 

24.270 

147.5 

3578.9 

1     8X2  6 

2.099 

62.46 

131.10 

5  10X  8  9 

25.718 

150.3 

3864.8 

1  10X2  9 

2.540 

66.94 

170.02 

6       X  9 

27.210 

153.1 

4165.3 

2       X3 

3.023 

71.42 

216.54 

6    2X   9  3 

28.743 

155.9 

4481.6 

2    2X3  3 

3.548 

75.59 

268.19 

6    4X  9  6 

30  317 

158.7 

4811.9 

2    4X3  6 

4.115 

79.69 

327.93 

6     6X   9  9 

31.933 

161.5 

5158.5 

2    6X3  9 

4.724 

83.90 

396.32 

6     8X10 

33.592 

164.2 

5516  6 

2     8X4 

5.375 

87.82 

472.01 

6  10X10  3 

35.292 

166.9 

5891. 

2  10X4  3 

6  067 

91.60 

555.74 

7       X10  6 

37.035 

169.6 

6283.5 

3       X4  6 

6.802 

95  .  33 

648.40 

7     4X11 

40.646 

174.8 

7106.8 

3     2X4  9 

7.579 

99.10 

751.08 

7     8X11  6 

44.426 

179.9 

7993. 

3    4X5 

8.398 

102.7 

862.41 

8       X12 

48.373 

184.9 

8944. 

3    6X5  3 

9.259 

106.2 

983.24 

8     4X12  6 

52.487 

189.8 

9964.1 

3    8X5  6 

10.161 

109.7 

1115.1 

8     8X13 

56.771 

194.6 

11050. 

3  10X5  9 

11.106 

113.2 

1256.1 

9       X1S  6 

61.222 

199.5 

12213. 

4       X6 

12.093 

116.5 

1409.4 

9    4X14 

65  .  840 

204.2 

13444. 

4    2X6  3 

13.123 

119.8 

1572.1 

9    8X14  6 

70  628 

208.7 

14743. 

4    4X6  6 

14.192 

123.1 

1746.9 

10       X15 

75.583 

213.3 

16125. 

4    6X6  9 

15.305 

126.3 

1932.7 

10    6X15  9 

83.330 

220.1 

18342. 

4     8X7 

16.460 

129.4 

2130.5 

II       X16  (• 

91.455 

226.8 

20738. 

4  10X7  3 

17.656 

132.5 

2338.6 

12       X18 

108.84 

239.4 

26060. 

5       X7  6 

18.895 

135.5 

2560.3 

276 


FLOW    OF    WATER    IN 


TABLE  67. 

Egg-shaped  Sewers  flowing  one-third  full  depth.  Based  011  Kutter's 
formula  with  n  =  .015. 

Giving  the  value  of  a,  and  also  the  values  of  the  factors  c\/r  and  ac^/r 
for  use  in  the  formula: — 

v  =  c\/r  X  \/s  and  Q  =  ac\/r  X  \A7 

The  egg-shaped  sewer  referred  to  has  a  vertical  diameter  1 .5  times  the 
greatest  transverse  diameter,  D,  that  is,  the  diameter  of  the  top  of  the 
sewer. 

Area  of  egg-shaped  sewer  flowing  one-third  full  depth  =  D'2  X  .284. 
Perimeter  of  egg-shaped  sewer  flowing  one-third  full  depth  =  D  X  1.3747. 
Hydraulic  mean  depth  of  egg-shaped  sewer  flowing  one-third  full  depth 
=  D  X  .2066. 


Size  of 
sewer 
ft.  in.  ft.  in. 

a=area 
in 
square 
feet. 

For  ve- 
locity 

c^/r 

For  dis- 
charge 

ac\/r 

Size   of 
sewer 
ft.  in.    ft.  in. 

a=area 
in 
square 
feet. 

For  ve- 
locity 

cVr 

For  dis- 
charge 

ac\/r 

1        Xl   6 

.284 

30.41 

8.637 

5    2X  7  9 

7.581 

103.7 

785.86 

1     2X1  9 

.387 

34.38 

13.303 

5     4X  8 

8.078 

106.1 

856.67 

1     4X2 

.505 

38.16 

19.269 

5    6X  8  3 

8.591 

108.3 

930.54 

1     6X2  3 

.639 

42.23 

26.986 

5    8X  8  6 

9.120 

110.6 

1008  7 

1     8X2  6 

.789 

45.39 

35.815 

5  10X  8  9 

9.664 

112.9 

1091  . 

1  10X2  9 

.955 

48.74 

46.546 

6       X  9 

10.224 

115. 

1175.8 

2       X3 

1  136 

52.09 

59.  173 

6    2X  9  3 

10.800 

117.3 

1266.4 

2    2X3  3 

1.333 

55.29 

73.696 

6    4X  9  6 

11.391 

119.4      1359.8 

2    4x3  6 

1.546 

58.58 

90.568 

6     6X  9  9 

12.999 

121.5      1458.1 

2    6X3  9 

1.776 

61.58 

109.37 

6    8X10 

12.622 

123.7      1561. 

2     8X4 

2.020 

64.49 

130.26 

6  10X10  3 

13.261 

125.8      1668.8 

2  10X4  3    2.280 

67.46 

153.80 

7       X10  6 

13.916 

127.9      1779.4 

3       X4  6 

2.556 

70.48 

180.14 

7     4X11 

15.273 

131.9     2014.1 

3    2X4  9 

2  .  848 

73.24 

208.98 

7     8X11  6 

16.693 

135.8  \  2266.7 

3    4X5 

3.156 

75.98 

239.79 

8       X12 

18.176 

139.9 

2542.7 

3    6X5  3 

3.479 

78.63 

273.54 

8    4X12  6 

19.722 

143.7 

2833.8 

3    8X5  6 

3.818 

81.31 

310.44 

8     8X13 

21.332 

147  .  5 

3146.2 

3  10X5  9 

4.173 

84.03 

350.67 

9       X13  6 

23.004 

151.3 

3480.7 

4       X6 

4.544 

86.61 

393.55 

9    4X14 

24.739 

155. 

3834.7 

4    2X6  3 

4.931      88.98 

438.75 

9    8X146 

26.538 

158.6 

4208.4 

4    4X6  6 

5.333 

91.60 

488.50 

10       X15 

28.400 

162.1 

4604.7 

3    6X6  9 

5.751 

94.08 

541.04 

10    6X15  9 

31.311 

167.5 

5245.3 

4     8X7 

6.189  I  96.57 

597.29 

11       X16  6 

34.364 

172.6 

5932.1 

4  10X7  3 

6.635 

99.10 

657.53 

12       X18 

40.892 

183.1 

7489. 

5       X7  6 

7.100 

101  3 

719.27 

OPEN    AND    CLOSED    CHANNELS. 


277 


TABLE  68. 

Giving  velocities  and  discharges  of  Circular  Pipes,  Sewers  and  Conduits, 

iled  on  Kutter's  formula,  with  n  —  .013. 

(I  =  diameter. 

v  =-mean  velocity  in  feet  per  second. 

Q  —  discharge  in  cubic  feet  per  second. 


d  = 

=  5" 

d  = 

=  6" 

d* 

=  7" 

d  = 

r  8" 

d 

=  9" 

Slope 

lia 

V 

Q 

V 

Q 

V 

Q 

V 

Q 

V 

Q 

40 

3.35 

.456 

3.89 

.762 

4.40 

1.17 

4.90 

1.71 

5.37 

2  37 

70 

2.53 

.344 

2.94 

.576 

3.33 

.889 

3.7 

1.29 

4.06 

1.79 

100 

2  12 

.288 

2  46 

.482 

2.79 

.744 

3.1 

1.08 

3.40 

1.50 

2CO 

1.50 

.204 

.74 

.341 

1.97 

.526 

2.19 

.765 

2  4 

1.06 

300 

1.22 

.166 

.42 

.278 

.61 

.430 

1.79 

.624 

1.96 

.868 

400 

1.06 

.144 

.23 

.241 

1  39 

.372 

1.55 

.54 

1.7 

.75 

500 

1.01 

.137 

.17 

.230 

33 

.  355 

1.48 

.516 

1.62 

.717 

GOO 

.865 

.118 

. 

.197 

.14 

.304 

1.26 

.441 

1.39 

.613 

d  = 

10" 

d  = 

:  11" 

d  = 

r  o" 

d  = 

r  r 

d  = 

r  2" 

60 

4.76 

2.59 

5.14 

3.39 

5.5 

4  32 

5.84 

5.38 

6.18 

6.6 

80 

4.12 

2.24 

4  45 

2.94 

4.77 

3.74 

5  05 

4  66 

5  35 

5.72 

100 

3.68 

1. 

3.98 

2.63 

4.26 

3.35 

4.52 

4.16 

4.78 

5  15 

200 

2.61 

1.42 

2.82 

1.86 

3.01 

2.37 

32 

2.95 

3.38 

3.62 

3CO 

2.13 

1.16 

2.3 

1.52 

2.46 

1.93 

2.61 

2.4 

2  76 

2.95 

400 

1.84 

.5 

1.99 

1.31 

2.13 

1.67 

2  26 

2.08 

2.39 

2.57 

500 

1.65 

.9 

1.78 

1.17 

1.91 

1.5 

2.02 

1.86 

2.14 

2  29. 

600 

1.5 

.82 

1.62 

1.07 

1.74 

1.37 

1.84 

1.70 

1.95 

2.09 

d  == 

r  3" 

d  = 

r  4" 

d  = 

r  6" 

d  = 

i'  8" 

d  = 

1'  10" 

100 

5.04 

6.18 

5.29 

7.38 

5.78 

10  21 

6.25 

13.65 

6  70 

17.71 

200 

3.56 

4.37 

3.74 

5.22 

4.09 

7  22 

4.43 

9.65 

4.74 

12.52 

300 

2.91 

3.57 

3.05 

4.26 

3.34 

5.89 

3.61 

7.88 

3  87 

10.22 

400 

2.52 

3.09 

2.64 

3.69 

2.89 

5.10 

3.12 

6.82 

3.35 

8.85 

500 

2.25 

2.77 

2.36 

3  30 

2  58 

4.56 

2.8 

6.1 

3. 

7.92 

000 

2.06 

2.52 

2.16 

3.01 

2.36 

4.17 

2  56 

5.57 

2.74 

7.23 

700 

1  90 

2.34 

2. 

2.79 

2.18 

3.86 

2  37 

5.16 

2  53 

6.69 

800 

1.78 

2.19 

1.87 

2.61 

2.04 

3.61 

2.21 

4.83 

2.37 

6.26 

d  = 

2'  0" 

d  = 

2'  2" 

d  = 

I'  4" 

d  = 

I'  6" 

d  = 

2'  8" 

200 

5.05 

15.88 

5.35 

19.73 

5.65 

24.15 

5.92 

29.08 

6.21 

34.71 

400 

3.57 

11.23 

3.78 

13.96 

3  .  99 

17.07 

4.19 

20.56 

4.39 

24  54 

600 

2.92 

9.17 

3.09 

11.39 

3.26 

13.94 

3.42 

16.79 

3  59 

20.04 

800 

2  53 

7.94 

2.67 

9.87 

2.82 

12.07 

2  96 

14.54 

3.11 

17.35 

1000 

2.26 

7.1 

2.39 

8.82 

2  52 

10.8 

2.65 

13. 

2  78 

15.52 

1250 

2.02 

6.35 

2.14 

7.89 

2.26 

9  66 

2  37 

11.63 

2.48 

13.88 

1500 

1.84 

5.8 

1.95 

7.2 

2.06 

8.82 

2  16 

10.62 

2.27 

12.67 

1800 

1.68 

5.29 

1.78 

6.58 

1.88 

8.05 

1.97 

9.69 

2.07 

11.57 

278 


FLOW    OF    WATEK    IN 


TABLE  G8. 

Giving  velocities  and  discharges  of  Circular  Pipes,  Sewers  and  Conduits, 
based  on  Kutter's  formula,  with  n  —  .013. 
d  —  diameter. 

v  =  mean  velocity  in  feet  per  second. 
Q  =  discharge  in  cubic  feet  per  second. 


d  -.- 

2'  10" 

d  = 

3'  0" 

d  = 

3'  2" 

d  = 

3'  4" 

d  = 

3'  6" 

Slope 

1  in 

V 

Q 

V 

Q 

V 

Q 

V 

Q 

» 

Q 

500 

4.10 

25.84 

4  26 

30.14 

4.43 

34.90 

4.59 

40.08 

4.74 

45.66 

750 

3.34 

21.10 

3.48 

24.61 

3.61 

28.50 

3.75 

32.72 

3  87 

37.28 

1000 

2.89 

18-27 

3.01 

21.31 

3.13 

24.68 

3.25 

28.34 

3.35 

32.28 

1250 

2.59 

16.34 

2.69 

19.06 

2.80 

22.07 

2.90 

25.35 

3. 

28.87 

1500 

2.36 

14.92 

2.46 

17.40 

2.55 

20.15 

2.65 

23.14 

2.73 

26.36 

1750 

2.19 

13.81 

1  2.28 

16.11 

2.36 

18.66 

2.45 

21.42 

2.53 

24.40 

2000 

2.05 

12.92 

2.13 

15.07 

2.21 

17.45 

2.29 

20.04 

2.37 

22.83 

2640 

1.78 

11.24 

1.85 

13.12 

1.92 

15.19 

2. 

17.44 

2.06 

19.87 

d  = 

3'  8" 

d  = 

3'  10" 

d  = 

4'  0" 

d  = 

4'  6" 

d  = 

5'  0" 

500 

4.90 

51.74 

5.06 

58.36 

5.21 

65.47 

5.64 

89.75 

6.05 

118.9 

750 

4. 

42.52 

4.13 

47.65 

4.25 

53.46 

4.61 

73.28 

4.94 

97.09 

1000 

3.4C 

36.59 

3.58 

41.27 

3.68 

46.3 

3.99 

63.47 

4.28 

84.08 

1250 

3.1 

32.72 

3.2 

36.91 

3.29 

41.41 

3.57 

56.76 

3.83 

75.21 

1500 

2.83 

29  87 

2.92 

33.69 

3.01 

37.8 

3.26 

51.82 

3.49 

68.65 

1750 

2.62 

27.66 

2.7 

31.2 

2.78 

34.5 

3.01 

47.97 

3.24 

63.56 

2000 

2.45 

25.87 

2.53 

29.18 

2.61 

32.74 

2.82 

44.88 

3.02 

59.46 

2640 

2.13 

22  59 

2.2 

25.4 

2.27 

28.49 

2.46 

39.06 

2.63 

51.75 

d  ~ 

5'  6" 

d  = 

6'  0" 

d== 

6'  6" 

d  = 

7'  0" 

d  = 

7'  6" 

750 

5.27 

125.2 

5.58 

157.8 

5.88 

195. 

6  18 

237.7 

6.46 

285.3 

1000 

4.56 

108.4 

4.83 

136.7 

5.1 

168.8 

5.35 

205.9 

5.59 

247.1 

1500 

3.72 

88.54 

3.95 

111.6 

4.16 

137.9 

4.37 

168.1 

4.57 

201.7 

2000 

3  22 

76.67 

3.42 

96.66 

3.60 

119.4 

3.78 

145.6 

3.95 

174.7 

2500 

2.88 

68.58 

3.06 

86.45 

3  22 

106.8 

3.38 

130.2 

3.53 

156.3 

3000 

2.63 

62.6 

2.79 

78.92 

2.94 

97.49 

3.09 

118.8 

3.23 

142.6 

3500 

2.44 

57.96 

2.58 

73.07 

2.72 

90.26 

2.86 

110. 

2.99 

132.1 

4000 

2.28 

54.21 

2.42 

68.35 

2.55 

84.43 

2.67 

102.9 

2.8 

123.5 

d  = 

8'  0" 

d  = 

S'  6" 

d  = 

9'  0" 

d  = 

9'  6" 

d  — 

10'  0" 

1500 

4.76 

239.4 

4.95 

281.1 

5.14 

327. 

5.31 

376.9 

5.49 

431.4 

2000 

4  12 

207.3 

4.29 

243.5 

4.45 

283.1 

4  6 

326.4 

4.76 

373.6 

2500 

3.69 

195.4 

3.84 

217.8 

3.98 

253.3 

4.12 

291.9 

4.25 

334.1 

3000 

3.37 

169.3 

3.50 

198.8 

3.63 

r>31  2 

3.76 

266.5 

3.88 

305. 

3500 

3.12 

156  7 

3.24 

184. 

3.36 

214. 

3.48 

246.7 

3.6 

282.4 

4000 

2.92 

146.6 

3.03 

172  2 

3.15 

200.2 

3.25 

230.8 

3  36 

264.2 

4500 

2.75 

138.2 

2.86 

162.3 

2  97 

188.7 

3.07 

217.6 

3.17 

249.1 

5000 

2.61 

131.1 

2.71 

154. 

2.81 

179.1 

2.91 

206.4 

3.01 

236.3 

OPEN    AND    CLOSED     CHANNELS. 


279 


TABLE  69. 

Giving  velocities  and  discharges  of  Egg-Shaped  Sewers,  based  on  Kut- 
ter's  formula,  with  n  =  .013.  Flowing  full  depth.  Flowing  f  full  depth. 
Flowing  i  full  depth. 

v  =.meaii  velocity  in  feet  per  second. 

Q  =  discharge  in  cubic  feet  per  second. 


Size  of  Sewer  2'  9"  x  3'  0" 


Slope 

liii 

Full  1 

)epth 

i  Fr.ll 

Depth 

i  Full  : 

Depth 

V 

Q 

V 

Q 

V 

Q 

100 

7.94 

36.48 

8.46 

25.57 

6.21 

7.06 

200 

5.61 

25.8 

5.98 

18.08 

4.39 

4.09 

300 

4.58 

21.06 

4.88 

14.76 

3.59 

4.07 

500 

3.55 

16.31 

3.78 

11.43 

2.78 

3.16 

700 

3. 

13.79 

3.2 

9.66 

2.35 

2.67 

1000 
1200 

2.51 
2.29 

11.54 
10.53 

2.67 
2.44 

8.08 
7.38 

1.96 
1.79 

2.23 
2.04 

1500 

2.05 

9.42 

2.18 

6.6 

1.6 

1.82 

Siz 

e  of  Sewer 

2'  2"  x  3'  3 

100 

8  41 

45.35 

8.94 

31.72 

6.59 

8.78 

200 

5.95 

32.07 

6.32 

22.43 

4.66 

6.21 

300 

4.85 

26.19 

5.16 

18  31 

3.80 

5.07 

500 

4.01 

21.64 

4.26 

15.14 

3.14 

4.19 

700 

3.18 

17.14 

3.38 

11.99 

2.49 

3.32 

1000 

2  66 

14  .  34 

2.83 

10.03 

2.08 

2.78 

1200 

2.43 

13.09 

2.58 

9.15 

1.9 

2.53 

1500 

2.17 

12.71 

2.31 

8.19 

1.7 

2  26 

Siz 

e  of  Sewer 

2'  4"  x  3'  6 

150 

7.24 

45.26 

7.68 

31.63 

5.69 

8.8 

300 

5.12 

32. 

5.43 

22.37 

4.02 

6.22 

600 

3.62 

22.63 

3.84 

15.81 

2.84 

4.4 

1000 

2.8 

17.53 

2.97 

12.25 

2.2 

3.41 

1250 

2.51 

15.68 

2.66 

10.96 

1.97 

3.05 

1500 

2.29 

14.31 

2.43 

10. 

1.8 

2.78 

1750 

2.12 

13  25 

2.25 

9.26 

1.67 

2.58 

2000 

1  98 

12.39 

2.1 

8.66 

1.56 

2.41 

Siz 

a  of  Sewer 

2'  6"  x  3'  9 

" 

300 

5  37 

38.57 

5.71 

26.99 

4.2 

7.5 

600 

3.8 

27.27 

4.04 

19.08 

2.98 

5.31 

1000 

2.94 

21.12 

3.13 

14.78 

2.31 

4.11 

1250 

2.63 

18.89 

2  8 

13.22 

2.06 

3.68 

1500 

2.4 

17.25 

2.55 

12.07 

1.88 

3.36 

1750 

2  22 

15.97 

2  37 

11.17 

1.74 

3.11 

2000 

2.08 

14.94 

2.21 

10.45 

1  63 

2.91 

2640 

1  81 

13. 

1.93 

9.1 

1.42 

2  53 

280 


FLOW    OF    WATER    IN 


TABLE  69. 

Giving  velocities  and  discharges  of  Egg-Shaped  Sewers,  based  on  Kut- 
ter's  formula,  with  n  =  .013.  Flowing  full  depth.  Mowing  f  full  depth. 
Flowing  ^  full  depth. 

v  —  velocity  in  feet  per  second. 

Q  =  discharge  in  cubic  feet  per  second. 


Slope 
1  in 

Size  of  Sewer  2'  8"  x  4'  0" 

Full  Depth 

f  Full  Depth 

4  Full  Depth 

V 

Q 

V 

Q 

V 

Q 

500 
750 
1000 
1250 
1500 
1750 
2000 
2640 

4.35 
3.55 
3  08 
2.75 
2.51 
2.32 
2.17 
1.89 

35.57 
29.04 
25.15 
22.49 
20.53 
19.01 
17.78 
15.48 

4.62 
3.77 
3.27 
2.92 
2.67 
2.47 
2.31 
2.01 

24.87 
20.30 
17.58 
15.73 
14.36 
13.29 
12  43 
10.82 

3.42 
2.79 
2.42 
2.16 
1.97 
1.83 
1.71 
1.49 

6.91 
5.64 
4  89 
4.37 
3.99 
3.69 
3.45 
3.01 

Siz< 

3  of  Sewer 

2'  10"  x  4' 

3" 

500 

4.54 

41.90 

4.82 

29.26 

3.57 

8.15 

750 

3.70 

34.21 

3.93 

23  89 

2.92 

6.66 

1000 

3.21 

29.63 

3.41 

20.69 

2.52 

5.76 

1250 

2.87 

26.50 

3.05 

18.50 

2.26 

5.15 

1500 

2.62 

24.19 

2.78 

16.89 

2.06 

4.70 

1750 

2.42 

22  39 

2.57 

15.64 

1.91 

4  36 

2000 

2.27 

20.95 

2.41 

14  63 

1.78 

4.07 

2640 

1.97 

18.23 

2.10 

12.73 

1.55 

3.55 

Siz 

e  of  Sewer 

3'  0"  x  4'  6 

500 

4.72 

48.83 

5.01 

34.11 

3.73 

9.54 

750 

3.85 

39.87 

4.09 

27.85 

3.04 

7.79 

1000 

3.33 

34.53 

3.54 

24.12 

2.64 

6.74 

1250 

2.98 

30.88 

3.17 

21.57 

2.36 

6.03 

1500 

2.72 

28.19 

2.89 

19.69 

2.15 

5.50 

1750 

2.52 

26.10 

2.67 

18.23 

1.99 

5.10 

2000 

2.36 

24.41 

2.50 

17.05 

1.86 

4.77 

2640 

2.05 

21.25 

2.18 

14.84 

1.62 

4.15 

Siz 

e  of  Sewer 

3'  2"  x  4'  8 

" 

500 

4.90 

56.52 

5.20 

39.48 

3.87 

11.04 

750 

4. 

46.15 

4.25 

32.24 

3.16 

9.01 

1000 

3.46 

39  97 

3  68 

27  92 

2.74 

7.80 

1250 

3.10 

35.75 

3.29 

24.97 

2.45 

6.98 

1500 

2.83 

32.63 

3. 

22.79 

2.23 

6.37 

1750 

2.62 

30.21 

2.78 

21.10 

2.07 

5.90 

2000 

2.45 

28.26 

2.60 

19.74 

1  93 

5.52 

2640 

2.13 

24.60 

2.26 

17.18 

1.68 

4.80 

OPEN    AND    CLOSED    CHANNELS. 


281 


TABLE  69. 

Giving  velocities  and  discharges  of  Egg-Shaped  Sewers,  based  on  Kut- 
ter's  formula,  with  n  =  .013.  Flowing  full  depth.  Flowing  $  full  depth. 
Flowing  %  full  depth. 

v  =  mean  velocity  in  feet  per  second. 

Q  =  discharge  in  cubic  feet  per  second. 


Siz 

e  of  Sewer 

3'  4"  x  5'  0 

Slope 
1   in 

Full  . 

Depth 

f  Full 

Depth 

i  Full  ] 

Depth 

v 

Q 

V 

Q 

V 

Q 

500 
750 
1000 
1250 
1500 
1750 
2000 
2640 

5.08 
4.15 
3.59 
3.21 
2.93 
2.72 
2.54 
2.21 

64.89 
52.98 
45.88 
4i. 
37.46 
34.68 
32.44 
28.24 

5.39 
4.40 
3.81 
3.41 
3.11 
2.88 
2.69 
2  34 

45  25 
36  .  95 
32. 
28.62 
26.13 
24.19 
22.63 
19  69 

4.01 
3.27 
2.83 
2.53 
2.32 
2.14 
2.01 
1.74 

12.67 
10.35 
8.96 
8.01 
7.32 
6.77 
6.34 
5.51 

Si? 

e  of  Sewer 

3'  6"  x  5'  3 

500 
750 
1000 
]  250 
1  500 
1750 
2000 
2640 

5.26 
4.29 
3.72 
3.32 
3.03 
2.81 
2.63 
2.29 

73.97 
60.39 
52  .  30 
46.78 
42.70 
39.53 
36.98 
32.19 

5.57 
4  55 
3.94 
3.52 
3.21 
2.98 
2.78 
2.42 

51.56 
42.10 
36.46 
32.61 
29.77 
27.56 
25.78 
22.44 

4.15 
3.39 
2.94 
2.62 
2.40 
2.22 
2^08 
1.81 

14.45 

11.80 
10.22 
9.14 
8  34 

7.72 
7.22 
6  29 

Siz 

e  of  Sewer 

3'  8"  x  5'  6 

500 
750 
1000 
1250 
1500 
1750 
2000 
2640 

5.43 
4.43 
3  84 
3  43 
3.13 
2.9 
2  71 
2.36 

83.81 
68  43 
59.26 
53. 
48.39 
44.8 
41  9 
36.47 

5.75 
4.69 
4.07 
3.64 
3.32 
3.07 
2.87 
2.50 

58.45 
47.72 
41.33 
36.97 
33.74 
31.24 
29.22 
25.44 

4.29 
3.50 
3.03 
2.71 
2.48 
2.29 
2.14 
1.87 

16.39 
13.38 
11.59 
10.37 
9.46 
8.76 
8.19 
7.13 

Siz 

e  of  Sewer 

3'  10"  x  5' 

9" 

750 
1000 
1250 
1500 
1750 
2000 
2640 
3000 

4  56 
3  95 
3  53 
3  23 
2.99 
2.79 
2.43 
2.28 

77.08 
66.76 
59.71 
54.51 
50.46 
47.2 
41.09 
38.54 

4.84 
4.19 
4.03 
3.42 
3.17 
2.96 
2.58 
2.42 

53.75 
46.55 
41.63 
38. 
35.19 
32.91 
28  65 
26  87 

3.62 
3.13 
2.8 
2  56 
2.37 
2.22 
1.93 
1.81 

15.11 
13.08 
11.7 
10.68 
9.89 
9.25 
8.05 
7.55 

282 


FLOW    OF    WATER    IN 


TABLE  69. 

Giving  velocities  and  discharges  of  Egg-Shaped  Sewers,  based  on  Kut- 
ter's  formula,  with  n  =  .013.  Flowing  full  depth.  Flowing  f  full  depth. 
Flowing  £  full  depth. 

v  —  mean  velocity  in  feet  per  second. 

Q  =  discharge  in  cubic  feet  per  second. 


Slope 
1  in 

Size  of  Sewer  4'  0"  x  Q'  0" 

Full  Depth 

f  Full  Depth 

i  Full  Depth 

V 

Q 

V 

Q 

V 

Q 

1000 
1250 
1500 
1750 
2000 
2640 
3000 
3500 

1000 
1250 
1500 
1750 
2000 
2640 
3000 
3500 

1250 
1500 
1750 
2000 
2640 
3000 
3500 
4000 

1250 
1500 
1750 
2000 
2640 
3000 
3500 
4000 

4.07 
3.64 
3.32 
3.07 
2  88 
2.50 
2.35 
2.17 

74.82 
66  91 
61.09 
56.66 
52.90 
46.04 
43.19 
39.99 

4.31 
3.85 
3.52 
3.26 
3.05 
2.65 
2.49 
2.30 

52.14 
46.64 
42.57 
39.41 

36.87 
32.09 
30.10 

27.87 

3.22 
2.88 
2.63 
2.44 
2.28 
1.98 
1.86 
1.72 

14.66 
13.12 
11.97 
11.08 
10.37 
9.02 
8.46 
7.84 

Size  of  Sewer  4'  2"  x  6'  3" 

4.18 
3.74 
3.41 
3.16 
2  96 
2.57 
2.41 
2.29 

83.48 
74.66 
68.16 
63.10 
59.03 
51.38 
48.19 
44.62 

4.43 
3.96 
3.61 
3.34 
3.13 
2.72 
2.55 
2.36 

58.12 
51.98 
47.45 
43.93 
41.09 
35.77 
33.55 
31.06 

3.32 
2.96 
2.71 
2.51 
2.34 
2.04 
1.91 
1.77 

16.37 
14.64 
13.37 
12.38 
11.58 
10.07 
9.45 
8.75 

Size  of  Sewer  4'  4"  x  6'  6" 

3.84 
3.5 
3.24 
3.03 
2.64 
2.48 
2.29 
2.14 

82.79 
75.57 
69.97 
65.45 
56.97 
53.44 
49.47 
46.28 

4.07 
3.71 
3.44 
3.21 

2.8 
2.62 
2.43 

2.27 

57.73 
52.7 
48.79 
45.64 
39.72 
37.26 
34.5 
32.27 

3.05 
2.78 
2.58 
2.41 
21 
1.97 
1.82 
1.7 

16.27 
14.85 
13.45 
12.86 
11   19 
10.5 
9.72 
9.09 

Size  of  Sewer  4'  6"  x  6'  9" 

3.94 
3  6 
3.33 
3.11 
2.71 
2.54 
2.35 
22 

91.61 
83  63 
77.43 
72.42 
63.04 
59.13 
54.75 
51.21 

4.17 
3.81 
3.52 
3.3 

2.87 
2.69 
2.49 
2.33 

63.84 
58.27 
53  95 
50.47 
43.93 
41.21 
38.15 
35.68 

3.13 

2.85 
2.65 
2.47 
2.15 
2.02 
1.87 
1.75 

18.01 
16.44 
15.22 
14.24 
12.39 
11.62 
10.76 
10.07 

OPEN    AND    CLOSED    CHANNELS. 


288 


TABLE  69. 

Giving  velocities  and  discharges  of  Egg-Shaped  Sewers,  based  on  Kut- 
ter's  formula,  with  n  =  .013.  Flowing  full  depth.  Flowing  f  full  depth. 
Flowing  £  full  depth. 

v  =  mean  velocity  in  feet  per  second. 

Q  —  discharge  in  cubic  feet  per  second. 


Si; 

:e  of  Sewer 

4'  8"  x  7'  C 

1" 

Slope 
1   in 

Full 

Depth 

}  Full 

Depth 

i  Full 

Depth 

V 

Q 

V 

Q 

V 

Q 

1250 
1500 
1750 
2000 
2640 
3000 
3500 
4000 

4.04 
3.68 
3.41 
3.19 
2.78 
2.60 
2.41 
2.26 

101. 
92.17 
85  .  34 
79.82 
69.48 
65.18 
60.34 
56.44 

4.27 
3.9 
3.61 
3.38 
2  94 
2.76 
2.55 
2.39 

70.34 
64.21 
59.45 
55.61 
48.4 
45.4 
42.04 
39.31 

3.21 
2.93 
2  71 
2.54 
2.21 
2.07 
1.92 
1.79 

19.87 
18.14 
16.79 
15.7 
13.67 
12.83 
11.87 
11.11 

Siz 

e  of  Sewer 

4'  10"  x  7' 

3" 

1250 
1500 
1750 
2000 
2640 
3000 
3500 
4000 

4.13 
3  77 
3.49 
3.26 
2.84 
2.66 
2.47 
2.31 

110.8 
101.1 
93.63 
87.59 
76.24 
71.51 
66.21 
61.93 

4.37 
3.99 
3.69 
3.45 
3.01 
2.82 
2.61 
2.44 

77  16 
70.43 
65.21 
61. 
53.09 
49.8 
46.11 
43.13 

3.29 
3.01 

2.78 
2.60 
2  27 
2.13 
1.97 
1  .84 

21.86 
J9.96 
18.48     . 
17.28 
15.04 
14.11 
13.06 
12.22 

Siz 

e  of  Sewer 

5'  0"  x  7'  6 

" 

1500 
1750 
2000 
2640 
3000 
3500 
4000 
5000 

3.86 
3.57 
3.34 
2.91 
2.73 
2  .  52 
2.36 
2.11 

110.8 
102.6 
95.95 
83.51 
78.34 
72.53 
67.84 
60.68 

4.08 
3.78 
3.53 
3.07 
2.88 
2.67 
2.5 
2.23 

77.07 
71.35 
66.75 
58.1 
54.5 
50.45* 
47.2 
42.21 

3.07 
2.84 
2.66 
2.32 
2.17 
2.01 
1.88 
1.68 

21.82 
20.2 
18.9 
16.45 
15.43 
14.28 
13.36 
11.95 

Siz 

e  of  Sewer 

5'  4"  x  8'  0 

" 

1500 
1750 
2000 
2640 
3000 
3500 
4000 
5000 

4.02 
3.72 
3.48 
3.03 
2.84 
2.63 
2.46 
2.2 

131.4 

121.7 
113.8 
99.1 
92.95 
86.05 
80  49 
72. 

4  26 
3.94 
3.69 
3.21 
3.01 
2.79 
2.61 
2.33 

91.61 
84.81 
79.33 
69.05 
64.77 
60. 
56.1 
50.18 

3.21 
2.97 

2.78 
2.42 
2.27 
2.1 
1  97 
1  76 

25.95 

24  .  02 
22.47 
19.56 
18.35 
17. 
15  89 
14.21 

]P.       J. 

(  M.  AM.  Soc.  C.  E.) 

CIVIL  AND  HYDRAULIC  ENGINEER, 

BOX  917,  STATION  C,  LOS  ANGELES,  CALIFORNIA. 


CONSULTING  BNGINJBBR 

For  Irrigation,  Water  Works,  Sewerage,   Canals,  Ditches,   Pipe  Lines, 

Reservoirs,  Dams,  Land  Drainage  and  River  Embankments. 

The  Discharge  of  Rivers,   Streams.  Ditches  and  Canals  Measured. 

Hydraulic  Investigations  a  Specialty. 


IRRIGATION    CA.NA.LS 

AND 

Other    Irrigation    W^oris, 

AND 

THE  FLOW  OF  WATER   IN  IRRIGATION  CANALS 

DITCHES,  FLUMES,  PIPES,  SEWERS, 

CONDUITS,  ETC., 

WITH 


Simplifying  and  Facilitating  the  Application  of  the  Formulae  of 
KUTTEK,  D'AKCY  AND  BAZIN, 


BY 


P.  J.    FLYNN,    C.  E., 


Member  of  the  American  Society  of  Civil  Engineers;  Member  of  the  Technical  Society  of  the 

Pacific  Coast;  Late  Executive  Engineer,  Public  Works  Department,  Punjab,  India. 
Author  of  "  Hydraulic  Tables  based  on  Kutter's  Formula,"  "  Flow  of  Water  in  Open  Channels,"  &c. 


TWO    VOLUMES    BOUND    TOGETHER. 

711  pages,  92  tables,  211  illustrations. 


Bv        .     . 

Box  917,  Station  C,  LOS  ANGELES,  CAL. 


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Materials  for  Office  Work  Supplied. 


J.  McMuLLEN,  President.  H.  KRUSI,  Chief  Engineer. 

J.  M.  TAYLOR.  Sec'y  and  Treas.  H.  S.  WOOD.  )         . 

GEO.  W.  CATT,  C.  E.,  Vice  President.  J.  B.  C.  LOCKWOOD,  '     r 

San  Francisco  Bridge  Company 

Established  1877.  Capital  (paid  up),  $25O,OOO.  Incorporated  1883. 

ENGINEERS  AND  CONTRACTORS. 


42  Market  St.,  San  Francisco,  Oal, 
''     Occidental  Block,  Seattle,  Wash. 


CONTRACTORS  FOR  STEAM  EXCAVATION  AND  DREDGING  FOR 

THE  IMPROVEMENT  OF  NAVIGATION  AND 

RECLAMATION  OF  LANDS. 

Special  Machinery  for  the  Economical  Excavation  of  Large  Canals. 

STEAM  SHOVEL  AND  ROCK  EXCAVATION. 

(See  Cut,  page  266.) 


Designers  and   Builders  of    Railroad    and    Highway 

Bridges,  Sub.  and  Superstructure,  Pile  Driving, 

Dock  and   Pier  Building  and   Flume 

Construction. 


During  the  current  year  we  have  constructed  works  to  the  value  of  over 
a  million  and  a-half  dollars,  and  which  required  the  handling  of  two  and  one- 
half  million  cubic  yards  of  material,  and  consumed  twenty-two  million  feet 
of  lumb-  r,  twenty  thousand  piles,  and  three  and  a-half  million  pounds  of 
steel  and  iron.  Built  fifteen  linear  miles  of  railroad  trestle  bridges  in  1890, 
and  one  mile  of  railroad  truss  bridges.  With  a  plant  that  represents  an  in- 
vestment of  over  one  hundred  and  fifty  thousand  dollars,  and  a  corps  of 
experienced  engineers  and  superintendents,  and  thirteen  years'  experience, 
we  have  facilities  and  equipment  for  the  execution  of  this  kind  of  work  with 
the  greatest  skill,  thoroughness  and  economy. 


Plans  and  Estimates  Furnished.      Correspondence  Solicited. 


A  U  O  .     M  AY  E  R  , 

Civil  and  Sanitary  and  Contracting  Engineer, 

Room    12,   Burdiek   Block, 

Cor.  Spring  and  Second  Sts.  P.  O.  Box  995,  Station  C, 

LOS   ANGELES,   CAL. 


WILL  FURNISH 

PLANS,  SPECIFICATIONS  AND  ESTIMATES 

FOR 

Sewerage  of  Cities;  the  Disposal  and  Utilization  of  Sewage  of 
Country  Houses;  Waterworks,  Irrigation,  Etc.,  Etc. 


WORK    EXAMINED    AND    SUPERINTENDED. 

BUFF    &    BERGER, 

IMPROVED 

engineering  and  Surveying  Instruments, 

No.  9  Province  Court,  Boston,  Mass. 


They  aim  to  secure  in  their  instruments: — Accuracy  of  division;  Sim- 
plicity in  manipulation;  Lightness  combined  with  strength;  Achromatic  telescope, 
with  high  power;  Steadiness  of  Adjustment*  under  varying  temperatures;  Stiff- 
ness to  avoid  any  tremor,  even  in  a  strong  wind,  and  thorough  workmanship  in 
every  part. 

Their  instruments  are  in  general  use  by  the  U.  S.  Government  Engineers, 
Geologists,  and  Surveyors,  and  the  range  of  instruments,  as  made  by  them 
for  River,  Harbor,  City,  Bridge,  Tunnel,  Railroad  and  Mining  Engineering, 
sis  well  as  those  made  for  Triangulation  or  Topographical  Work  and  Land 
Surveying,  etc.,  is  larger  than  that  of  any  other  firm  in  the  country. 

Illustrated   Manual  and  Catalogue  sent  on  Application. 


THE  PACIFIC  FLUSH  TANK  CO. 

Los   ANGELES, 


MANUFACTURERS   OF 


The  Miller  and  Cosmos  Automatic  Siphons 


FOR    FLUSHING    SEWERS, 

Housedpains,    Water  Closets,    Urinals,    Etc. 


Well  adapted  for  Intermittent  Sub-Soil  Irrigation. 


Our  Siphons  stand  unequaled ;  they  are  the  simplest  and  most  efficient 
in  the  world ;  they  act  promptly  when  fed  by  the  smallest  supply  of  water 
or  sewage,  and  cannot  get  out  of  order.  They  are  durable  and  very  easily 
set.  They  consist  of  only  two  solid  castings  and  have  120  moving  parts. 
Satisfaction  guaranteed.  Sold  and  delivered  at  Eastern  prices. 

Send  for  pamphlet. 

PACIFIC   FLUSH  TANK  CO. 


"...    It  (the  MILLER)  is  uiuiuestiouably  a  very  simple  and  reliable  apparatus." 

THE  J.  L.  MOTT  IRON  WORKS,  N.  Y. 

"...    Both  the  MILLHR  and  COSMOS  deserve  the  first  place  among  automatic  flushing 
svices  for  sewers."  P.  J.  FLYNN,  C.  E. 


LACY  MANUFACTURING  CO. 


CALIFORNIA    IRRIGATION    HYDRANT,  (Patented  March  31,  1891.) 

MANUFACTURERS    OF 

Steel  £  Iron  Pipe,  Irrigation  Supplies.  Hydrants,  Gates,  etc, 


Office,  i«9^  West  First  Street. 


1,08  ANGEI/ES,  CAI,. 


Spreckels  Bros.  Commercial  Co.  j    J.  D.  Spreckels  &  Bros. 

SOLE  IMPORTERS,  SOLE  IMPORTERS, 

San  Diego,  Cal.  San  Francisco,  Cal. 


Made  of  Samples  taken  from  5O,OOO  Bbls.  "GILLINGHAM"  im- 
ported in  189O  for  the  Spring  Valley  Water  Works.  [51.OOO 
Bbls.  used  in  construction  of  their  dam  at  San  Mateo.]  Tests 
made  by  HERMANN  SCHUSSLER,  Chief  Engineer,  under  the  following  conditions. 

Briquettes  made  of  pure  cement,  mixed  with  water,  with  a  cross  section  of  one 
square  inch,  kept  in  the  molds  for  24  hours  after  mixing,  being  covered  with  a  damp 
cloth  and  during  rest  of  the  term  kept  immersed  in  water. 

Average  breaking  strain     \                                          Average  breaking  strain 
Age.                      in  pounds  per  sq.  inch.                      Age.                      in  pounds  per  sq.  inch. 
1    Day 4O4  9    Days 642 

2  "   447        14   "   7O5 

3  "   541        42   "   8O1 

4  "   588 

No  other  London    Portland   Cement  can  show  such  a   remarkable  result: 


Tlie  Cement  manufactured  by  the  "  GILLINGHAM  "  Company  is  noted  for  its  Uniform 
Quality  and  Great  Strength. 


PARTIAL  LIST  OF  NOTABLE  STRUCTURES 

ON  WHICH  "GILLINGHAM"  CEMENT  HAS  BEEN  USED. 


California  Sugar  Refinery, 
Leland  Stanford  University, 
D.  N.  &  E.  Walters'  Building, 
Lachmaii  &  Jacobi,  Wine  Vaults, 
New  City  Hall,  San  Francisco, 
Sea  Wall  Construction, 
Corralitos  Water  Works, 
Western  Beet  Sugar  Factory, 
Hibernia  Bank, 
Donahue  Building, 
Doyle  Building, 
H.  J.  Crocker  Building, 
Eureka  Court  House, 
Pacific  Rolling  Mills, 
U.  O.  Mills  Building, 
Jas.  G.  Fair  Building, 
Mercantile  Library  Building, 
Farmers  Union  Flour  Mill, 
Piedmont  Cable  Rail  Road, 


Golden  Feather  Channel  Dam, 

Laurel  Hill  Cemetery  Association, 

Weinstock  &  Lubin  Wine  Vault, 

Los  Angeles  Cable  Railway, 

Los  Angeles  City  Water  Co. 

Los  Angeles  Public  Sewers, 

Stowell  Cement  Pipe  Co. 

Frink  Bros.  Cement  Pipe  Co. 

Los  Angeles  Court  House, 

Bear  Valley  Irrigation  Co. 

East  Whitter  Land  and  Water  Co. 

Drarta  Mount.  Irrigation  and  Canal  Co. 

Sweet  water  Dam, 

Dealers  aiid  Irrigating  Co's  throughout 

Southern  Caliiornia, 
Hotel  del  Coronada. 

And  numerous  other  prominent  con- 
structions throughout  the  Pacific  Coast. 


8*e>x*re>r*    JPi*3e>    Oo. 


MANUFACTURERS    OF 


Salt-Glazed  Vitrified  Iron  Stone 

SEWER  *  WHTER  PIPE 


Irrigation  Pipe,  Culvert  Pipe, 

Well  Tubing,  Drain  Tile, 

Fire  Brick,      Fire  Clay. 

TElftR  COTTfl  CHWflEY  PIPE  flflD  TOPS. 


Office  and  Yard,  No.  248  BROADWAY,  Cor.  THIRD. 

LOS    ANQELES,    CAL. 


FACTORY,  LOS  ANGELES,  CAL. 


California  Sewer  Pipe  Company 

Standard  Patterns  of  Sewer  Pipe  and  Fittings. 


OFFICE, 


SEWER   PIPE 


248  BROADWAY,  near  THIRD, 
Los  Angeles,  Cal. 


RRIGATION  AT 
HOME  AND  ABROAD. 


Were  you  aware,  my  friend, 
that  in  these  piping  times  of 
industrial  progress  and  devel- 
opment we  were  making  his- 
tory very  fast — and  history  of 

_^  a  mighty  interesting  kind,  too? 

Such  is  the  fact;  and  in  no  section  of  the  country  are  the 
guide-posts  of  prosperity  being  located  faster  than  through- 
out that  vast  domain  which  reaches  from  the  plains  to  the 
Pacific  Coast. 

IRRIGATION  has  given  the  impetus,  and  irrigation 
will  build  a  future  for  the  West,  grand  and  magnificent. 
The  history  of  irrigation  development  is  being  made 
every  day,  and  the  historian  is 

The   Irrigation.  Age 

(  Pioneer  journal  of  its  kind  in  the  world.) 

ENGINEERS  —  Do  you  want  to  keep  posted  on  news  of 
construction  work? 

INVESTORS  —  Do  you  want  to  keep  close  watch  upon  the 
irrigation  bond  as  a  means  of  investment? 

CAPITALISTS — Do  you  want    to    know  where  lie  the 
lands  that  are  easily  brought  under  water? 

FARMERS  —  Do  you  want  to  know  how  to  obtain  the 
biggest  returns  from  the  soil  ? 

Of  course  you  do,  and  The  Irrigation  Age  will  tell  you 
all  you  want  to  know. 


SALT  LAKE, 

26  W.  Third  South. 


DENVER,         SAN  FRANCISCO, 

1115  Sixteenth  St.  Chronicle  Bldg 


Paper 


DO  tl^e  Rest. 


Which  means  that  you  send  us  your  subscription  and  take  advertising  space. 

we  believe  the  people  of  the  country  know  a  good  thing  when  they  see  it,  and  that's 
why  we  want  them  to  see 

The  Irrigation  Age 

(Pioneer  Journal  of  its  kind  in  the  world.1) 


CHAPTER  I.— ADVERTISING. 

The  Kilbourne  £  Jacobs  Manufacturing  Co.,  of 

Columbus,  Ohio,  says: 

Referring  to  our  '"ad"  which  we  placed  with 
you  for  six  months,  we  desire  to  say  that  we  are 
well  pleased,  for  it  has  brought  us  many  in- 
quiries. We  shall  continue  it  six  months  longer. 

The  F.  C.  Austin  Manufacturing  Co.,  of  Chicago, 

says: 

We  are  pleased  with  your  paper.  So  far  as 
our  "  ad  "  is  concerned,  we  have  reason  to  attach 
direct  good  to  your  efforts. 


Lord  &  Thomas,  Chicago,  say: 

Your  paper  cannot  but  be  of  great  interest  to 
those  who  are  engaged  in  irrigation  enterprises, 
and  we  believe  you  have  a  field  which  you  can 
fill  to  the  advantage  of  investor  and  those  on  the 
other  side. 


The  Irrigation  Machinery  Co.,  of  Denver,  Colo., 

says: 

We  have  obtained  better  results  from  our  ad- 
vertising in  THE  IRRIGATION  AGE  than  from 
any  other  publication.  It  reaches  the  irrigation 
interests  of  the  United  States  very  generally.  It 
is  a  splendid  medium. 


CHAPTER    II.— SUBSCRIPTION. 

Col.  R.  J.  Hinton  says: 

On  my  recent  tour  I  encountered  THE  AGE 
at  every  turn .  I  found  it  in  the  hands  of  engin- 
eers, business  men  and  farmers.  Its  circula- 
tion for  a  new  journal  is  marvelous. 

The  Denver  Times  says: 

THE  AGE  should  be  supported  for  the  work 
it  is  doing.  It  is  a  public  benefactor. 

James  Kirkpatrick,  of  Dillon,  Mont.,  says: 

No  farmer  who  irrigates  can  afford  to  be  with- 
out THE  AGE  any  more  than  lie  can  be  without 
head-gates  in  his  ditches. 

L.  Bradford  Prince,  Governor  of  New  Mexico, 

says: 

THE  AGE  is  valuable  to  the  West.  It  is  ad- 
mirable in  make-up  and  general  appearance. 

5.  J.  Gilmore,  President  of  the  Colorado  Irriga- 
tion Society,  says: 

Allow  me  to  congratulate  you  on  the  general 
character  and  soundness  of  the  articles  in  your 
paper. 

S.   W.  Winn,  Secretary  of  the  Syndicate  Land 

and  Irrigation  Co. ,  Kansas  City,  says: 
I  believe  the  public  interest  in  irrigation  will 
be  greatly  improved  by  the  vigorous,  intelligent 
way  you  are  conducting  THE  AGE. 


We  umnt  you*  Subscription  and  me  uiant  your  Advertising  patronage 

AGE 


TUB    IRRIGATION 

( BY  THE  SMYTHE,  BRITTON  &  POORE  CO.) 


DENVER, 

1115  Sixteenth  St. 


SALT  LAKE, 

26  W.  Third  South. 


SAN  FRANCISCO, 

Chronicle  Bldg. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN     INITIAL     FINE     OF     25     CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  5O  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


OCT 


APR    5  1968 


i«  W  i«    v  c. 

MAR  2  2  '68  -8  AM 

LOAM 


LD  'Jl-o 


36  37 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


